The focus of our research is on the development of novel parallel numerical algorithms and tools appropriate for state-of-the-art mathematical models used in complex scientific applications, and in particular numerical simulations. The proposed research program is by nature multi-disciplinary, interweaving aspects of applied mathematics, computer science, as well as those of several specific applications, as porous media flows, elasticity, wave propagation in multi-scale media.

Our first objective is to develop numerical methods and tools for complex scientific and industrial applications, that will enhance their scalable execution on the emergent heterogeneous hierarchical models of massively parallel machines. Our second objective is to integrate the novel numerical algorithms into a middle-layer that will hide as much as possible the complexity of massively parallel machines from the users of these machines.

The research described here is directly relevant to several steps of the numerical simulation chain. Given a numerical simulation that was expressed as a set of differential equations, our research focuses on mesh generation methods for parallel computation, novel numerical algorithms for linear algebra, as well as algorithms and tools for their efficient and scalable implementation on high performance computers. The validation and the exploitation of the results will be performed with collaborators from applications and it will be based on the usage of existing tools. In summary, the topics studied in our group are the following:

Numerical methods and algorithms

Mesh generation for parallel computation

Solvers for numerical linear algebra

Computational kernels for numerical linear algebra

Validation on numerical simulations

In the engineering, researchers, and teachers communities, there is a
strong demand for simulation frameworks that are simple to install and
use, efficient, sustainable, and that solve efficiently and accurately
complex problems for which there are no dedicated tools or codes
available. In our group we develop FreeFem++ (see http://

getting a quick answer to a specific problem,

prototyping the resolution of a new complex problem.

The current users of FreeFem++ are mathematicians, engineers, university professors, and students. In general for these users the installation of public libraries as MPI, MUMPS, Ipopt, Blas, lapack, OpenGL, fftw, scotch, is a very difficult problem. For this reason, the authors of FreeFem++ have created a user friendly language, and over years have enriched its capabilities and provided tools for compiling FreeFem++ such that the users do not need to have special knowledge of computer science. This leads to an important work on porting the software on different emerging architectures.

Today, the main components of parallel FreeFem++ are:

definition of a coarse grid,

splitting of the coarse grid,

mesh generation of all subdomains of the coarse grid, and construction of parallel datat structures for vectors and sparse matrices from the mesh of the subdomain,

call to a linear solver,

analysis of the result.

All these components are parallel, except for point (5) which is not in the focus of our research. However for the moment, the parallel mesh generation algorithm is very simple and not sufficient, for example it addresses only polygonal geometries. Having a better parallel mesh generation algorithm is one of the goals of our project. In addition, in the current version of FreeFem++, the parallelism is not hidden from the user, it is done through direct calls to MPI. Our goal is also to hide all the MPI calls in the specific language part of FreeFem++.

Iterative methods are widely used in industrial applications, and preconditioning is the most important research subject here. Our research considers domain decomposition methods and iterative methods and its goal is to develop solvers that are suitable for parallelism and that exploit the fact that the matrices are arising from the discretization of a system of PDEs on unstructured grids.

One of the main challenges that we address is the lack of robustness and scalability of existing methods as incomplete LU factorizations or Schwarz-based approaches, for which the number of iterations increases significantly with the problem size or with the number of processors. This is often due to the presence of several low frequency modes that hinder the convergence of the iterative method. To address this problem, we study direction preserving solvers in the context of multilevel domain decomposition methods with adaptive coarse spaces and multilevel incomplete decompositions. A judicious choice for the directions to be preserved through filtering or low rank approximations allows us to alleviate the effect of low frequency modes on the convergence.

We also focus on developing boundary integral equation methods that would be adapted to the simulation of wave propagation in complex physical situations, and that would lend themselves to the use of parallel architectures, which includes devising adapted domain decomposition approaches. The final objective is to bring the state of the art on boundary integral equations closer to contemporary industrial needs.

The design of new numerical methods that are robust and that have well proven convergence properties is one of the challenges addressed in Alpines. Another important challenge is the design of parallel algorithms for the novel numerical methods and the underlying building blocks from numerical linear algebra. The goal is to enable their efficient execution on a diverse set of node architectures and their scaling to emerging high-performance clusters with an increasing number of nodes.

