Keywords
 A6.1. Methods in mathematical modeling
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.1.4. Multiscale modeling
 A6.1.5. Multiphysics modeling
 A6.2. Scientific computing, Numerical Analysis & Optimization
 A6.2.1. Numerical analysis of PDE and ODE
 A6.2.7. High performance computing
 A6.3.1. Inverse problems
 A6.5. Mathematical modeling for physical sciences
 A6.5.1. Solid mechanics
 A6.5.4. Waves
 B3. Environment and planet
 B3.3. Geosciences
 B3.3.1. Earth and subsoil
 B4. Energy
 B9.2.1. Music, sound
 B9.5.2. Mathematics
 B9.5.3. Physics
 B9.5.5. Mechanics
1 Team members, visitors, external collaborators
Research Scientists
 Helene Barucq [Team leader, INRIA, Senior Researcher, HDR]
 Henri Calandra [TotalEnergies, Industrial member]
 Juliette Chabassier [INRIA, Researcher]
 Julien Diaz [INRIA, Senior Researcher, HDR]
 Augustin Ernoult [INRIA, Researcher]
 Florian Faucher [INRIA, Researcher]
 Stefano Frambati [TotalEnergies, Industrial member]
 Ha Ngoc Pham Howard Faucher [INRIA, Researcher]
 Xavier Lacoste [TotalEnergies, Industrial member]
 Jie Meng [TotalEnergies, Industrial member, from May 2022]
 Jeanne Pellerin [TotalEnergies, Industrial member, until Aug 2022]
Faculty Members
 Marc Durufle [BORDEAUX INP, Associate Professor]
 Sebastien Tordeux [UPPA, Associate Professor, HDR]
PostDoctoral Fellow
 Chengyi Shen [INRIA, from Jun 2022]
PhD Students
 Julien Besset [INRIA]
 Guillaume Castera [INRIA]
 Lola Chabat [UPPA, from Oct 2022]
 Marine Deheuvels [INRIA]
 Ibrahima Djiba [INRIA]
 Arjeta Heta [UPPA]
 Augustin Leclerc [INSA ROUEN NORMANDIE]
 Victor MartinsGomes [UPPA]
 Matthias Rivet [UPPA, from Oct 2022]
 Margot Sirdey [ONERAInria]
 Alexis Thibault [UPPA]
 Vinduja Vasanthan [INRIA]
 Nicolas Victorion [INRIA]
Technical Staff
 Aurélien Citrain [INRIA, Engineer]
 Olivier Geber [INRIA, until Apr 2022]
 Paloma Martinez [INRIA, Engineer, from May 2022]
Interns and Apprentices
 Chahdi Balbal [INRIA, Intern, from Jun 2022 until Sep 2022]
 Lola Chabat [INRIA, Intern, from Mar 2022 until Aug 2022]
 Lara Dib [INRIA, Intern, from Mar 2022 until Aug 2022]
 Johan Hedman [INRIA, Intern, from Feb 2022 until Sep 2022]
 Thibaut Marron [TotalEnergies, Intern, from Mar 2022 until Aug 2022]
 Aurélie Scuotto [INRIA, Intern, from Jun 2022 until Sep 2022]
 Coralie Vernay [BORDEAUX INP, Intern, from May 2022 until Jun 2022]
 Brad Wagijo [INRIA, Intern, from Apr 2022 until Aug 2022]
Administrative Assistant
 Sylvie Embolla [INRIA]
External Collaborators
 Yuto Bekki [MAX PLANCK Institute]
 Prithwitosh Dey [MAX PLANCK Institute]
 Damien Fournier [MAX PLANCK Institute]
 Laurent Gizon [MAX PLANCK Institute]
 Christian Gout [INSA Rouen, HDR]
 Neelanchal Joshi [MAX PLANCK Institute]
 ZhiChao Liang [MAX PLANCK Institute]
 Mamadou N'diaye [Université Polytechnique des Hauts de France]
 Jordan Philidet [MAX PLANCK Institute]
 Antoine Tonnoir [Insa Rouen]
2 Overall objectives
Imagine trying to describe a place with exactness from more or less numerous and precise memories, or guessing the content and internal structures of an object after having observed it only partially, without ever touching it because it is inaccessible or very fragile? These are the objectives of Makutu team, where recordings of reflected waves correspond to the memories. Waves can be seismic, electromagnetic or acoustic and Makutu focuses its research on the characterization of Earth's subsurface, of the Sun, and of musical instruments. An important component of Makutu's work is the improvement of the resolution methods for direct problems, in order to simulate the propagation of waves in complex media. The characterization and reconstruction of objects using noninvasive approaches then need the resolution of an inverse problem, with efficient forward modeling at the center.
Makutu is an industrial Inria projectteam joint with TotalEnergies, in partnership with University of Pau and Pays de l'Adour, Institut Polytechnique de Bordeaux and CNRS. The team is bilocated, one part is hosted by UPPA and the other is hosted by Inria on the University of Bordeaux campus. It is a followup of Magique3D (Advanced Modeling in 3D Geophysics) and its research topics have expanded are summarized as “Experimentalbased modeling and simulation of wave propagation to characterize geophysical and heliophysical media and to design complex objects" with the new name Makutu (magicians in Maori).
The numerical simulation of waves propagating in complex media (the direct problems solved by Makutu) requires the development of advanced numerical methods but the research does not stop there. Indeed, to probe a medium or reconstruct an object from reflected waves measurements (the inverse problems addressed by Makutu), it is important to accurately solve systems of partial differential equations that model all the waves that can be measured. As the complexity of the physical models goes hand in hand with the complexity of the calculations, Makutu is particularly committed in the development and analysis of appropriate mathematical models as well as in the design and study of advanced numerical methods taking into account the characteristics of the physics considered.
Makutu's research has many facets, with final goals ranging from the development of opensource prototype codes written to assess new ideas, to software packages to be ported to an industrial environment. Makutu's research activities are inspired by a strong interdisciplinary industrial and academic partnership. The team's contributions are at the interface of applied analysis, numerical analysis, and scientific computing. The size of some of our problems projects us into the High Performance Computing (HPC) environment and dictates the choices we make for certain approximation spaces that are conducive to massive parallelism.
Makutu has important contributions in the field of highorder discretization methods along with highorder time schemes. Whatever the application is, numerical schemes are all designed with a view to reduce computational time or limit memory consumption, while maintaining a high level of accuracy. Sometimes, it is also necessary to work on the mathematical models themselves whose brute complexity can be a source of difficulty or even blockage for the numerical simulations. One of the originality of the team is to collaborate with experimenters to compare measurements and numerical data in order to calibrate the models. All these contributions are significant steps to reach the final team's objectives which are expressed as the resolution of complex inverse problems. Largescale computing is then an important part of our activity, which we carry out taking into account the three pillars that make up HPC, i.e. computing time, storage and precision. Recently, the team has started to work on the use of machine learning to assist the numerical schemes they develop in order to control the numerical pollution (or dispersion) which becomes very strong in largescale computations. This is particularly the case in geophysics where several hundred wavelengths can be propagated. It is worth noting that we take particular care in developing our numerical methods so that they can be used for a wide range of applications, whether the calculations are done in an HPC environment or on a simple laptop.
3 Research program
Makutu's research program decomposes itself into four axes that are: (1) Methodological contributions to the simulation of mechanical and electromagnetic waves in complex media; (2) Seismic imaging; (3) Helioseismology; (4) Musical Acoustics. Each axis shares the same objective to realize simulations of real phénomena. To achieve this, one needs real data and advanced mathematical models and highorder numerical schemes that are compatible with highperformance computing architectures.
To obtain real data, in addition to its current collaborations with scientists both from Academia and Industry, Makutu is developing a new branch of research activities by carrying out its own laboratory measurements. For instance, in order to take into account porosity, parameters such as viscosity, attenuation, thermodynamic effects, etc., must be integrated, and their impact must be properly analyzed before considering using them to characterize the propagation media. This constitutes a clear step ahead for Makutu, and opens up new prospects of contributing to the characterization of very complex media based on wave field measurements.
Regarding the development of numerical schemes, Makutu is developing highorder Discontinuous Galerkin (DG) methods and highorder time schemes. The coupling of DG methods with other techniques of discretization is also under consideration. TrefftzDG and Hybridizable DG methods have been developed both for poroelastic waves and electromagnetic waves. HDG and HDG+ formulations are also under study for helioseismology.
The research activities of members of Makutu share a common theme of using numerically computed wavefield measurements to reconstruct the propagation medium they passed through before recording. The medium can be reconstructed by identifying either the physical parameters or the geometrical parameters that characterize it. In each case, the next step is to solve an inverse problem that is nonlinear and illposed. To solve it, Makutu is focusing on the Full Waveform Inversion (FWI), which is a highdefinition imaging method widely used in the field of geophysics.
4 Application domains
Makutu research program is organized around three principal domains of applications: geophysical exploration, solar imaging, and music. Each of them requires a relevant panel of significant contributions requiring achievements in laboratory measurements, modeling, mathematical analysis, advanced numerical schemes and massively parallel software development. Recently, the team has added experimental contributions to feed simulations with real data and also improve modeling through better calibration. Makutu's application domains can be regrouped into a longstanding activity dedicated to subsurface imaging, and two more recent activities dedicated to solar imaging and the development of numerical wind instruments. Each field of application is not compartmentalized in the methodological sense of the term: equations, numerical schemes and programming practices are shared and possibly adapted to the underlying application.
4.1 Geophysical exploration
Geophysical exploration is a historical field for the team (see e.g 62, 66, 67, 69.Geophysical exploration has been driven for a very long time by the goal of finding hydrocarbons. Today, it is evolving towards a very proactive direction in favor of renewable energies and Makutu commits part of its research activities in this direction, in the framework of industrial and international collaborations. Industrial partnership with TotalEnergies has evolved to the transformation of Makutu into an industrial projectteam since January 2022. The dedicated research project targets monitoring of CO2 storage through the development of a new numerical branch in GEOSX for seismic propagation and inversion. As far as geothermical energy is concerned, Makutu is member of the international project SEE4GEO lead by C. Morency from Lawrence Livermore National Laboratory. The project combines experimental research in the field and in laboratory with numerical developements in the continuity of CHICkPEA project previously funded by UPPA (20182021).
Inversion is central for geophysical exploration and Makutu focuses on Full Waveform Inversion (FWI) as a highfidelity solution methodology for reconstructing the physical parameters from observed data. FWI can be carried out in timedomain 65, 87, 97, 98 or in frequency domain 92, 91, 90. Its main feature is to avoid the formation of the large Jacobian matrix by computing the gradient of the misfit functional using the adjointstate method 70. A detailed review of FWI for geophysical applications can be found in 89.
4.1.1 Deep geothermal energy
Obtaining accurate images of natural reservoirs is critical for their management and exploitation and seismic imaging is an efficient tool (see 86, 85 and their references therein. One example is with deep geothermal energy which requires precise imaging of deep fractured reservoirs filled with geothermal fluids. Standard seismic imaging is based upon inverting mechanical waves which have difficulties to detect them, whereas electromagnetic waves are more sensitive. We see here a clear interest of coupling seismic with electromagnetic methods and this is what Makutu began developing with CHICkPEA project ended in 2021. The team is now involved in project SEE4GEO funded by ADEME, in the framework of Geothermica call.
4.1.2 Shallow geothermal energy
Regarding shallow geothermal energy, Makutu worked until May 2022 with RealTimeSeismic SME in the framework of the FEDERPoctefa Pixil project in order to use surface waves for a better imaging of shallow reservoirs. Surface waves have long been considered as noise in seismograms because they were used to study the subsurface at depths. In shallow geothermal energy, surface waves contain interesting information on the first layers of the subsurface. Inverting them is challenging because the surface waves are of high amplitude while propagating slowly. They therefore pose difficulties for multifrequency optimization methods.
4.1.3 CO2 injection monitoring
The reduction of greenhouse gases in the atmosphere is a societal topic of the utmost importance, with the Paris Agreement setting ambitious goals for many countries. One fundamental pillar of greenhouse emission management is Carbon Capture Utilisation and Storage (CCUS) 99. With this strategy, carbon dioxide produced on or offsite is sequestered and injected into depleted reservoirs, thus offsetting an important portion of current CO2 emissions. The successful and safe implementation of this strategy requires the prediction, monitoring and surveillance of stored CO2 over long periods, which presents significant challenges in terms of seismic acquisition, seismic inversion and numerical simulation. These tools, coupled with stateoftheart flow simulations, are vital in order to support the injection operations with vital realtime and longterm information. Moreover, specific challenges related to the physics of injected CO2, such as viscosity, temperature and multiphase fluid conditions push to the limits our current numerical models, and require ambitious new multiphysics simulations to support safe and costeffective CO2 injection operations. For example, some recent publications like 96, 102 have shown that the combination of CO2brine flow with wave propagation provides efficient simulations for the monitoring of sequestered CO2. Makutu is currently developing numerical methods for this new application, in collaboration with TotalEnergies, as a new computational branch of the opensource multiphysics simulator GEOSX.
4.2 Solar imaging
Helioseismology studies the interior and dynamics of the Sun based on the observation of wave oscillation in the solar photosphere. These movements can be observed at the surface by the Dopplergrams given by groundbased or satelliteborne observatories. In recent years, methods for understanding Earth subsurfaces have opened up new ways to study the interior of the Sun as in the case with helioseismology and the interior of stars with aesteroseismology from oscillation observed at their surface. Techniques in helioseisomolgy is generally divided into global and local helioseismology. The first approach studies frequencies of oscillations modes, cf. 71. On the other hand, local helioseimology, which adapts techniques of geophysical seismic interferometry studies, measures local wave propagation and works with the full 3D observed wavefield, and is thus more adapted to study additional features such largescale flows in active region, sun spots and plage, cf. 82, 81.
Makutu extends its activity on terrestrial seismology to studying the Sun, for the latter offers a vast wealth of problems to be explored both for direct modeling as well as inversion. The collaboration between Makutu and the solar group at the Max Planck institute for Solar research MPS at MPS brings together the expertise of MPS in solar physics and seismology and that of Makutu in numerical simulation of wave propagation and largescale inversion in geophysics. This ongoing collaboration dating from 2016 obtains its official mark with the creation of associated team ANTS which started in 2019 and ended in 2022. The main goal of the collaboration is the creation of a computational framework for accurate and efficient simulation of solar oscillation to be used in full waveform inversion, e.g. for 3D solar flow.
The stochastic nature of solar oscillation is described by random righthand source term, and in using statistical analysis, under appropriate assumptions (e.g. the convenient source assumption), power spectrums and timedistance diagrams can obtained from the deterministic Green kernel of modeling wave equation, cf. 80. In this way, the Green kernel becomes a crucial object in local helioseismology, and its accurate and efficient computation is the main goal of forward modeling. In addition to appropriate numerical schemes, investigation of radiation boundary conditions is required in order to describe accurately waves above cutoff frequencies.
Up until 2021, the focus has been put on acoustic waves which are identified with pridges in observed solar power spectrum. Acoustic waves at low frequencies can be adequately described by a scalar equation. The thesis of Rouxelin 2021 studied convected Helmholtz which allows for a simplified description of the effect of convection on acoustic waves. Recent and ongoing works extend the investigation to vector wave equation to include gravity and differential rotation. The latter is particularly of interest due to the recent discovery of inertial waves in the Sun. This is subject of the thesis of Chatbat which starts in October 2022, and the goal of which is to create an inhouse software to compare accurately eigenvalues for the solar wave equation with differential rotation. The remaining challenge is to include full 3d flow to the vector equation, which is the goal for the next year.
The above works lay the necessary foundation for inversion of solar parameters such as flow and active region sound speed. Current stateofthe art tools in these references is linear inversion using Born approximation 78. In additional they are carried out in 1D or 2D. It is thus interesting to apply nonlinear inversion such as Full Waveform Inversion in 3D cf. 76 to these problems.
4.3 Musical acoustics
This field of application is a subject of study for which the team is willing to take risks. We propose using a mix of experimental and numerical approach in order to study and design musical instruments. Makers have designed wind musical instruments (as flutes, trumpets, clarinets, bassoons...) in the past through “trial and error” procedures by performing a geometrical calibration of musical instruments in order to improve their accuracy, tone, homogeneity and even their sound volume, ergonomics, and robustness. During the past few decades, musical acoustics has been in a process of rationalizing the empiric understanding of instrument makers in order to formulate a scientific approach to future evolution. Our research proposal is along this axis of research by proposing new mathematical models based on our solid experience in terms of wave propagation in media with interfaces that can significantly change the sound. As was done in geophysical exploration, we propose to assist the modelling process with laboratory experiments. Direct comparison between simulations and experiments will allow to assess the model error. For this purpose, an experimental device has been developed in collaboration with I2M, Mechanics Laboratory of the University of Bordeaux and Humeau Factory, Montpon Ménestérol, and is currently in use.
4.3.1 Modeling
Although the playing context should always be the final reference, some aspects of the behavior of a wind instrument can be firstly characterized by its entry impedance which quantifies the DirichlettoNeumann map of the wave propagation in the pipe in the harmonic domain. This impedance can be both measured 79, 72 and computed with simulations based on accurate and concise models of the pipe 94, 68100, 74. A more realistic approach accounts for the embouchure 83, 68, 63, 64, 101, which is modeled as a nonlinear oscillator coupled with the pressure and acoustic velocity at the entry of the pipe, allowing to predict the sound qualities. Mathematical properties of the underlying models are not yet totally understood, and adequate models still need to be developed. This is particularly true when accounting for dissipation phenomena, junctions of pipes, pipe porosity and rugosity, embouchures...
To reproduce the sound of instruments, timedependent models are more suitable. Here, nonlinear lumped elements induce an “autooscillatory” behavior of the instrument. The models currently available in the literature are meant to reproduce viscothermal effects, pipe junctions, pipe radiation, lips oscillation, etc. They do not necessarily possess adequate mathematical properties to ensure stable simulations and they should be improved using asymptotic analysis methods or Lagrangian formalism.
4.3.2 Numerical methods
As far as numerical developments are concerned, the accuracy of the calculations is essential. Indeed, for some aspects like the sounding frequency, a deviation of 1% between the predictions and the observations is unacceptable. Moreover, contrary to what the team is used to do for geophysics or astrophysics thanks to HPC, numerical methods for acoustical musics must be frugal to be run on personal computers by acousticians and makers. Makutu has a wide range of numerical methods that have been implemented in its codes for linear problems. New numerical schemes will have to be implemented to take into account the nonlinearities of timedependent models.
4.3.3 Virtual workshop
Beyond the idea of mathematically modeling musical instruments, Makutu wishes to develop a virtual workshop whose vocation will be twofold: (i) support the manufacturers to design new instruments; (ii) recreate the sound of old and historical instruments. To implement this idea, we propose to elaborate optimization techniques that are wellknown in the team to define optimal geometries to meet given specifications. This can be used to reconstruct existing instruments from acoustic measurement or to design new instruments by fixing relevant quantitative objective which is a research activity by its own 75. Behind the idea of the virtual workshop is also the intention to hear the instruments, from the knowledge of their shape and playing regime. For that purpose, timedomain models are essential.
5 Social and environmental responsibility
Makutu recognizes the importance of conducting research in a responsible and sustainable way. We are committed to ensuring that our work has a positive impact on society and the environment.
In terms of social responsibility, Makutu members ensure that their research is inclusive and accessible to all members of society. The team prides itself on bringing together researchers from diverse social and cultural backgrounds. It makes its results and publications available to the general public and is involved in scientific dissemination activities.
In terms of environmental responsibility, Makutu strives to minimize the environmental impact of its research. Wherever possible, the team works to reduce its carbon footprint by implementing environmentally friendly practices and maintaining remote collaborations to limit international travel. It is also engaged in a research program dedicated to sustainable energy. In particular, it is contributing to the development of advanced software for monitoring CO2 storage and is studying complex models that can assist in the development of geothermal drilling by avoiding the devastating creation of microearthquakes.
Overall, Makutu is committed to conducting research in a responsible and sustainable manner and is committed to having a positive impact on society and the environment.
6 Highlights of the year
6.1 Transformation into an industrial project team
After many years of collaboration with Total, Makutu has become a joint team with TotalEnergies, now hosting 4 researchers from the company. This transformation was made around a research program on CO2 storage monitoring, in collaboration with Lawrence Livermore National Laboratory and Stanford University. Two theses have been started, a postdoctoral fellow has been recruited as well as two research engineers.
7 New software and platforms
7.1 New software
7.1.1 OpenWind