Increased communication cost is one of the main challenges in high performance computing that we address in our research by investigating algorithms that minimize communication, as communication avoiding algorithms. We propose to integrate the minimization of communication into the algorithmic design of numerical linear algebra problems. This is different from previous approaches where the communication problem was addressed as a scheduling or as a tuning problem. The communication avoiding algorithmic design is an aproach originally developed in our group since 2007 (initially in collaboration with researchers from UC Berkeley and CU Denver). While at mid term we focus on reducing communication in numerical linear algebra, at long term we aim at considering the communication problem one level higher, during the parallel mesh generation tool described earlier.

We study the simulation of compositional multiphase flow in porous media with different types of applications, and we focus in particular on reservoir/bassin modeling, and geological CO2 underground storage. All these simulations are linearized using Newton approach, and at each time step and each Newton step, a linear system needs to be solved, which is the most expensive part of the simulation. This application leads to some of the difficult problems to be solved by iterative methods. This is because the linear systems arising in multiphase porous media flow simulations cumulate many difficulties. These systems are non-symmetric, involve several unknowns of different nature per grid cell, display strong or very strong heterogeneities and anisotropies, and change during the simulation. Many researchers focus on these simulations, and many innovative techniques for solving linear systems have been introduced while studying these simulations, as for example the nested factorization [Appleyard and Cheshire, 1983, SPE Symposium on Reservoir Simulation].

The research of F. Nataf on inverse problems is rather new since this activity was started from scratch in 2007. Since then, several papers were published in international journals and conference proceedings. All our numerical simulations were performed in FreeFem++.

We focus on methods related to time reversal techniques. Since the seminal paper by [M. Fink et al., Imaging through inhomogeneous media using time reversal mirrors. Ultrasonic Imaging, 13(2):199, 1991.], time reversal is a subject of very active research. The main idea is to take advantage of the reversibility of wave propagation phenomena such as it occurs in acoustics, elasticity or electromagnetism in a non-dissipative unknown medium to back-propagate signals to the sources that emitted them. Number of industrial applications have already been developped: touchscreen, medical imaging, non-destructive testing and underwater communications. The principle is to back-propagate signals to the sources that emitted them. The initial experiment, was to refocus, very precisely, a recorded signal after passing through a barrier consisting of randomly distributed metal rods. In [de Rosny and Fink. Overcoming the difraction limit in wave physics using a time-reversal mirror and a novel acoustic sink. Phys. Rev. Lett., 89 (12), 2002], the source that created the signal is time reversed in order to have a perfect time reversal experiment. Since then, numerous applications of this physical principle have been designed, see [Fink, Renversement du temps, ondes et innovation. Ed. Fayard, 2009] or for numerical experiments [Larmat et al., Time-reversal imaging of seismic sources and application to the great sumatra earthquake. Geophys. Res. Lett., 33, 2006] and references therein.

We are interested in the development of fast numerical methods for the simulation of electromagnetic waves in multi-scale situations where the geometry of the medium of propagation may be described through caracteristic lengths that are, in some places, much smaller than the average wavelength. In this context, we propose to develop numerical algorithms that rely on simplified models obtained by means of asymptotic analysis applied to the problem under consideration.

Here we focus on situations involving boundary layers and *localized* singular
perturbation problems where wave propagation takes place in media whose geometry or material
caracteristics are submitted to a small scale perturbation localized around a point, or a surface,
or a line, but not distributed over a volumic sub-region of the propagation medium. Although a huge
literature is already available for the study of localized singular perturbations and boundary layer
pheneomena, very few works have proposed efficient numerical methods that rely on asymptotic
modeling. This is due to their natural functional framework that naturally involves singular functions,
which are difficult handle numerically. The aim of this part of our reasearch is to develop and analyze
numerical methods for singular perturbation methods that are prone to high order numerical approximation,
and robust with respect to the small parameter caracterizing the singular perturbation.

We focus on computationally intensive numerical algorithms arising in the data analysis of current and forthcoming Cosmic Microwave Background (CMB) experiments in astrophysics. This application is studied in collaboration with researchers from University Paris Diderot, and the objective is to make available the algorithms to the astrophysics community, so that they can be used in large experiments.

In CMB data analysis, astrophysicists produce and analyze
multi-frequency 2D images of the universe when it was 5% of its
current age. The new generation of the CMB experiments observes the
sky with thousands of detectors over many years, producing
overwhelmingly large and complex data sets, which nearly double every
year therefore following Moore's Law. Planck
(http://

We have released a version of FreeFem++ (v 3.42) which introduces new and important features related to high performance computing:

improved interface,

improved interface with PETSc library,

improved interface with HPDDM (see above).

This release enables, for the first time, end-users to run the very same code on computers ranging from laptops to clusters and even large scale computers with thousands of computing nodes.

Laura Grigori was an Invited speaker at the ACM/IEEE Supercomputing'15,
International Conference for High Performance Computing, Networking,
Storage, and Analysis, Austin, November 2015,
http://

Frédéric Nataf, with V. Dolean and P. Jolivet, published a SIAM lecture note book on domain decomposition methods. The four draft versions on HAL https://

Laura Grigori was elected the Chair of the SIAM SIAG on Supercomputing (SIAM special interest group on supercomputing) for the period of January 2016 - December 2017. She was nominated by a Committee and elected by the members of this SIAG.

FeeFrem++

Scientific Description

FreeFem++ is a partial differential equation solver. It has its own language. FreeFem++ scripts can solve multiphysics non linear systems in 2D and 3D.

Problems involving PDE (2d, 3d) from several branches of physics such as fluid-structure interactions require interpolations of data on several meshes and their manipulation within one program. FreeFem++ includes a fast 2d-tree-based interpolation algorithm and a language for the manipulation of data on multiple meshes (as a follow up of bamg (now a part of FreeFem++ ).

FreeFem++ is written in C++ and the FreeFem++ language is a C++ idiom. It runs on Macs, Windows, Unix machines. FreeFem++ replaces the older freefem and freefem+.

Functional Description

FreeFem++ is a PDE (partial differential equation) solver based on a flexible language that allows a large number of problems to be expressed (elasticity, fluids, etc) with different finite element approximations on different meshes.

Partner: UPMC

Contact: Frederic Hecht

Scientific Description

HPDDM is an efficient implementation of various domain decomposition methods (DDM) such as one- and two-level Restricted Additive Schwarz methods, the Finite Element Tearing and Interconnecting (FETI) method, and the Balancing Domain Decomposition (BDD) method. This code has been proven to be efficient for solving various elliptic problems such as scalar diffusion equations, the system of linear elasticity, but also frequency domain problems like the Helmholtz equation. A comparison with modern multigrid methods can be found in the thesis of Pierre Jolivet.

Functional Description

HPDDM is an efficient implementation of various domain decomposition methods (DDM) such as one- and two-level Restricted Additive Schwarz methods, the Finite Element Tearing and Interconnecting (FETI) method, and the Balancing Domain Decomposition (BDD) method.

Participants: Pierre Jolivet and Frédéric Nataf

Contact: Pierre Jolivet and Frédéric Nataf

Keyword: Large scale

Functional Description

This library solves linear systems on parallel computers from PCs based on multicore processors to large scale computers. It implements recent parallel algorithms issued from domain decomposition methods and parallel approximate factorizations.

Partners: CNRS - UPMC

Contact: Laura Grigori

Submodules:

Sparse Toolbox

Keywords: Preconditioner - Interactive method - Linear system

Participants: Laura Grigori and Rémi Lacroix

Contact: Laura Grigori

not yet publicly available

Block Filtering Decomposition preconditioner

Keywords: Preconditioner - Linear system

Functional Description

Iterative methods are used in many industrial and academic applications to solve large sparse linear systems of equations, and preconditioning these methods is often necessary to accelerate their convergence. Several highly used preconditioners as incomplete LU factorizations are known to have scalability problems, often due to the presence of several low frequency modes that hinder the convergence of the iterative method. To address this problem, we work on filtering preconditioners. A judicious choice of the filtering vector allows to alleviate the effect of low frequency modes, and can accelerate significantly the convergence of the iterative method.