Name:
Open Wind Instrument Design

Keywords:
Wave propagation, Inverse problem, Experimental mechanics, Time Domain, Physical simulation

Scientific Description:
Implementation of first order finite elements for wind musical instrument simulation. Implementation of the Full Waveform inversion method for wind musical instrument inversion. Implementation of energy consistent numerical schemes for time domain simulation of reedtype wind musical instrument.

Functional Description:
Simulation and inversion of wind musical instruments using onedimensional finite element method with tonholes or valves and fingering chart. The software has three functionnalities. First, the software takes the shape of a wind instrument and computes the acoustical response (answer to a given frequential excitation). Second, the software takes the instrument shape and the control parameters of a musician, and computes the produced sound and the time evolution of many acoustical quantities. Last, the software takes a measured acoustical response and computes the corresponding instrument geometry (inner bore and tone holes parameters).

Release Contributions:
 New input file formats (compatibility with other software, use of other units, unified file, etc)  Possibility to have conical side holes and pistons  Modal calculation of the frequency response
 URL:
 Publications:

Contact:
Juliette Chabassier

Participants:
Juliette Chabassier, Augustin Ernoult, Alexis Thibault, Robin Tournemenne, Olivier Geber, Guillaume Castera, Tobias Van Baarsel
7.1.2 Hou10ni

Keywords:
2D, 3D, Elastodynamic equations, Acoustic equation, Elastoacoustic, Frequency Domain, Time Domain, Discontinuous Galerkin

Scientific Description:
Hou10ni simulates acoustic and elastic wave propagation in time domain and in harmonic domain, in 2D and in 3D. It is also able to model elasto acoustic coupling. The time domain solver is based on the second order formulation of the wave equation and the space discretization is achieved using Interior Penalty Discontinuous Galerkin (IPDG) Method. Both IPDG and Hybridizable Discontinuous Galerkin (HDG) Methods are implemented in the frequency domain solver. Recently, the HDG version has been extender to poroelastic and conducting poroelastic (poroelastic+electromagnetic) media.

Functional Description:
This software simulates the propagation of waves in heterogeneous 2D and 3D media in timedomain and in frequency domain. It is based on an Interior Penalty Discontinuous Galerkin Method (IPDGM) and allows for the use of meshes composed of cells of various order (padaptivity in space).

News of the Year:
In 2022, we have focuses the 3D seismoelectomagnetic equations and compared various approximation of the frequencydependent coupling coefficient.
 URL:

Publications:
hal01513597, hal01957131, hal01388195, hal01972134, hal01957147, hal02152117, hal02486942, hal02408315, hal02911686, hal03464413, tel03442300, tel03014772, hal01656440, hal01662677, hal01623953, hal01623952, hal01513597, hal01519168, hal01254194, hal01400663, hal01400656, hal01400643, hal01313013, hal01303391, hal01408981, tel01304349, hal01184090, hal01223344, hal01207897, hal01184111, hal01184110, hal01184107, hal01207906, hal01184104, hal01207886, hal01176854, hal01408705, hal01408700, tel01292824, hal01656440, hal00931852, hal01096390, hal01096392, hal01096385, hal01096324, hal01096318, tel01133713, tel00880628

Contact:
Julien Diaz

Participants:
Conrad Hillairet, Elodie Estecahandy, Julien Diaz, Lionel Boillot, Marie Bonnasse, Marc Fuentes, RoseCloe Meyer, Vinduja Vasanthan, Arjeta Heta
7.1.3 haven

Name:
timeHArmonic waVe modEling and INversion using Hybridizable Discontinuous Galerkin Discretization

Keywords:
Inverse problem, Wave Equations, Geophysics, Helioseismology, Discontinuous Galerkin, MPI, Large scale, Wave propagation, 3D, 2D

Scientific Description:
Many applications such as seismic and medical imaging, material sciences, or helioseismology and planetary science, aim to reconstruct properties of a non directly accessible or nonvisible interior. For this purpose, they rely on waves whose propagation through a medium interrelates with the physical properties (density, sound speed, etc.) of this medium. Haven is a software designed to perform imaging with waves, following an algorithm that comprises of two main stages: In the data acquisition stage, the medium response to probing waves is recorded (e.g., seismic waves from Earthquakes recorded by ground network). In the second stage, we rely on a reconstruction procedure which iteratively updates an initial model of physical parameters, so that numerical simulations approach the measurements. This procedure is employed, for instance, for seismic (reconstruction of subsurface layers) and medical (disease diagnostic) imaging.

Functional Description:
The software solves timeharmonic forward and inverse wave problems for acoustic and elastic media using the Hybridizable Discontinuous Galerkin method for discretization. It combines MPI and OpenMP parallelism to solve largescale applications such as Earth's imaging and helioseismology.

News of the Year:
 Several choices of viscoacoustic and viscoelastic models have been added for the propagation,  New propagators dedicated to helioseismology have been implemented
 URL:
 Publications:

Contact:
Florian Faucher

Participant:
Florian Faucher
7.1.4 MONTJOIE

Keywords:
High order finite elements, Edge elements, Aeroacoustics, High order time schemes

Scientific Description:
Montjoie is designed for the efficient solution of timedomain and timeharmonic linear partial differential equations using highorder finite element methods. This code is mainly written for quadrilateral/hexahedral finite elements, partial implementations of triangular/tetrahedral elements are provided. The equations solved by this code, come from the ”wave propagation” problems, particularly acoustic, electromagnetic, aeroacoustic, elastodynamic problems.

Functional Description:
Montjoie is a code that provides a C++ framework for solving partial differential equations on unstructured meshes with finite elementlike methods (continuous finite element, discontinuous Galerkin formulation, edge elements and facet elements). The handling of mixed elements (tetrahedra, prisms, pyramids and hexahedra) has been implemented for these different types of finite elements methods. Several applications are currently available : wave equation, elastodynamics, aeroacoustics, Maxwell's equations.
 URL:

Contact:
Marc Durufle

Participants:
Juliette Chabassier, Marc Durufle, Morgane Bergot
7.1.5 GEOSX

Keywords:
Physical simulation, Multiphysics modelling

Functional Description:
GEOSX is an opensource, multiphysics simulator developed cooperatively by Lawrence Livermore National Laboratory, Stanford University, and TotalEnergies. Its goal is to open up new horizons in modeling carbon storage and other subsurface energy systems. This includes:  taking advantage of the ongoing revolution in highperformance computing hardware, which is enabling ordersofmagnitude gains in performance, but also forcing a fundamental rethink of our software designs,  enriching the physics used in industrial simulations, allowing complex fluid flow, thermal, and geomechanical effects to be handled in a seamless manner,  developing highlyscalable algorithms for solving these coupled systems,  and improving workflows for modeling faults, fractures, and complex geologic formations. Inria contributes to the seismic wave propagators of GEOSX, and to its python interface. Inria also contributes advanced workflows for seismic inversion, and CO2 storage an monitoring.

News of the Year:
Projectteam Makutu has contributed to the integration of seismic propagators based on Q1 SEM (spectral element method), and to the development of the python interface (pyGEOSX), with the goal of later using it to integrate a complete seismic inversion workflow via full waveform inversion (FWI). These developments will carry on and expand in 2022.
 URL:

Contact:
Randolph Settgast
7.1.6 Gar6more2D

Keywords:
Validation, Wave propagation

Functional Description:
This code computes the analytical solution of problems of waves propagation in two layered 3D media such as acoustic/acoustic acoustic/elastodynamic acoustic/porous porous/porous,based on the Cagniardde Hoop method.

News of the Year:
In the framework of collaboration with Peter Moczo (Comenius University Bratislava and Slovak Academy of Sciences), David Gregor, Josef Kriztek, Miriam Kristekova (Comenius University Bratislava), Arnaud Mesgouez, Gaëlle LefeuveMesgouez (Inrae, Avignon University) and Christina Morency (Laurence Livermore National Laboratory) and we have implemented the coupling between elastic and poroelastic media. The obtained results are presented in an article of Geophysical Journal Internation 15.
 URL:
 Publications:

Contact:
Julien Diaz

Participants:
Abdelaâziz Ezziani, Julien Diaz

Partner:
Université de Pau et des Pays de l'Adour
7.1.7 GoTem3

Keywords:
Trefftz, Electromagnetic waves, GMRES, Iterative method

Functional Description:
GoTem3 is domain decomposition platform based on the ultraweak formualtion of Cessenat and Després for the solution of diffraction problems posed on regular grids. It uses matrix free strategies as well as local and global preconditioners to solve cases involving more than a billion degrees of freedom on a single computational core.

News of the Year:
The Phd thesis of Margot Sirdey has been defended on December 22, 2022

Contact:
Sebastien Tordeux
8 New results
8.1 Methodological contributions to the simulation of mechanical and electromagnetic waves in complex media
8.1.1 Linearly implicit energypreserving time discretisation for nonlinear wave equations
Participants: Juliette Chabassier, Guillaume Castera.
Nonlinear phenomena can occur in vibrating structures, such as piano strings, due to large deformations or nonlinear constitutive state laws. Integration of nonlinear models in space and time can be achieved accurately in several ways, but preserving an energy identity at the discrete level is an effective way to address numerical stability when coupling with other systems (as in the case of the piano). Gradientbased integrators achieve this objective at the cost of solving a nonlinear system at each time step. New formulations called Invariant Energy Quadratization (IEQ) and Scalar Auxiliary Variable (SAV) require only the inversion of a linear system while preserving a discrete energy identity. This work presents a convergence analysis of an interleaved time integrator based on IEQ and $\theta $scheme and numerical illustrations.This work was presented at the international conference WAVES 2022: Guillaume Castera, Juliette Chabassier, Paul Fisette. Linearly implicit energy consistent time discretisation for nonlinear wave equations. WAVES 2022  15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jul 2022, Palaiseau, France. ⟨hal03757200⟩
This work has been done in collaboration with Paul Fisette, université catholique de Louvain, Belgium.
8.1.2 TrefftzDG methods and Tent Pitcher algorithm for spacetime integration of wave problems
Participants: Hélène Barucq, Henri Calandra, Julien Diaz, Vinduja Vasanthan.
We explored the optimization of TrefftzDiscontinuous Galerkin methods with the TentPitcher algorithm and the elaboration of boundary conditions adapted to them. We consider these methods in the framework of the firstorder acoustic wave equation in timedomain. The idea of Trefftz methods is to use local solutions of the considered Partial Differential Equations as basis functions. Such a formulation has the advantage of being posed on the skeleton of the mesh only and characteristics of the analytical solutions are injected into the discrete solution through the basis functions, which leads us to expect the obtained numerical solution to be more precise. However, the resulting scheme is implicit in timedomain, which leads to an increased computational cost. This is the reason why we investigated TentPitcher algorithms. The TentPitcher algorithm is a spacetime meshing algorithm introduced for hyperbolic problems, that consists in constructing a causal mesh which allows to solve the problem elementbyelement.
We have developed a TrefftzDG framework for solving the acoustic wave equation using TentPitching algorithms. In 2022, we have extended the existing code to unstructured meshes, which led to a modified TentPitching algorithm and we have proposed a parallel version of our TrefftzDG framework, which is carried out with the MPI library.
A second part of our work consisted in designing and implementing artificial boundary methods in order to consider simulations in very large domains. We derives a formulation for the TrefftzDiscontinuous Galerkin methods with Perfectly Matched Layers for the acoustic wave equation, which involves the computation of analytical solutions for this new system of equations because the principle of the Trefftz methods relies on the use of local solutions as basis functions. This is done by computing the Green’s functions for the timedomain acoustic wave equation using the CagniardDe Hoop method. Finally, we implement these boundary conditions into the TrefftzDiscontinuous Galerkin solver with TentPitching on structured meshes and present the obtained results.
This work has been done in the framework of DIP and has been presented in several congresses, such as ECCOMAS 20 (jun. 2022) and Waves 19 (jul. 2022) and is the topic of the PhD. of Vinduja Vasanthan, defended on December, 8th 52.
8.1.3 Optimized Finite Differences methods and Machine Learning to reduce numerical dispersion for the wave equation
Participants: Hélène Barucq, Henri Calandra, Florian Faucher, Nicolas Victorion.
We consider the wave equation in acoustic media and evaluate the performance of Finite Difference (FD) schemes. The objective is to reduce the computational cost while maintaining the accuracy avoiding numerical dispersion. To do so, we study the size of stencils and optimized weight for the spatial derivative to obtain the best results in terms of computational cost. We review the optimized coefficients that have been introduced in the literature to minimize the numerical dispersion and we compare their performance on different test cases, with the perspective to reduce as much as possible the number of points per wavelength. To go further we propose a non conventional method, based on Machine Learning to remove numerical dispersion. Here, we simulate on a coarse grid and a small stencil. Hence the simulation is fast but numerical dispersion appears, which we correct with a Machine learning. This correction is applied during the simulation at selected time steps. Consequently, we reduce run time while avoiding the numerical dispersion.
This work has been presented at the Mathias conference 28. It is a collaboration with Emmanuel Franck (Tonus, Inria, Nancy Grand Est).
8.1.4 Modal computation for open waveguides
Participants: Hélène Barucq, Marc Duruflé, Augustin Leclerc.
The study of electromagnetic (EM) wave propagation is essential for considering the impact of Human’s technologies on the environment. For instance, the offshore wind energy is transported through twisted dynamic cables, which armours prevent a significant portion of the waves to irradiate outside the cable. Nevertheless, a remaining and possibly significant part might escape from the cable. Hence, our aim is to look at their scattering in the large stretch of sea water. To consider this problem, we propose to modelize the cable and the surrounding water by an open 3D waveguide, which is an invariant domain according to the cable direction and which is unbounded in the two other directions. We then take a modal approach for the resolution. Moreover, although Maxwell equations govern the propagation of EM waves, they are simplified to the Helmholtz equation, by considering Transverse Magnetic waves.Before studying the EM field far away from the cable, we focus on its behavior in its vicinity. We use absorbing boundary conditions around the cable. We have analyze their relevance, especially at low frequency. This work is part of a PhD program which started in October 2021. The topic has been proposed by the SME Kraken Subsea and is now the heart of a collaboration between this SME, Makutu and INSA Rouen with Christian Gout and Antoine Tonnoir. It has been presented at Waves Conference in July 22.8.1.5 Polynomialreproducing spline spaces from fine zonotopal tilings
Participants: Hélène Barucq, Henri Calandra, Julien Diaz, Stefano Frambati.
Given a point configuration A, we uncover a connection between polynomialreproducing spline spaces over subsets of conv(A) and fine zonotopal tilings of the zonotope Z(V) associated to the corresponding vector configuration. This link directly generalizes a known result on Delaunay configurations and naturally encompasses, due to its combinatorial character, the case of repeated and affinely dependent points in A. We prove the existence of a general iterative construction process for such spaces. Finally, we turn our attention to regular fine zonotopal tilings, specializing our previous results and exploiting the dual graph of the tiling to propose a set of practical algorithms for the construction and evaluation of the associated spline functions. The construction of the spline spaces is presented in JCAM 11.8.1.6 Practical unstructured splines: Algorithms, multipatch spline spaces, and some applications to numerical analysis
Participants: Hélène Barucq, Henri Calandra, Julien Diaz, Stefano Frambati.
In this work, we build on our previous results on simplex spline spaces to construct a polynomialreproducing space of unstructured splines on multipatch domains of arbitrary shape and topology. The traces of these functions on the subdomain boundaries reproduce the usual traces of standard polynomial bases used in discontinuous Galerkin (DG) approximations, allowing to borrow many theoretical and practical tools from these methods. Concurrently, we recast some theoretical results on the construction and evaluation of spaces of simplex splines into an explicit, algorithmic form. Together, these efforts allow to formulate a practical, efficient and fully unstructured multipatch discontinuous Galerkinisogeometric analysis (DGIGA) scheme that bridges the gap between some current multipatch isogeometric analysis (IGA) approaches and the more traditional meshbased interior penalty discontinuous Galerkin (IPDG) method. We briefly discuss the advantages of this unified framework for timeexplicit hyperbolic problems, and we present some interesting numerical examples using the acoustic wave equation. This work has been published in JCP 14.8.1.7 Frequencydomain acoustic wave modeling via unstructured isogeometric analysis: performance and pollution study
Participants: Hélène Barucq, Henri Calandra, Julien Diaz, Stefano Frambati.
Many works have shown the usefulness of Isogeometric Analysis (IGA) 84 for the solution of the Helmholtz equation. In particular, the increased regularity of Bspline functions and their uniform shape often translate into a better precision per degree of freedom, a wider spectral convergence and a consequently reduced numerical pollution compared to standard finite element (FE) approaches (see, e.g., 73). Recent advances in unstructured spline spaces 11 have allowed a new, fully unstructured IGA paradigm to emerge, with some intersting applications to explicittime wave propa gation. This scheme, based upon an unstructured point cloud, allows to produce IGA patches with full regularity and arbitrary domain topology. Moreover, these patches can be coupled via discontinuous Galerkin (DG) terms, yielding a fully unstructured multi patch DGIGA, or even the usual DG scheme as a limiting case. In this work, we explore the usefulness of this new paradigm for frequencydomain wave propagation. In particular, we study the convergence and spectral properties of this unstructured IGA multipatch scheme on some selected models. We focus on its behavior with respect to the point cloud density and the number of degrees of freedom, and we analyze its computational performance, precision and numerical pollution. We also show how the generalized topology of domains allowed by this pointcloud formulation allows to go beyond the usual tensorproduct IGA geometries. Finally, we give some perspective on how the meshfree character of this formulationcan be used to recover the location of sharp discontinuities starting from a smooth initial mode. This work has been presented at ECCOMAS conference (Oslo, June, 27)8.1.8 Trefftz methods for Maxwell equations
Participants: Margot Sirdey, Sébastien Tordeux.
The simulation of timeharmonic electromagnetic waves requires a matrix inversion whose cost, especially in threedimensional cases, increases quickly with the size of the computational domain. This is a tangible issue regarding the memory consumption. Trefftz methods consist in using a discontinuous Galerkin method whose basis functions are specific to the considered physical problem and thus reduce numerical dispersion phenomena. We propose an iterative Trefftz solver based on a domain decomposition method which will reduce considerably the memory consumption. However, iterative Trefftz methods based on a plane wave approximation are illconditioned. To overcome this problem, we propose improvements of the Cessenat and Després preconditioner and a basis reduction. A matrixfree strategy allows to avoid the assembly of the matrix associated to the linear system and GMRES solver does not require the computation of the inverse anymore. This is a joint work with Sébastien Pernet (ONERA). It has been presented in several congresses at ECCOMAS conference (Oslo) 44 Waves (Palaiseau) 42 and JCJC Sophia Antipolis 43 and a preprint has been written 55. Margot Sirdey has defended her PhD thesis 51.8.1.9 Mixed precision sparse direct solver applied to 3D wave propagation.
Participants: Florian Faucher.
Efficient numerical simulation of wave propagation phenomena is needed in several applications such as seismic imaging, nondestructive testing, or helioseismology. In this work, we consider timeharmonic waves and the hybridizable discontinuous Galerkin discretization method for which the efficiency of the wave propagator relies on the performance of finding the solution of systems of sparse linear equations. These systems have multiple sparse righthand sides associated with several sources. This motivates the use of direct solvers which can efficiently reuse the LU factors to compute the solution of multiple righthand sides at the cost however of a high memory footprint. Fortunately, matrices arising from the discretization of partial differential equations have been shown to have a lowrank property and the BlockLow Rank (BLR) format has been used to design fast direct solvers with reduced asymptotic complexity. Very recent work describes how the BLR LU factorization algorithm can benefit from mixed precision arithmetic. In the context of 3D frequencydomain wave equations, the BLR factorization in 32bit single precision arithmetic has been shown to provide accurate enough solutions. In this talk, we will explain why and how we can exploit lower precision formats (such as 24 and 16 bit arithmetics) in the representation of BLR blocks, while preserving a satisfactory accuracy. This allows us to reduce the memory footprint of the solver by further compressing both the LU factor matrices and the working space without affecting the precision of the solution. The performance using recent features of the MUMPS sparse direct solver, including mixed precision, is analyzed with largescale 3D acoustic and elastic experiments using hawen software, 77.
This is a joint work with the MUMPS group, in particular Patrick Amestoy (ENS Lyon), JeanYves L'Excellent (ENS Lyon), Théo Mary (Sorbonne University) and Chiara Puglisi. This work has been presented at ECCOMAS Conference, 24.
8.1.10 Iterative Trefftz methods for anisotropic acoustic problems equations
Participants: Hélène Barucq, Ibrahima Djiba, Sébastien Tordeux.
We are developing a numerical framework for the anisotropic wave equation thanks to a Trefftz method. We aim at solving a time harmonic problem without any matrix inversion. We resort to a Cessenat Després preconditioner and to a GMRES solver to accelerate the convergence of the algorithm wich allows to compute the solution of the considered problem with a low memory cost. A research report should be published in March 2023.8.1.11 A HDG framework for convected Helmholtz equation.
Participants: Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux.
In this work, we introduce three variants of the HDG method based on two weak formulations of the convected Helmholtz equation. Two of them are standard HDG methods with the same interpolation degree for all the unknowns and the last uses a higher interpolation degree for the volumetric scalar unknown. For those three numerical methods, a detailed analysis including local and global wellposedness, as well as convergence estimates is carried out. We then provide implementation details and numerical experiments to illustrate our theoretical results. A paper is currently under minor revisions.8.2 Seismic imaging
8.2.1 Experimental characterization and modeling of electromagnetic waves generated by seismoelectric conversion at porous media interfaces
Participants: Hélène Barucq, Victor Martins Gomes.
Inside fluidbearing porous media, mechanical disturbances created by traveling seismic waves entail the conversion of seismic into electromagnetic (EM) energy. Two forms of conversion, electrokinetic in nature, have been continually investigated in the context of subsurface exploration: the first consists of a wavefield strictly bounded to the seismic wave, therefore referred as coseismic fields, while the other only happens when the physical properties change, ergo at geological interfaces, and it radiates independently of the seismic waves, with EMvelocities (usually bigger than ${10}^{6}$ m/s). Due to the sensitivity of the latter to lithology changes, in special variation in the porefluid, it is pertinent to nearsurface investigation as a complement to seismic reflection, much like electromagnetic controlledsource. Because of that, there is a continuous effort to develop and promote the seismoelectric methods as an indirect geophysical procedure based on electrokinetic conversions. However the large number of parameters involved, and the lack of comprehensive understanding of these phenomena delays a widespread use of seismolectrics: currently there are two main theoretical descriptions, but thus far, none validated in a proper quantitative manner. As a contribution to the existing knowledge about seismictoEM conversions, we propose an easily reproducible experimental setup, capable of measuring both conversions at the same time, with satisfactory signaltonoise ratio. This setup allows the reproduction of diverse geological settings, including porous layers filled with different fluids, a peculiarity with respect to previous experiments designed to study the same subject. In parallel, an existing numerical code, built upon the most frequently used set of seismoEM governing equations, was properly adapted to model the experiment, hence opening the path to comparisons between theory and laboratory measurements. As a consequence, a series of measurements in both homogeneous and layered media were conducted, as well as their corresponding numerical modeling. Simulations showed that even though amplitude disagreements exist, overall the theoretical predictions successfully agree with experimental data. Additionally, by studying, experimentally and numerically, the effects of layer thinning on the interface response, it was observed that a boosting of the measured signals happens when the layer has a thickness equal to half the Pwavelength in this layer (P, as usual, refers to compression waves). At last, the effect of fluid conductivity on interfacegenerated EM waves was investigated. It was noticed that, in the experiment realized, amplitudes decrease with increasing conductivity, whereas the ratio between interface response and co seismic amplitudes increase. Also, comparison with numerical simulations confirmed again that theory succeeds in providing a fair representation of experiments. This work has been done in collaboration with Daniel Brito (LFCR, CNRS, UPPA), Stéphane Garambois (Isterre, Grenoble) and Clarisse Bordes (LFCR, CNRS, UPPA). It was the subject of a Ph.D. thesis funded by E2S UPPA (CHICkPEA project) defended the 5th of December 2022 50. Some of the results have been presented at EGU in May (see 41).
8.2.2 Pulsedlaser source characterization in laboratory seismic experiments
Participants: Julien Diaz, Chengyi Shen.
The present study aimed to characterize the properties of a lasergenerated seismic source for laboratoryscale geophysical experiments. This consisted of generating seismic waves in aluminum blocks and a carbonate core via pulsedlaser impacts and measuring the wavefield displacement via laser vibrometry. The experimental data were quantitatively compared to both theoretical predictions and 2D/3D numerical simulations using a finite element method. Two wellknown and distinct physical mechanisms of seismic wave generation via pulsedlaser were identified and characterized accordingly: a thermoelastic regime for which the incident laser power was relatively weak, and an ablation regime at higher incident powers. The radiation patterns of the pulsedlaser seismic source in both regimes were experimentally measured and compared with that of a typical ultrasonic transducer. This study showed that this pointlike, contactfree, reproducible, simpletouse lasergenerated seismic source was an attractive alternative to piezoelectric sources for laboratory seismic experiments, especially those concerning small scale, submeter measurements.This work was published in Geomechanics and Geophysics for GeoEnergy and GeoResources 16, in collaboration with Clarisse Bordes, Daniel Brito, Federico Sanjuan (LFCR, UPPA), and Stéphane Garambois (ISterre).
8.2.3 Analytical solutions for elasto/poroelastic coupling
Participant: Julien Diaz.
Our software Gar6more computes the analytical solution of waves propagation problems in 2D homogeneous or bilayered media, based on the Cagniardde Hoop method. In the bilayered case, we had implemented the following coupling: acoustic/acoustic, acoustic/elastic, acoustic poroelastic, elastic/elastic, poroelastic/poroelastic. In the framework of collaboration with Peter Moczo (Comenius University Bratislava and Slovak Academy of Sciences), David Gregor, Josef Kriztek, Miriam Kristekova (Comenius University Bratislava), Arnaud Mesgouez, Gaëlle LefeuveMesgouez (Inrae, Avignon University) and Christina Morency (Laurence Livermore National Laboratory) and we have implemented the coupling between elastic and poroelastic media. The obtained results are presented in an article of Geophysical Journal International 15.8.2.4 Full Waveform Inversion on Seismic Data including Surface Waves.
Participants: Hélène Barucq, Julien Diaz, Florian Faucher, Chengyi Shen.
Makutu collaborated with RealTimeSeismic (RTS) SME as part of the FEDERPoctefa PIXIL project (Pyrenees Imaging eXperience: an InternationaL network) on the topic of Full Waveform Inversion (FWI), with a particular focus on the surface waves. The PIXIL project focuses on geophysical method development for geothermal surveys, where surface waves carry essential information of nearsurfaces especially for shallow geothermal explorations. A good image of the nearsurface can further help improve deep imaging.
The collaboration RTS/Inria within the PIXIL project followed 3 main axes: data exchange/analyses, FWI strategy establishment and acquisition parameterization design. We aim at building a FWI tool suitable for surface waves and ultimately applying it onto real data acquired by RTS in a nearsurface seismic exploration. The core of the numerical tool is a Fortran HPC code, named HAVEN 77 developed by Florian Faucher in timeharmonic domain featuring the Hybridizable Discontinuous Galerkin method. We conducted 2D synthetic case studies in order to establish Multilevel Strategies for FWI on seismic data including surface waves. A tradeoff between robustness and highresolution is achievable by elaborating suitable strategies such as combining seismic tomography and FWI featuring frequency groups, regularization and filtering. Meanwhile, Bash and Python programs are created to assist HAVEN for userfriendly concerns as well as data pre/postprocessing, for instance, automatization of executions, data processing and visualization.
We constructed, tested and validated a new costfunction in the FrequencyWavenumber (FK) domain following the suggestions of literatures tackling surface waves 95, 88. The FWI results confirm the major advantage of such a costfunction: the “attraction basin” is larger and smoother than in the FrequencySpace (FX) domain, which is a favorable condition for the convergence of the FWI result towards the targeted model. We showed also that the strategy of multilevel inversion combining cycles of ascending and descending frequencies can help us escape local minima. A FWI featuring strong surface waves may work with both robustness and highresolution in the FK domain.
8.2.5 Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion.
Participant: Florian Faucher.
we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the scattered waves. Conventional DT relies on the Fourier diffraction theorem, which is applicable under the condition of weak scattering. However, if the object has high contrasts or is too large compared to the wavelength, it tends to produce multiple scattering, which complicates the reconstruction. We give a survey on diffraction tomography and compare the reconstruction of low and high contrast objects. We also implement and compare the reconstruction using the full waveform inversion method which, contrary to the Born and Rytov approximations, works with the total field and is more robust to multiple scattering.
This is a joint work with Clemens Kirisits (University of Vienna), Michael Quellmalz (TU Berlin), Otmar Scherzer (University of Vienna) and Eric Setterqvist (RICAM). A book chapter has been published as part of Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, Springer International Publishing, 49.
8.2.6 Quantitative inverse problem in viscoacoustic media under attenuation model uncertainty.
Participant: Florian Faucher.
We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of viscoacoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is performed by an iterative minimization algorithm. Firstly, we investigate the robustness of the algorithm with respect to attenuation model uncertainty, that is, when different attenuation models are used to simulate synthetic observation data and for the inversion, respectively. Secondly, to handle datasets with multiple reflections generated by wall boundaries around the domain, we perform inversion using complex frequencies, and show that it offers a robust framework that alleviates the difficulties of multiple reflections. To illustrate the efficiency of the algorithm, we perform numerical simulations of ultrasound imaging experiments to reconstruct a synthetic breast sample that contains an inclusion of highcontrast properties. We perform experiments in two and three dimensions, where the latter also serves to demonstrate the numerical feasibility in a largescale configuration.
This is a joint work with Otmar Scherzer (University of Vienna), a papar has been published in the Journal of Computational Physics, 13.
8.2.7 Quantitative Analysis of Seismic Waves with Computational and LaboratoryScale Experiments.
Participants: Marine Deheuvels, Florian Faucher.
We recover physical properties of a material with a focus on the attenuation, using a laboratoryscale sample. We develop a method to accurately invert the attenuation models, and demonstrate its efficiency with 3D simulations in the frequency domain considering different rheological viscoelastic models. First, we consider a simplified numerical case where we avoid wave reflections from boundaries. Our analysis allows to characterize the wave behavior and the attenuation properties of the medium. Here, we use a complex wavenumber analysis, to recover a complexvalued mechanical modulus that accounts for the viscoelastic behavior. Secondly, we consider numerically an experimental configuration, with freesurface conditions on the sample boundaries, and measurements restricted to the faces of the sample. In this case, the freesurface boundaries lead to multiple reflections and wave conversions that must be taken into account to analyze both the body waves and surface waves displacements to recover the representative viscoelastic properties. Finally, we carry out laboratoryscale experiments on various rock samples designed to find out their attenuation properties. For this purpose, we run an experimental setup using piezoelectric transmitters acting as a seismic source, and a laserdoppler vibrometer for noncontact timedomain measurements. Then, we have to recover the appropriate attenuation laws and their corresponding parameters, depending on the nature of samples. This eventually serves to build initial models to perform iterative reconstruction with Full Waveform Inversion.
This is the subject of Marine Deheuvels Ph.D. at UPPA, she is supervised by Daniel Brito (UPPA) and Florian Faucher. This work has been presented at the conference EGU 35 and at the conference AGU 57.
8.2.8 Highresolution seismic tomography on a carbonate core.
Participants: Julien Diaz, Chengyi Shen.
We submitted an article to Geophysical Journal International to communicate our experimental and numerical work on highresolution seismic tomography performed on a carbonate core at the laboratoryscale. The experimental part was done in the Laboratoire des Fluides Complexes et leurs Réservoirs (LFCR). The numerical simulation was performed by Hou10ni HPC code developed by our team. We developed an automate experimental prototype involving a pointlike pulsedlaser (PL) or a piezoelectric transducer (PZT) as seismic sources and a singlepoint Laser Doppler Vibrometer (LDV) as a receiver. The PLLDV setup is successfully applied to produce seismic propagation in the megahertz range and used to study the Pwave velocities inside the carbonate core through tomography. The seismic tomography obtained from both the PLLDV and the PZTLDV datasets are compared with an Xray CTscan image of the carbonate core. In parallel, numerical tests on synthetic data, simulated by Hou10ni, are run to study the hyperparameters and resolution of tomography, which helped us establish an optimal inversion strategy involving multigrids. The tomography results are completed with a sensitivity analysis through spike tests. Therefore, we validated an experimental prototype featuring seismic sources of multiphysics origins for highresolution measurements in laboratory as well as a tomography workflow: we propose an original and efficient geophysical coreprobing configuration based on the PLLDV setup leading to a more accurate tomographic Pvelocities reconstruction as compared to the PZTLDV setup. This work is in collaboration with Daniel Brito and Clarisse Bordes of LFCR, Jean Virieux and Stéphane Garambois of ISTerre, as well as the DMEX Center for Xray Imaging.
8.2.9 Frequency analysis of the seismoelectric coupling operator
Participants: Hélène Barucq, Julien Diaz, Arjeta Heta.
Pride's equations 93 model seismoelectric effects resulting from the coupling between seismic and electromagnetic waves in porous media. They are thus equations of dynamic in porous media coupled with Maxwell's equations. The coupling is achieved in terms of a coefficient $L$ which is defined in the time domain as a Fourier integral operator. The exact $L$ is thus difficult to discretize and is approximate by a leading term ${L}_{0}$ independent of the frequency. When considering the time harmonic equations, the associated $L$ is the inverse of a square root in the frequency. We address the idea of using approximate timeharmonic coupling terms defined as rational or polynomial functions of the frequency. By this way, it would be possible to switch from timeharmonic coupling terms to timedependent ones. In practice, $L$ is replaced in the time domain by a constant coefficient ${L}_{0}$ which should only reproduce the coupling accurately in the low frequency range. We have obtained approximate expressions of the coupling terms which can be derived in a frequency regime limited by the cutoff frequency. We use Padé approximants to approximate the square root by rational functions of frequency. Numerical experiments show that actually ${L}_{0}$ reproduces correctly the seismoelectric effect at low frequencies while higherorder rational approximations of $L$ perform better at mid and high frequencies. This work is the topic of Arjeta Heta's Ph.D. thesis, it is a collaboration with Cristina Morency in the framework of the SEE4GEO project 10.1.2. It has been presented in a digital poster at the AGU conference in Chicago (Dec.2022)58.8.2.10 Elastic Full Waveform Inversion in the frequency domain with hybridizable discontinuous Galerkin method
Participants: Hélène Barucq, Florian Faucher, Ha Pham.
Seismic Full Waveform Inversion has clearly demonstrated its efficiency in providing accurate quantitative information of the subsurface. Its implementation strongly depends on the resolution of the forward problem which is performed repeatedly in an iterative inversion process. In this work, we perform seismic FWI when the forward problem is solved with a facebased discontinuous finite element method. Discontinuous finite elements are particularly efficient for solving wave equations in heterogeneous media since with hpadaptivity feature, they not only can handle the topography of the propagation domain but also resist numerical pollution, which can be important in largescale computations. Herein, we consider a Hybridizable Discontinuous Galerkin method based upon a mixed formulation of the problem coupled with static condensation. The computational burden mostly comes from the resolution of the global discrete problem whose size is proportional to only the degrees of freedom of the mesh skeleton. We work with the elastic wave equation in the frequency domain. We consider two different mixed formulations, the socalled strainstress, and stressstrain formulations. This first one is widely used while the second one allows us to easily consider varying parameters inside the cells of the mesh. The HDG approximation of the elastic wave is the first step in the design of FWI process. The second and critical step consists in deriving the adjoint state in the same approximation framework. This turns out not to be an obvious task and thus deserves some attention. We illustrate the numerical performances of the HDGbased FWI with timeharmonic elastic wave equations on two and three dimensional test cases.
This work has been presented at the Mathias conference 31. subsubsectionOptimized Full Waveform Inversion for seismic in GEOSX:
Participants: Hélène Barucq, Julien Besset, Henri Calandra, Stefano Frambati.
The reduction of energy carbon footprint justifies the recent major programs launched on CO2 storage in existing reservoirs known to geologists. Numerical simulation plays a key role in their implementation by providing a lowcost means of monitoring. This is a global concern that explains the use of opensource software platforms facilitating knowledge sharing and collaborations. Regarding monitoring aspects, Full Waveform Inversion (FWI) has demonstrated its ability in probing the subsurface accurately. FWI is an iterative process in which we need to solve forward problems in largescale propagation domains whose discretization involves more than 108 cells each. Implementing an FWI algorithm needs thus an optimized architecture in terms of memory management and GPUCPU computation. Among the existing opensource platforms, GEOSX targets such architecture. Moreover, GEOSX offers a multiphysics approach ready for reservoir simulation and offering the perspective of coupling with seismic.During this year, we have developed a FWI workflow for GEOSX equipped with spectral elements for solving the forward problem. We have also investigated the opportunity of using Reduced Order Models (ROM) that are lowdimensional problems for fast simulations providing accurate solutions of the original problem. This approach has been widely used in computational fluid dynamics and seems to be gaining the interest of geophysicists as recent papers testify. However, the construction of ROM using for example Krylov subspace method or Propper Orthogonal Decomposition (POD) requires solving an eigenvalue problem, which tends to be computationally expensive. Hence, we are now considering the idea of introducing Physicsinformed Machine Learning. This work has been presented at the conference Mathias Days in October 2022 (see 26).
8.3 Helioseismology
8.3.1 Loworder PrandtlGlauertLorentz based Absorbing Boundary Conditions for solving the convected Helmholtz equation with Discontinuous Galerkin methods
Participants: Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux.
We construct Absorbing Boundary Conditions (ABCs) for the convected Helmholtz equation that are easy to implement in a Hybridizable Discontinuous Galerkin (HDG) formulation. The construction is based upon the PrandtlGlauertLorentz map which transforms the convected Helmholtz equation into the regular Helmholtz equation. The new ABCs are thus issued from classical BaylissGunztburgerTurkel ABCs and are valid for carrier flows that vary inside the computational domain but become uniform far away from the source. They lead to accurate numerical results for low and intermediate Mach numbers using a HDG formulation with the acoustic potential and the total flux as unknowns. This work has been published in the preprint 12. It has been presented at CANUM 2022 in Evian 45, Waves 2022 23 in Palaiseau and as an invited talk at CMAM  Computational Methods in Applied Mathematics 46 in Vienna.8.3.2 Outgoing modal solutions for Galbrun's equation in helioseismology.
Participants: Hélène Barucq, Florian Faucher, Ha Pham.
We construct modal outgoing Green's kernels for the simplified Galbrun's equation under spherical symmetry, in the context of helioseismology. The coefficients of the equation are C² functions representing the solar interior model S, complemented with an isothermal atmospheric model. We solve the equation in vectorial spherical harmonics basis to obtain modal equations for the different components of the unknown wave motions. These equations are then decoupled and written in Schrödinger form, whose coefficients are shown to be C² apart from at most two regular singular points, and to decay like a Coulomb potential at infinity. These properties allow us to construct an outgoing Green's kernel for each spherical mode. We also compute asymptotic expansions of coefficients up to order r³ as r tends to infinity, and show numerically that their accuracy is improved by including the contribution from the gravity although this term is of order r³. In particular, these works allow us to (1) efficiently compute the solar power spectra for different configurations, and (2) evaluate the performance of radiation boundary conditions for applications to 3D.
This is a joint work with Laurent Gizon and Damien Fournier of the Max Plank Institute for Solar system research in Göttingen (MPS), supported by the INRIA associated team ANTS between Makutu and MPS. These results have been presented in conference ECCOMAS 30.
8.3.3 Efficient computation of modal Green's kernels for vectorial equations in helioseismology under spherical symmetry.
Participants: Hélène Barucq, Florian Faucher, Ha Pham.
We investigate the numerical computation of physical modal Green's kernels for the timeharmonic Galbrun's equation in helioseismology under spherical symmetry. These kernels are the coefficients of the 3D Green's kernels in the vector spherical harmonic expansion. In a previous work, we have characterized the physical kernels for the isothermal radial solar background model SAtmoI and provide their wellposedness results. Here, we provide an algorithm to compute efficiently these kernels for all receiver and source positions in a region of interest and develop the technical ingredients for its implementation. The kernels are built from the solution of a scalar wave equation for the radial displacement. The solution and its derivative which are both necessary to assemble the Green's kernel are obtained by solving a firstorder system using the HDG method. This approach extends previous works considering a scalar wave equation and allows to model not only the pressure modes but also the surface and internal gravity waves. While being physically more interesting, this problem raises additional numerical difficulties. In particular, the solution of the Schrödinger equation for the radial displacement is singular without attenuation and it is thus preferable to solve the original equation. Moreover, for low frequencies and highmodes, the potential switches sign in the atmosphere which requires the position of the artificial boundary to be further away from the solar surface in order to capture the correct physical solution.
This is a joint work with Laurent Gizon and Damien Fournier of the Max Plank Institute for Solar system research in Göttingen (MPS), supported by the INRIA associated team ANTS between Makutu and MPS. These results have been presented in conference ECCOMAS 30.
8.3.4 Imaging individual active regions on the Sun's far side with improved helioseismic holography
Participant: Hélène Barucq.
Helioseismic holography is a useful method to detect active regions on the Sun’s far side and improve space weather forecasts. We aim to improve helioseismic holography by using a clear formulation of the problem, an accurate forward solver in the frequency domain, and a better understanding of the noise properties. Building on the work of Lindsey et al., we define the forward and backwardpropagated wave fields (ingression and egression) in terms of a Green’s function. This Green’s function is computed using an accurate forward solver in the frequency domain. We analyse overlapping segments of 31 hr of SDO/HMI dopplergrams, with a cadence of 24 hr. Phase shifts between the ingression and the egression are measured and averaged to detect active regions on the far side. The phase maps are compared with direct EUV intensity maps from STEREO/EUVI. We confirm that mediumsize active regions can be detected on the far side with high confidence. Their evolution (and possible emergence) can be monitored on a daily time scale. Seismic maps averaged over 3 days provide an active region detection rate as high as 75as low as 7attributed to the use of a complete Green’s function (all skips) and to the use of all observations on the front side (full pupil). Improved helioseismic holography enables the study of the evolution of mediumsize active regions on the Sun’s far side.
This is a joint work with Laurent Gizon and Dan Yang of the Max Plank Institute for Solar system research in Göttingen (MPS), supported by the INRIA associated team ANTS between Makutu and MPS. This work is published in Astronomy & Astrophysics, 18.
8.4 Musical Acoustics
8.4.1 Comparative study of French and German bassoons
Participant: Augustin Ernoult.
The French "Basson" and the German "Fagott" are both descendants of the baroque bassoon. They have evolved differently by adding side holes, lengthening the main bore and changing the shape of the reed. These two cousins are played with different fingerings and have a slightly different sound colour: the French bassoon having the reputation of having a more nasal and less homogeneous timbre over the whole range. The aim of this work was to identify the sound differences between a Fagott and a Bassoon and to relate them to their geometry through acoustic considerations. The two instruments studied were played by a professional Fagott player, familiar with the French bassoon. Each bassoon is played with two reeds: its own reed and a single plastic reed, all fitted with a pressure sensor. The external sound and reed pressure are recorded for musical excerpts and a chromatic scale allowing, for each signal, the calculation of the average spectrum over a given range of notes (e.g. the first register). These recordings are complemented by a set of geometric measurements (main bore and holes) and impedance measurements for each fingering of the two instruments. Some notes are also played by an artificial mouth on both instruments with similar control parameters, avoiding the musician's "reflex" adaptation. This set of measurements makes it possible to quantify the difference between the two instruments in terms of acoustic properties and radiated spectrum. Furthermore, it gives the possibility to calculate the transfer function between the spectrum of the reed and the spectrum of the external sound. The evolution of this quantity along the frequency axis can be related to manufacturing elements such as the length of the hole chimney, the dimensions of the radiating apertures and the associated radiating impedance, the tone hole network, etc. This transfer function is also calculated for each instrument. This transfer function is also calculated from the geometry of the instrument using a simple wave propagation model.
This work was presented at the Vienna Talks 2020/22 held in Vienna (Austria) in September 2022. 39
This comparison was complemented by the specific study of the effect of long stacks on the sound of these instruments. The bassoon has side holes a few tens of millimetres long, much longer than other wind instruments. When closed, the quarterwave resonances of these "chimneys" create acoustic shorts in parallel with the bore. At these resonant frequencies, close to 2kHz, it is expected that the waves will not propagate beyond the socalled chimney, affecting both the input impedance and the radiated sound. Using parametric studies with varying stack lengths, these effects on impedance and radiated sound were measured for a French bassoon and a simplified conical 'model instrument'. The effects are clear on the model instrument, especially when several chimneys have the same length. For the bassoon, the passive filter effect remains, but its importance on the sound is faded due to changes in the oscillation regime and directivity, as confirmed by simulations. The effect is audible under laboratory conditions, but is of the same order of magnitude as the spatial level variations due to the directivity of the instrument. Therefore, it is unlikely that, under normal playing conditions, a chimney length increase of 5 mm, as observed between the German and French bassoon, would lead to a significant change in timbre.
This work is the subject of a presentation at the 2022 French Acoustical Congress 38 the German annual Conference on Acoustics 40 and an article under review in the Journal of the Acoustical Society of America 54.
8.4.2 Benchmark study on wind instrument models
Participants: Juliette Chabassier, Augustin Ernoult.
With the aim of updating the Pafi Instrumental Factoring Support Platform, we listed and compared existing tools for calculating the acoustic input impedance of wind instruments. A working group was set up, bringing together a dozen French research teams with expertise in modelling and resolution methods using transfer matrices, 1D finite elements, 3D finite elements, multimodal methods, waveguides, etc. This group defined a set of geometries for the calculation of impedance. This group has defined a set of standard resonator geometries involving different propagation conditions (cylinder, cone, elbow, side hole, etc.) or radiation (closed, with baffle, etc.). The input impedances of these tubes were calculated using the expertise of the working group members and then pooled on a collaborative platform. The resulting database can be used for comparative studies, model verification and comparison with an experimental database. Its analysis will make it possible to make an informed choice of methods and models to be implemented in an invoice support tool, taking into account their validity, versatility, complexity of implementation and the necessary computing resources. The analysis of a few cases has already brought to the fore consensus and cases for which further research is necessary.
In parallel to this benchmark on numerical models for their verification, an experimental campaign is underway to create an exhaustive reference database for model validation (the notions of verification and validation are based on ASME criteria), and the estimation of uncertainties associated with measurements. In particular, the random inter/intra measurement and inter/intra sample uncertainty is quantified. The experimental campaign is based on numerous batches of five specimens each. The experimental design allows for consolidated experimental results regarding taper, edge effects, boundary conditions and materials. The manufactured specimens have already been tested in two different laboratories with varying characterisation methods and should be extended to other institutions. The first results allow the establishment of a reproducible measurement protocol. This campaign gives first estimates of the variability of the measurements and allows to test different aspects of the experimental design.
This work was the subject of two presentations at the French Acoustics Congress in Marseille in April 2022. 37, 48
8.4.3 Transmission line coefficients for viscothermal acoustics in conical tubes
Participants: Juliette Chabassier, Alexis Thibault.
Viscothermal acoustic propagation in gases contained in rigid straight or conical tubes is considered. Assuming that the wavelength is much larger than the boundary layer thickness and the tube radius, the pressure and flow rate are shown to be solutions of a pair of coupled 1D differential equations, formulated as transmission line equations involving complex loss coefficients. The derivation of these loss coefficients, which is usually performed in cylinders, is generalised here to conical geometries. In the wellknown case of circular cylinders, the Zwikker–Kosten (ZK) theory is used. For circular cones, the expression for the loss coefficients is derived. It involves spherical harmonics of complex order, instead of Bessel functions for circular cylinders, and makes the hydraulic radius appear as a relevant natural geometrical parameter. We show that replacing the classical radius by the hydraulic radius in the ZK theory provides an affordable and accurate approximation to the derived analytical model for cones. The proposed formulae are used to calculate the input impedance of a cone, and compared to a 3D reference. In an ideal setting, the use of spherical harmonics or hydraulic radius in the 1D method accurately approximates the full 3D method, and increases the accuracy by about two orders of magnitude compared to the ZK theory.
This work has been published in a journal of acoustics: Alexis Thibault, Juliette Chabassier, Henri Boutin, Thomas Hélie. Transmission line coefficients for viscothermal acoustics in conical tubes. Journal of Sound and Vibration, Elsevier, 2022, 543, pp.117355. ⟨10.1016/j.jsv.2022.117355⟩. 17
8.4.4 Modelling the influence of a porous wall on the acoustic propagation in a wind instrument
Participants: Juliette Chabassier, Alexis Thibault.
The inner wall of wind instruments can sometimes be porous or rough (wooden instruments, 3D prints); this condition modifies the acoustic properties of the instrument. We seek to model the coupling between an acoustic medium and a porous medium with a rigid skeleton, with the fluid satisfying the linearised NavierStokes equations in each domain. In the pores, or near the bore wall, air viscosity and thermal diffusion induce energy dissipation with a nonrational dependence on the complex frequency. A linear model of acoustic propagation in the porous medium is obtained from the theory of periodic homogenisation, which allows the formal separation of the microscopic and macroscopic scales. It is put in the form of It is put in the form of a Hamiltonian system with interaction ports, thus highlighting the structure of energy storage, exchange and dissipation within the model. A reduced model of the coupling between the porous wall and the 1D acoustic propagation in the bore of the instrument is proposed. A numerical scheme is established for the simulation in time of the 1D acoustic wave propagation taking into account the wall properties. This scheme verifies a discrete energy balance similar to that of the continuous model, and can be stably coupled to other subsystems (radiation, nonlinear mouthpiece). Simulations of reed instruments with nonuniform porosity will be presented.
This work was presented at the CFA 2022 national conference: Alexis Thibault, Juliette Chabassier, Henri Boutin, Thomas Hélie. Modelling the influence of a porous wall on the acoustic propagation in a wind instrument. CFA 2022  16th French Congress of Acoustics, Apr 2022, Marseille, France. ⟨hal03673860⟩
This work has been done in collaboration with Thomas Hélie and Henri Boutin (STMS, UMR9912, CNRSSUIRCAM).
8.4.5 Modelling the influence of a porous wall on the acoustic propagation in a wind instrument
Participants: Juliette Chabassier, Alexis Thibault.
Thermoviscous acoustic propagation in an isothermal corrugated rigidwalled tube is considered. At long wavelengths, it is equivalent to a 1D transmission line equation, in which the coefficients depend on the solution of a 2D scattering problem. It is shown that these coefficients exhibit predictable behaviour at low, high and intermediate frequencies. These results are demonstrated on a numerical example.
This work was presented at the international conference WAVES 2022: Henri Boutin, Juliette Chabassier, Thomas Hélie, Alexis Thibault. Thermoviscous acoustic propagation in thin rough tubes. WAVES 2022  15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jul 2022, Palaiseau, France. ⟨hal03780126⟩
This work has been done in collaboration with Thomas Hélie and Henri Boutin (STMS, UMR9912, CNRSSUIRCAM).
8.4.6 Influence of touch on the sound of the piano
Participants: Juliette Chabassier, Guillaume Castera.
What influence can the artist's touch have on the timbre of the piano? This question can be addressed through the modelling of piano sounds using the keystroke as the only input. In order to simulate sounds with the greatest precision from a real touch, physical models of each element of the instrument (hammer head and neck, string(s), soundboard, radiation in the air) have been developed and implemented in the Montjoie software of INRIA Bordeaux Sud Ouest. Limiting ourselves to modelling the vibroacoustic part excludes the mechanics which allows the hammer to be set in motion by the artist pressing the key. It is therefore essential to provide the vibroacoustic model with a fine representation of the forces exerted by the mechanics on the hammer as input data. In this case, our approach uses the force exerted by the escapement stick and by the repetition lever on the hammer handle, forces that are very complex to measure or estimate. A mechanics model implemented in the Robotran software at the Catholic University of Leuven in Belgium can calculate this force from any keystroke data. It is thus possible to analyse the repercussions of the subtleties brought in by the artist on the sound spectra, and to compare different simulations according to the type of touch used at the fingerboard, in particular the differences between legato and staccato or the dynamics between piano and forte.
This work was presented at the CFA 2022 national conference: Guillaume Castera, Timmerman Sébatien, Juliette Chabassier, Paul Fisette. Influence of touch on piano sound. French Congress of Acoustics, Apr 2022, Marseille, France. ⟨hal03842214⟩
This work has been done in collaboration with Paul Fisette and Sébastien Timmermans, université catholique de Louvain, Belgium.
8.4.7 Control parameters for reed wind instruments or organ pipes including reed flow
Participant: Juliette Chabassier.
Sound synthesis of a pipe coupled to a reed requires fine tuning of the physical parameters of the underlying model. Although the geometry of the pipe is often well known, the parameters of the onedegreeoffreedom reed model are effective coefficients (mass, crosssection, etc.) and are difficult to evaluate. Studies of this coupled system have mainly focused on models without the reedinduced flow, and have presented two dimensionless parameters, which respectively describe the ratio between the supply pressure and the closing pressure of the reed, and a dimensionless opening of the reed at rest. The inclusion of the reed flow in the model and the subsequent scaling of the equations leads to a third dimensionless quantity, which we will call kappa. Varying the reed frequency with constant parameters over different pipe sizes shows some stability of the model when put into this form. Using a realtime sound synthesis tool, the parameter space is explored while the reed damping is also varied.
This work was presented at the international conference DAFx20in22: Chabassier, Juliette, and Auvray, Roman. Control parameters for reed wind instruments or organ pipes with reed induced flow. In DAFx 20in22 Sep 2022, Vienna, Austria
This work has been done in collaboration with Roman Auvray, Modartt, Toulouse, France.
8.4.8 Direct computation of modal parameters for wind instruments
Participant: Juliette Chabassier.
The parameters of the modal expressions for the input impedance of wind instruments can be calculated from the telegrapher's equations with radiating boundary conditions at the bell. Onedimensional finite elements are used for the spatial discretization. If the models can be put into a specified form, the modal parameters can be calculated directly by solving a generalized eigenvalue problem. Viscothermal effects can also be taken into account, as well as open or closed side holes. The modal deformations can be visualised along the instrument. The parameters of the modal expressions for the input admittance of flutelike instruments can also be calculated.
This work has been published in a journal of acoustics: Juliette Chabassier, Roman Auvray. Direct computation of modal parameters for musical wind instruments. Journal of Sound and Vibration, Elsevier, 2022, 528, pp.116775. ⟨10.1016/j.jsv.2022.116775⟩. ⟨hal03613608⟩
This work has been done in collaboration with Roman Auvray, Modartt, Toulouse, France.
8.4.9 Understanding and predicting the acoustic properties of heritage instruments: the case of a Besson trumpet from the Musée de la Musique de Paris
Participants: Juliette Chabassier, Augustin Ernoult, Tobias van Baarsel.
Playing historical wind instruments is often in conflict with the conservation and protection of museum collections. Some of the musical and acoustic properties of these instruments are therefore unknown. Theoretical models can predict some of these properties from the knowledge of the geometry of the instruments alone. A collaboration between the Makutu Inria Bordeaux Sud Ouest team, the Musée de la Musique  Philharmonie de Paris, the Institut Technologique Européen des Métiers de la Musique (ITEMM) in Le Mans and the Centre de Recherche et de Restauration des Musées de France (C2RMF), led to a procedure applied to the collection of the Besson Museum, which was a large wind instrument factory, and more particularly to several natural trumpets dating from the beginning of the 20th century. The geometry of the instruments was measured noninvasively using Xray tomography at the C2RMF. After extracting their bore (evolution of the inner diameter), their input impedance was calculated. For one specific trumpet (E.0925), the simulated data were compared with the measurements with excellent agreement. Despite many uncertainties about how these instruments were played, simulated sounds can be calculated. An 'acoustic facsimile' of E.0925 was made from the Xray and impedance data and played by a professional natural trumpeter. This allows the simulated sounds to be compared with the sounds played by humans.
This work has been presented at several meetings and at the international conference Vienna Talk 25 and during the Congrès Français d'Acoustique 2022 36.
This work has been done in collaboration with Clotilde Boust, Marguerite Jossic, Sebastian Kirsch, Elsa Lambert, Romain Viala.
9 Bilateral contracts and grants with industry
9.1 Bilateral contracts with industry

Makutu research agreement.
Period: January 2022 – December 2026; Amount: 350000 per year.

Tent Pitcher algorithm for spacetime integration of wave problems
Period: 2019 November  2022 October, Management: INRIA Bordeaux SudOuest, Amount: 165000 .

Numerical schemes assisted with Machine Learning for solving timedependent seismic wave problems
Period: 2021 November  2024 October, Management: INRIA Bordeaux SudOuest, Amount: 90000 euros.

Petrophysics in presalt carbonate rocks
Period: 2019 November  2022 September, Management: INRIA Bordeaux SudOuest, Amount: 110000 euros.
10 Partnerships and cooperations
10.1 International initiatives
10.1.1 Inria associate team not involved in an IIL or an international program
ANTS

Title:
Advanced Numerical meThods for helioSeismology

Duration:
2019 > 2022

Coordinators:
Laurent Gizon (gizon@mps.mpg.de) and Ha Pham Howard Faucher (ha.howard@inria.fr)

Partners:
 Max Plank Institut at Göttingen (Allemagne)

Inria contact:
Ha Pham Howard Faucher

Summary:
Makutu has had an Associate Team project, Advanced Numerical meThods for helioSeismology (ANTS), with the Max Planck Institute for Solar System Research (MPS), led by Laurent Gizon, which ended by the end of 2022. The objective was to develop advanced software for accurate simulation of stellar oscillations and for the reconstruction of the Sun's interior. The novelty and challenge come from working with convected vector wave equations in the presence of complex flow and gravity, for a more accurate description of the physical phenomenon. The software hawen uses Hybridizable Discontinuous Galerkin (HDG) approximation. The scientific project benefited from the expertise of Makutu in seismic imaging, and the expert knowledge of the MPS group on Solar physics, in order to design accurate and efficient methodology. The project also helped strengthen the ongoing collaboration between Makutu and MPS, that started five years ago. ANTS has been decisive to elevate the joint collaboration between Makutu and MPS. An ANR PRCI project is being submitted in 2023 to continue the collaboration. Two Ph.D. students from MPS will also visit Makutu in 2023 to improve their knowledge in applied mathematics.
10.1.2 Participation in other International Programs
SEE4GEO

Title:
SeismoElectric Effects for GEOthermal resource assessment and monitoring

Duration:
2021 > 2024

Coordinator:
Christina Morency (morency1@llnl.gov) LLNL (Lawrence Livermore National Laboratory, US department of Energy)

Partners:
 University of Hawaii at Mänoa (USA);
 University of Pau and the Pays de l'Adour, UPPA (France);
 TLS Geothermics, TLS (France),
 NORCE (Norway)

Inria contact:
Hélène Barucq

See also:
SEE4GEO on Geothermica website.

Summary:
Geothermal systems involve the injection of large amounts of fluid into the subsurface. Identifying fracture networks is of great importance to assess geothermal resources. Traditional seismic imaging techniques fail to resolve fluidphase properties, while purely electromagnetic (EM) approaches provide limited, lowresolution constraints on the rock structure. Seismoelectric effects (SEE) arise from the seismictoelectromagnetic conversion in naturally charged porous media with a certain degree of fluid saturation. With SEE, we leverage seismic and EM technique sensitivities. In this project, we offer an integrated SEE assessment for geothermal systems relying on numerical modelling, laboratory experiments and field surveys. Makutu is involved in the project as a joint team with UPPA (University of Pau and Pays de l'Adour).
10.2 International research visitors
10.2.1 Visits of international scientists
In the framework of the associate team ANTS, Makutu has welcomed a group of seven researchers from MPS from October 24 to October 28. They are listed in the section Team members, etc.
10.3 European initiatives
10.3.1 H2020 projects
MATHROCKS

Title:
Multiscale Inversion of Porous Rock Physics using HighPerformance Simulators: Bridging the Gap between Mathematics and Geophysics

Duration:
April 2018  March 2023

Coordinator:
Universidad Del Pais Vasco (EHU UPV)

Partners:
 BARCELONA SUPERCOMPUTING CENTER  CENTRO NACIONAL DE SUPERCOMPUTACION (Spain)
 BCAM  BASQUE CENTER FOR APPLIED MATHEMATICS (Spain)
 CURTIN UNIVERSITY OF TECHNOLOGY (Australia)
 PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE (Chile)
 REPSOL SA (Spain)
 UNIVERSIDAD CENTRAL DE VENEZUELA (Venezuela)
 UNIVERSIDAD DE BUENOS AIRES (Argentina)
 UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA (Spain)
 UNIVERSIDAD NACIONAL DE COLOMBIA (Colombia)
 UNIVERSITAT POLITECNICA DE CATALUNYA (Spain)

Inria contact:
Hélène BARUCQ

Summary:
We will develop and exchange knowledge on applied mathematics, highperformance computing (HPC), and geophysics to better characterize the Earth´s subsurface. We aim to better understand porous rocks physics in the context of elastoacoustic wave propagation phenomena. We will develop parallel highcontinuity isogeometric analysis (IGA) simulators for geophysics. We will design and implement fast and robust parallel solvers for linear equations to model multiphysics electromagnetic and elastoacoustic phenomena. We seek to develop a parallel joint inversion workflow for electromagnetic and seismic geophysical measurements. To verify and validate these tools and methods, we will apply the results to: characterise hydrocarbon reservoirs, determine optimal locations for geothermal energy production, analyze earthquake propagation, and jointly invert deepazimuthal resistivity and elastoacoustic borehole measurements. Our target computer architectures for the simulation and inversion software infrastructure consists of distributedmemory parallel machines that incorporate the latest Intel Xeon Phi processors. Thus, we will build a hybrid OpenMP and MPI software framework. We will widely disseminate our collaborative research results through publications, workshops, postgraduate courses to train new researchers, a dedicated webpage with regular updates, and visits to companies working in the area. Therefore, we will perform a significant role in technology transfer between the most advanced numerical methods and mathematics, the latest supercomputer architectures, and the area of applied geophysics.
10.3.2 Other european programs/initiatives
PiXiL

Title:
Multiscale Inversion of Porous Rock Physics using HighPerformance Simulators: Bridging the Gap between Mathematics and Geophysics

Duration:
September 2019  April 2022

Coordinator:
BARCELONA SUPERCOMPUTING CENTER  CENTRO NACIONAL DE SUPERCOMPUTACION (Spain)

Partners:
 BARCELONA SUPERCOMPUTING CENTER  CENTRO NACIONAL DE SUPERCOMPUTACION (Spain)
 BCAM  BASQUE CENTER FOR APPLIED MATHEMATICS (Spain)
 UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA (Spain)
 UNIVERSITAT de BARCELONA (Spain)
 REALTIMESEISMIC (RTS)
 PÔLE AVENIA

Inria contact:
Julien DIAZ

Summary:
Part of the FEDER Poctefa Program the PIXIL project is a transnational and multidisciplinary scientific and technological cooperation. Its main goal is to develop the most advanced tools to analyze the Earth's subsurface, with a special focus on fostering the uptake of geothermal energy in the region. The project will contribute to making the transPyrenean area a technology hub in subsoil characterization within two years. Its success is expected to boost the wealth and creation of jobs related to the generation and management of underground natural resources in the area.
 See also:
10.4 National initiatives
10.4.1 Depth Imaging Partnership (DIP)
The research agreement DIP between TotalEnergies and Inria lasts since 2009. It focuses on the development of highperformance numerical methods for solving wave equations in complex media with the objective of characterizing geological reservoirs. It is fully funded by TotalEnergies. It came to its end in December with the Ph.D. defense of V. Vasanthan. This agreement has served as a guideline for 15 years of joint research with TotalEnergies. A dozen PhDs in applied mathematics have been trained, more than half of whom are now employed by TotalEnergies, the others holding jobs in public or private research.
10.5 Regional initiatives
10.5.1 Regional Council of Nouvelle Aquitaine Grants
Revival

Title:
Revival

Duration:
20192024

Coordinator:
Inria

Partners:
University of Bordeaux, University of Montreal (Canada), Catholic University of Louvain (Belgium)

Inria contact:
Juliette CHABASSIER

Summary:
The objective is to develop numerical tools for the virtual restoration of heritage instruments.

Amount:
107 k€; half doctoral position of Guillaume Castera, half postdoctoral position (to be attributed)
10.5.2 Regional Council of Normandie Grants

Title:
Modeling and numerical simulation of electromagnetic wave propagation in offshore conductor cables: applications to the environmental impact on the marine ecosystem.

Duration:
20212024

Coordinator:
LMI Insa Rouen

Inria contact:
Hélène Barucq

Summary:
The objective is to develop a numerical library for simulating the radiation pattern of offshore conductor cables to assess their impact on the marine ecosystem.

Amount:
150 k€; doctoral position of Augustin Leclerc
11 Dissemination
11.1 Promoting scientific activities
11.1.1 Scientific events: organisation
 As part of the INRIA associateteam ANTS Makutu organized a oneweek workshop on computational helioseismology at the University of Pau with the Max Planck institute for Solar System Research. It was held from October 24th to 28th.
 Hélène Barucq coorganized a minisymposium (MS153) at ECCOMAS 2022 in OSLO, entitled Robust and Scalable Numerical Methods for Wave Propagation: Design, Analysis and Application, with Théophile ChaumontFrelet (Atlantis, Inria), Rabia Djellouli (CSUN, USA) and Axel Modave (Poems, CNRS).
Reviewer
Augustin Ernoult has selected papers for a special session in musical acoustics during Congrès Français d'Acoustique 2022.
11.1.2 Journal
Member of the editorial boards
Hélène Barucq is member of the editorial board of Mathematics and Computers in Simulation (Imacs Journal MATCOM).
Reviewer  reviewing activities
Members of Makutu are regular reviewers for the following journals:
 Geophysical Journal International
 International Journal for Numerical Methods in Engineering
 Journal of Computational Physics
 Mathematics of Computation
 Journal of Acoustical Society of America
 Journal of Sound and Vibration
 Inverse problems
 Geophysics
 SIAM Journal of Scientific Computing
 Journal of Mathematical Imaging and Vision
 Numerical Functional Analysis and Optimization
11.1.3 Leadership within the scientific community
 Augustin Ernoult is elected member of the "Groupe spécialisé d'acoustique musicale" (Gsam) of the french acoustical society.
 Hélène Barucq has been in charge of a mission for the Hcéres (High Council for the evaluation of research and higher education) consisting to participate in the writing of the Synthèse Nationale des Mathématiques (SNM, ) report which was presented in a press conference on 9/11/2022.
 Hélène Barucq coleads the ExaMa project (Methods and Algorithms for Exascale) with Christophe Prud'homme (University of Strasbourg, UNISTRA) which is one of the five targeted projects of the PEPR (Priority Research Programs and Equipment) Numpex funded by the French National Research Agency (ANR).
11.1.4 Scientific expertise
 Hélène Barucq acts as a scientific expert for the FWO (Research Foundation  Flanders
 Hélène Barucq is member of the steering committee of CATIE
 Hélène Barucq has been awarded as an Expert for the European Science Foundation (ESF) for the period 20222024.
 Hélène Barucq is the Chair of the Thematic Committee CT6, "Computer Science, Algorithms and Mathematics" at GENCI.
 Hélène Barucq coleads the ExaMA project (Methods and Algorithms for the Exascale) within the framework of the NumPEX PEPR, which will be launched in January 2023.
11.1.5 Research administration
 Augustin Ernoult is member of the Center Commitee of Inria Bordeaux SudOuest.
 Hélène Barucq is appointed member of the scientific board of the LMA2S (Laboratory of Mathematics Applied to Aeronautics and Space) created to federate the activities in Applied Mathematics which are carried out in seven departments of the ONERA.
 Juliette Chabassier is member of the Research Position Commission of Inria Bordeaux SudOuest.
 Julien Besset is elected member of Laboratory Commitee of LMAP.
 Julien Diaz is elected member of the Inria Technical Committee and of the Inria Administrative Board. He is appointed member of the Bureau du Comité des Projets (BCP) of Inria Bordeaux SudOuest. Since 2018, he has been the head of the Mescal team of LMAP.
11.2 Teaching  Supervision  Juries
11.2.1 Teaching
 Master : Sébastien Tordeux, Outils Mathématiques pour la Mécanique, 49 eq. TD, Master1, UPPA, France
 Master : Margot Sirdey and Sébastien Tordeux, Introduction to wave phenomena, 48 eq. TD, Master, UPPA, France
 Licence : Sébastien Tordeux, Applied Mathematics, 63 eq. TD, L1, UPPA, France
 Licence : Ibrahima Djiba, Mathématiques appliquées pour les sciences économiques, 12h Eq. TD, L2, UPPA, France
 Licence : Julien Besset, Calcul numérique, 12h Eq. TD, L2, UPPA, France
 Licence : Arjeta Heta, Algèbre linéaire, 12h Eq. TD, L2, UPPA, France
 Licence : Arjeta Heta, Introduction aux probabilités, 20h Eq. TD, L2, UPPA, France
 Master : Marine Deheuvels, Signal Processing, UPPA, Pau, France, 18 eq. TD.
 Master : Florian Faucher, Inversion/Optimization, UPPA, Pau, France, 6 eq. TD.
11.2.2 Supervision
 PhD defended: Victor Martins Gomez, Experimental characterization and modeling of seismoelectromagnetic waves, Université de Pau et des Pays de l'Adour, December 5th, Hélène Barucq and Daniel Brito (LFCR).
 PhD defended: Vinduja Vasanthan, TrefftzDG Methods and TentPitcher Algorithm for Spacetime Integration of Wave Problems, December 8th, Hélène Barucq and Julien Diaz.
 PhD defended: Margot Sirdey, Méthode de Trefftz pour l'électromagnétisme, December 19th, Sébastien Tordeux and Sébastien Pernet (Onera).
 PhD in progress : Alexis Thibault, Modeling and simulation of wind musical instruments, October 2020, Juliette Chabassier and Thomas Hélie (IRCAM).
 PhD in progress : Guillaume Castera, Modeling and simulation of the piano touch, October 2020, Juliette Chabassier and Paul Fisette (Louvain Cath. Univ., Belgium)
 PhD in progress: Nicolas Victorion, Numerical schemes assisted with Machine Learning for solving timedependent seismic wave problems, October 2021, Hélène Barucq, Florian Faucher and Emmanuel Franck (Inria Nancy GrandEst, Tonus)
 PhD in progress: Arjeta Heta, Advanced numerical schemes to model seismoelectric effects and improve characterization of geological reservoirs, September 2021, Hélène Barucq and Julien Diaz.
 PhD in progress: Ibrahima Djiba, Trefftz domain decomposition method for wave propagation in geophysics, October 2021, Hélène Barucq et Sébastien Tordeux
 PhD in progress: Augustin Leclerc, Modeling and numerical simulation of electromagnetic wave propagation in offshore cables: applications to the environmental impact on the marine ecosystem, October 2021, Hélène Barucq, Christian Gout (LMI Insa de Rouen) and Antoine Tonnoir (LMI Insa de Rouen)
 PhD in progress: Marine Deheuvels, from quantitative analysis of wave amplitudes to full waveform inversion, October 2020, Daniel Brito (UPPA) et Florian Faucher
 PhD in progress : Julien Besset, Development of an optimized computing environment integrating seismic in CO2 storage and monitoring, January 2022, Hélène Barucq et Henri Calandra
 PhD in progress: Matthias Rivet, Optimization of numerical fluxes in Trefftz domain decomposition for electromagnetism: regular approach or artificial intelligence? October 2022, Sébastien Pernet (Onera) and Sébastien Tordeux
 PhD in progress: Lola Chabat, Largescale spectral problems using hybridizable Galerkin discretization with application to helioseismology, October 2022, Ha Pham and Hélène Barucq
11.2.3 Juries
Hélène Barucq has been member of the HDR defense committee of:
 Paul Cupillard, Numerical simulation of the propagation of seismic waves in complex geological media, defended on March 22, University of Lorraine
Hélène Barucq has been referee for the Ph.D. dissertation of:
 David GASPERINI, entitled "A multiharmonic finite element method for the microDoppler effect, with an application to automotive radar sensing" delivered by the Universities of Lorraine and Liège (Belgium), defended the 31st of March in Nancy;
 Maria EL GHAOUI, entitled "Méthodes de Trefftz avec reconstruction de la dérivée normale appliquée aux équations elliptiques", delivered by ParisSorbonne universités and Saint Joseph University, Lebanon, Beirut (USJ), defended the 16th of May.
Hélène Barucq has been member of the Ph.D. defense committee of
 Aimen Ben Hadj Hassine, dissertation entitled "Inversion of the reflection waveform with unidirectional propagation", delivered by the University of Pau and Pays de l'Adour, defended in December 8th in Pau;
 Margot Sirdey, dissertation entitled "Trefftz iterative method for the simulation of electromagnetic waves in dimension three", delivered by the University of Pau and Pays de l'Adour, defended in December 19th in Pau.
 Patryk DEC, dissertation entitled "Time domain simulations for railways problems with nonperiodic geometry and properties", Université AixMarseille, defended the 4th of July
Juliette Chabassier has been member of the Ph.D. defence committee of:
 Akram BENI HAMAD, entitled "Modélisation et simulation numérique de la propagation d’ondes électromagnetiques dans les câbles coaxiaux." delivered by the Institut Polytechnique de Paris and by the University Of Sousse (Tunisia), defended the 30th of September in Paris;
Julien Diaz has been referee for the Ph.D. dissertation of:
 Akram BENI HAMAD, entitled "Modélisation et simulation numérique de la propagation d’ondes électromagnetiques dans les câbles coaxiaux." delivered by the Institut Polytechnique de Paris and by the University Of Sousse (Tunisia), defended the 30th of September in Paris;
Julien Diaz has been member of the Ph.D. defense committee of
 Javier ABREUTORRES, dissertation entitled "Imagerie de milieux salifères aux échelles crustales et expérimentales par méthodes de migration sismique et méthode de l’adjoint: applications marines", delivered by the University of Toulouse, defended the 15th of June in Toulouse;
 Ilyes MOUFID, dissertation entitled "Étude théorique et modélisation numérique du comportement acoustique des milieux poreux rigides en régime temporel" delivered by the University of Toulouse, defended the 6th of December in Toulouse;
11.2.4 Academic recruitment committees
Hélène Barucq has been member of the recruitment committees in:
 Nice University, professor position
 Montpellier University, professor position
 Pau and Pays de l'Adour University, professor position
 INSA de Rouen, professor position
 Antilles University, assistant professor position
11.3 Popularization
11.3.1 Education
Hélène Barucq has been member of the discussion panel during the EYIC Career Forum at ECCOMAS 2022, 100 attendees, see here for more information.
11.3.2 Interventions
 Augustin Ernoult made a presentation for the "unithé ou café", an internal seminar at Inria for all the staff, 08/06/2022
 Augustin Ernoult made a large audience presentation together with a public rehearsal of the music ensemble Proxima Centauri, December 6th 2022 in Talence
 Hélène Barucq and Stefano Frambati have participated to the Roundtable "Energie : enjeux et défis futurs" at the Forum Emploi Maths 2022, presenting the role and importance of mathematics in the energy industry to math students.
12 Scientific production
12.1 Major publications
 1 articleLocal strategies for improving the conditioning of the planewave UltraWeak Variational Formulation.Journal of Computational Physics441September 2021, 110449
 2 articlePolynomialreproducing spline spaces from fine zonotopal tilings.Journal of Computational and Applied Mathematics402March 2022, 113812
 3 articleImplementation of Hybridizable Discontinuous Galerkin method for timeharmonic anisotropic poroelasticity in two dimensions..International Journal for Numerical Methods in Engineering2021
 4 articleOutgoing modal solutions for Galbrun's equation in helioseismology.Journal of Differential Equations286June 2021, 494530
 5 articleConstruction and convergence analysis of conservative second order local time discretisation for linear wave equations.ESAIM: Mathematical Modelling and Numerical Analysis554July 2021, 15071543
 6 articleFull waveform inversion for bore reconstruction of woodwindlike instruments.Acta AcusticaNovember 2021
 7 articlePractical unstructured splines: Algorithms, multipatch spline spaces, and some applications to numerical analysis.Journal of Computational Physics471December 2022, 111625
 8 thesisUnstructured Isogeometric Analysis with Applications to Seismic Wave Propagation.Université de Pau et des Pays de l'AdourDecember 2021
 9 articleEfficient hybrid method for the modal analysis of optical microcavities and nanoresonators.Journal of the Optical Society of America. A Optics, Image Science, and Vision388July 2021, 1224
 10 articleDissipative timedomain onedimensional model for viscothermal acoustic propagation in wind instruments..Journal of the Acoustical Society of America1502August 2021, 11651175
12.2 Publications of the year
International journals
 11 articlePolynomialreproducing spline spaces from fine zonotopal tilings.Journal of Computational and Applied Mathematics402March 2022, 113812
 12 articleLoworder PrandtlGlauertLorentz based Absorbing Boundary Conditions for solving the convected Helmholtz equation with Discontinuous Galerkin methods.Journal of Computational Physics468November 2022
 13 articleQuantitative inverse problem in viscoacoustic media under attenuation model uncertainty.Journal of Computational Physics472January 2023, 111685
 14 articlePractical unstructured splines: Algorithms, multipatch spline spaces, and some applications to numerical analysis.Journal of Computational Physics471December 2022, 111625
 15 articleSeismic waves in medium with poroelastic/elastic interfaces: a twodimensional PSV finitedifference modelling.Geophysical Journal International2281January 2022, 551588
 16 articlePulsedlaser source characterization in laboratory seismic experiments.Geomechanics and Geophysics for GeoEnergy and GeoResources81February 2022
 17 articleTransmission line coefficients for viscothermal acoustics in conical tubes.Journal of Sound and Vibration543October 2022, 117355
 18 articleImaging individual active regions on the Sun's far side with improved helioseismic holography.Astronomy and Astrophysics  A&A2023
International peerreviewed conferences
 19 inproceedingsOn the construction of Shape Functions forSpacetime TrefftzDG Formulations of Wave Problems with Perfectly Matched Layers.Waves 2022  15th International Conference on Mathematical and Numerical Aspects of Wave PropagationPalaiseau, FranceJuly 2022
 20 inproceedingsSpacetime TrefftzDG Formulation for Modelling Wave Propagation in Unbounded Domains.ECCOMAS  The 8th European Congress on Computational Methods in Applied Sciences and EngineeringOslo, NorwayJune 2022
 21 inproceedingsThermoviscous acoustic propagation in thin rough tubes.WAVES 2022  15th International Conference on Mathematical and Numerical Aspects of Wave PropagationPalaiseau, FranceJuly 2022
 22 inproceedingsModal computation for openwaveguides.WAVES 2022  15th International Conference on Mathematical and Numerical Aspects of Wave PropagationPalaiseau, FranceJuly 2022
 23 inproceedingsLoworder Absorbing Boundary Conditions in HDGdiscretization of the convected Helmholtz equation.Waves 2022 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jul 2022, Palaiseau, FrancePalaiseau, FranceJuly 2022
Conferences without proceedings
 24 inproceedingsMixed precision sparse direct solver applied to 3D wave propagation.8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2022)Oslo, NorwayJune 2022
 25 inproceedingsUnderstand and predict acoustic properties of heritage instruments: the case of a Besson trumpet of the Musée de la Musique of Paris.VIENNATALK2020: FOURTH VIENNA TALK ON MUSIC ACOUSTICSVienna, AustriaSeptember 2022
 26 inproceedingsDesign for optimized Full Waveform Inversion forseismic in GEOSX: challenges and current trends.Mathias DaysMarne La Vallée, FranceOctober 2022
 27 inproceedingsFrequencydomain acoustic wave modeling via unstructured isogeometric analysis: performance and pollution study.ECCOMAS Congress 2022Oslo, NorwayJune 2022
 28 inproceedingsOptimized Finite Differences methods and Machine Learning to reduce numerical dispersion for the wave equation.Mathias Days 2022Marnela Vallée, FranceOctober 2022
 29 inproceedingsAtmospheric radiation boundary conditions for the wave equation in helioseismology.The 8th European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS Congress 2022Oslo, NorwayJune 2022
 30 inproceedingsEfficient computation of modal outgoing Green’s kernels in helioseismology.The 8th European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS Congress 2022Oslo, NorwayJune 2022
 31 inproceedingsElastic Full Waveform Inversion in the frequency domain with a facebased finiteelement method.Mathias Days 2022Marnela Vallée, FranceOctober 2022
 32 inproceedingsLinearly implicit energy consistent time discretisation for nonlinear wave equations.WAVES 2022  15th International Conference on Mathematical and Numerical Aspects of Wave PropagationPalaiseau, FranceJuly 2022
 33 inproceedingsInfluence du toucher sur le son du piano.Congrès français d'acoustiqueMarseille, FranceApril 2022
 34 inproceedingsOpenWind : une toolbox python au service de la recherche en acoustique musicale.16ème Congrès Français d'Acoustique, CFA2022Marseille, FranceApril 2022
 35 inproceedingsQuantitative Analysis of Seismic Waves Attenuation: Numerical Analysis and LaboratoryScale Experiments.EGU22Vienna, AustriaMay 2022
 36 inproceedingsPrédire les propriétés acoustiques des instruments du patrimoines: le cas d'une trompette Besson du Musée de la musique: [Prix Yves Rocard 2019].16ème Congrès Français d'Acoustique, CFA2022Marseille, FranceApril 2022
 37 inproceedingsÉtude comparative collaborative des modèles pour le calcul d’impédance d’instruments à vent.16ème Congrès Français d'Acoustique, CFA2022Marseille, FranceApril 2022
 38 inproceedingsÉtude expérimentale de l'effet des longues cheminées sur le son des instruments à vent: [Prix Yves Rocard 2019].16ème Congrès Français d'Acoustique, CFA2022Marseille, FranceApril 2022
 39 inproceedingsSpectrum difference between the German Fagott and the French Basson.Vienna Talk 2020/22Vienne, AustriaSeptember 2022
 40 inproceedings How does a closed long chimney affect the sound of conical reed wind instruments? 48th Annual Conference on Acoustics (DAGA), DAGA 2022  48th German Annual Conference on Acoustics Stuttgart / Online, Germany March 2022
 41 inproceedingsQuantitative comparison of seismoelectric laboratory data with numerical modelling based on electrokinetic theory.EGU General Assembly 2022Vienna, AustriaMay 2022
 42 inproceedingsIterative Trefftz method for threedimensional electromagnetic waves propagation.WAVESPalaiseau (FR), FranceJuly 2022
 43 inproceedingsTrefftz iterative method for threedimensional electromagnetic waves propagation.JCJCSophia Antipolis, France2022
 44 inproceedingsTrefftz iterative method for threedimensional electromagnetic waves propagation.ECCOMASOslo (Norway), FranceJune 2022
 45 inproceedingsA HDG Framework For Convected Wave Equations. Applications In Heliosesimology..Computational Methods in Applied MathematicsVienna, AustriaAugust 2022
 46 inproceedingsConditions aux Limites Absorbantes d'ordre faible pour l'équation de Helmholtz convectée.45ème Congrès d'Analyse NumériqueÉvianlesbains, FranceJune 2022
 47 inproceedingsModélisation de l'influence d'une paroi poreuse sur la propagation acoustique dans un instrument à vent.CFA 2022  16ème Congrès Français d'AcoustiqueMarseille, FranceApril 2022
 48 inproceedingsMise en place d’une base de données expérimentales, pour la validation de modèles de résonateurs et la comparaison de géométries et matériaux.16ème Congrès Français d'Acoustique, CFA2022Marseille, FranceApril 2022
Scientific book chapters
 49 inbookDiffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion.Handbook of Mathematical Models and Algorithms in Computer Vision and ImagingSpringer International PublishingApril 2022, 140
Doctoral dissertations and habilitation theses
 50 thesisCaractérisation Expérimentale et modélisation numérique des ondes électromagnétiques générées par conversion sismoélectrique aux interfaces dans les milieux poreux..Université de Pau et des Pays l'AdourDecember 2022
 51 thesisMéthode de type Trefftz pour la simulation d'ondes électromagnétiques à haute fréquence..Université de Pau et des Pays l'AdourDecember 2022
 52 thesisTrefftzDG Methods and TentPitcher Algorithm for Spacetime Integration of Wave Problems.Université de Pau et des Pays l'AdourDecember 2022
Reports & preprints
 53 miscFinetuning NeuralOperator architectures for training and generalization.January 2023
 54 miscExperimental study of the effect of the long chimney of a closed tonehole on the sound of a bassoon.December 2022
 55 miscUltraweak variational formulation for heterogeneous maxwell problem in the context of high performance computing.April 2022
 56 miscImaging individual active regions on the Sun's far side with improved helioseismic holography.December 2022
Other scientific publications
 57 inproceedingsAttenuation Measurements using Ultrasonic Seismic Waves Propagation: Numerical and LaboratoryScale Experiments.AGU22Chicago, United StatesDecember 2022
 58 inproceedingsApproximate Coupling Terms In Seismoelectric Theory: From Frequency Domain To Time Domain.AGU22  AGU Fall Meeting 2022Chicago (Illinois), US, United StatesDecember 2022
 59 miscTowards large scale DRP simulations: generation oflarge superresolution images and extraction oflarge pore network models.September 2022
12.3 Other
Scientific popularization
 60 miscModélisation et simulation numérique d’instruments de musique.September 2022
 61 inproceedingsReplicate the sound characteristics of a historical trumpet..Festival des 20 ans du SCRIMETalence, FranceJune 2022
12.4 Cited publications
 62 articleInverse problem for the Helmholtz equation with Cauchy data: reconstruction with conditional wellposedness driven iterative regularization.ESAIM: Mathematical Modelling and Numerical Analysis533May 2019, 10051030
 63 articleThe mechanism producing initial transients on the clarinet.The Journal of the Acoustical Society of America14262017, 33763386
 64 articleQuasistatic nonlinear characteristics of doublereed instruments.The Journal of the Acoustical Society of America12112007, 536546
 65 articleAbout the stability of the inverse problem in 1D wave equations—Application to the interpretation of seismic profiles.Applied Mathematics and Optimization511979, 147
 66 articleSpacetime TrefftzDG approximation for elastoacoustics.Applicable Analysis00August 2018, 1  16
 67 articleStability analysis of heterogeneous Helmholtz problems and finite element solution based on propagation media approximation.Mathematics of Computation863072017, 2129  2157
 68 articleDirect Simulation of Reed Wind Instruments.Computer Music Journal3342009, 4355
 69 articleHybridizable discontinuous Galerkin method for the twodimensional frequencydomain elastic wave equations.Geophysical Journal International2131April 2018, 637659
 70 inproceedingsIdentification of functional parameters in partial differential equations.Joint Automatic Control Conference121974, 155156
 71 articleHelioseismology.Reviews of Modern Physics7442002, 1073
 72 articleImproved precision in measurements of acoustic impedance spectra using resonancefree calibration loads and controlled error distribution.The Journal of the Acoustical Society of America12132007, 14711481
 73 articlePollution studies for high order isogeometric analysis and finite element for acoustic problems.Computer Methods in Applied Mechanics and Engineering3502019, 701718
 74 articleTransfer matrix of a truncated cone with viscothermal losses: application of the WKB method.Acta Acustica42May 2020
 75 articleWoodwind instrument design optimization based on impedance characteristics with geometric constraints.Journal of the Acoustical Society of America1485November 2020, 28642877
 76 phdthesisContributions to Seismic Full Waveform Inversion for Time Harmonic Wave Equations: Stability Estimates, Convergence Analysis, Numerical Experiments involving Large Scale Optimization Algorithms.Université de Pau et des Pays de l'AdourNovember 2017
 77 articlehawen: timeharmonic wave modeling and inversion using hybridizable discontinuous Galerkin discretization.Journal of Open Source Software657January 2021, 2699
 78 articleSensitivity kernels for timedistance helioseismologyEfficient computation for spherically symmetric solar models.Astronomy & Astrophysics6162018, A156
 79 articleAcoustical impedance measurements by the two‐microphone‐three‐calibration (TMTC) method.The Journal of the Acoustical Society of America8861990, 25332545
 80 articleComputational helioseismology in the frequency domain: acoustic waves in axisymmetric solar models with flows.Astronomy and Astrophysics  A&A600April 2017, A35
 81 articleLocal helioseismology.Living Reviews in Solar Physics212005, 6
 82 articleLocal helioseismology: threedimensional imaging of the solar interior.Annual Review of Astronomy and Astrophysics482010, 289338
 83 articleRealtime synthesis of clarinetlike instruments using digital impedance models.The Journal of the Acoustical Society of America11812005, 483494
 84 articleIsogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement.Computer methods in applied mechanics and engineering19439412005, 41354195
 85 inproceedingsSeismic imaging of supercritical geothermal reservoir using fullwaveform inversion method.Proceedings2019
 86 article3D seismic exploration across the deep geothermal research platform GroßSchönebeck north of Berlin/Germany.Geothermal Energy712019, 118
 87 inproceedingsThe seismic inverse problem as a sequence of before stack migrations.Conference on inverse scattering: theory and applicationSiam Philadelphia, PA1983, 206220
 88 phdthesisInversion of surface waves in an oil and gas exploration context.Université Grenoble Alpes (ComUE)2016
 89 articleA review of the adjointstate method for computing the gradient of a functional with geophysical applications.Geophysical Journal International16722006, 495503
 90 articleGaussNewton and full Newton methods in frequencyspace seismic waveform inversion.Geophysical Journal International13321998, 341362
 91 articleTwodimensional velocity models from wideangle seismic data by wavefield inversion.Geophysical Journal International12421996, 323340
 92 articleINVERSE THEORY APPLIED TO MULTISOURCE CROSSHOLE TOMOGRAPHY. PART 1: ACOUSTIC WAVEEQUATION METHOD 1.Geophysical prospecting3831990, 287310
 93 articleGoverning equations for the coupled electromagnetics and acoustics of porous media.Physical Review B50211994, 15678
 94 articleWebster's Horn Equation Revisited.SIAM Journal on Applied Mathematics6562005, 19812004
 95 phdthesisTwodimensional nearsurface seismic imaging with surface waves: alternative methodology for waveform inversion.Ecole Nationale Supérieure des Mines de Paris2013
 96 articleProperty modelling of a potential CO2 storage site using seismic inversion.EGUGA2013, EGU201310470
 97 bookInverse problem theory and methods for model parameter estimation.89siam2005
 98 bookInverse problem theory: methods for data fitting and model parameter estimation.Amsterdam, NetherlandsElsevier Science Publishers1987
 99 articleDemonstrating storage of CO2 in geological reservoirs: The Sleipner and SACS projects.Energy299102004, 13611369
 100 articleA comparison of a onedimensional finite element method and the transfer matrix method for the computation of wind music instrument impedance.Acta Acustica united with Acustica52019, 838
 101 articleSound production in recorderlike instruments. II. A simulation model.The Journal of the Acoustical Society of America10151997, 29252939
 102 articleInfluence of fluid displacement patterns on seismic velocity during supercritical CO2 injection: Simulation study for evaluation of the relationship between seismic velocity and CO2 saturation.International Journal of Greenhouse Gas Control462016, 197204