Participants: Laura Grigori, Rémi Lacroix and Frédéric Nataf

Partners: CNRS - UPMC

Contact: Laura Grigori

not yet publicly available

LORASC preconditioner

Keyword: Preconditioner

Participants: Laura Grigori and Rémi Lacroix

Contact: Laura Grigori

URL: not yet publicly available

NFF Nested Filtering Factorization

Keywords: Preconditioner - Interactive method - Linear system

Participants: Laura Grigori, Frédéric Nataf and Long Qu

Partners: UPMC - Université Paris-Sud

Contact: Laura Grigori

not yet publicly available

Our group continues to work on algorithms for dense linear algebra operations that minimize communication. During this year we focused on improving the performance of communication avoiding QR factorization as well as designing algorithms for computing rank revealing and low rank approximations of dense and sparse matrices.

We show how to perform TSQR and then reconstruct the Householder vector representation with the same asymptotic communication efficiency and little extra computational cost. We demonstrate the high performance and numerical stability of this algorithm both theoretically and empirically. The new Householder reconstruction algorithm allows us to design more efficient parallel QR algorithms, with significantly lower latency cost compared to Householder QR and lower bandwidth and latency costs compared with Communication-Avoiding QR (CAQR) algorithm. Experiments on supercomputers demonstrate the benefits of the communication cost improvements: in particular, our experiments show substantial improvements over tuned library implementations for tall-and-skinny matrices. We also provide algorithmic improvements to the Householder QR and CAQR algorithms, and we investigate several alternatives to the Householder reconstruction algorithm that sacrifice guarantees on numerical stability in some cases in order to obtain higher performance.

In this paper we introduce CARRQR, a communication optimal (modulo
polylogarithmic factors) rank revealing QR factorization based on tournament
pivoting. The factorization is based on an algorithm that computes
the decomposition by blocks of

We show that CARRQR reveals the numerical rank of a matrix in an analogous way to QR factorization with column pivoting (QRCP). Although the upper bound of a quantity involved in the characterization of a rank revealing factorization is worse for CARRQR than for QRCP, our numerical experiments on a set of challenging matrices show that this upper bound is very pessimistic, and CARRQR is an effective tool in revealing the rank in practical problems.

Our main motivation for introducing CARRQR is that it minimizes data transfer, modulo polylogarithmic factors, on both sequential and parallel machines, while previous factorizations as QRCP are communication sub-optimal and require asymptotically more communication than CARRQR. Hence CARRQR is expected to have a better performance on current and future computers, where commmunication is a major bottleneck that highly impacts the performance of an algorithm.

Our work focused on the design of robust algebraic preconditioners and domain decomposition methods to accelerate the convergence of iterative methods.

Optimized Schwarz methods (OSM) are very popular methods which were introduced by P.L. Lions for elliptic problems and Després for propagative wave phenomena. In , we have built a coarse space for which the convergence rate of the two-level method is guaranteed regardless of the regularity of the coefficients. We do this by introducing a symmetrized variant of the ORAS (Optimized Restricted Additive Schwarz) algorithm and by identifying the problematic modes using two different generalized eigenvalue problems instead of only one as for the ASM (Additive Schwarz method), BDD (balancing domain decomposition) or FETI (finite element tearing and interconnection) methods.

Starting from classical absorbing boundary conditions, we propose, in , a method for the separation of time-dependent scattered wave fields due to multiple sources or obstacles. In contrast to previous techniques, our method is local in space and time, deterministic, and also avoids a priori assumptions on the frequency spectrum of the signal. Numerical examples in two space dimensions illustrate the usefulness of wave splitting for time-dependent scattering problems.

We have continued to develop and further analyze new boundary integral formulation for wave scattering by complex objects.

We spent much effort investigating the potentialities of multi-trace formulations in terms of domain decomposition. We considered multi-trace formulations in this perspective. Indeed Multi-Trace Formulations are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. In , we introduced MTFs on simple model problems using concepts familiar to researchers in domain decomposition. This allowed us to get a new understanding of MTFs and a natural block Jacobi iteration, for which we determined optimal relaxation parameters. We then showed how iterative multitrace formulation solvers are related to a well known domain decomposition method called optimal Schwarz method: a method which used Dirichlet to Neumann maps in the transmission condition. We finally showed that the insight gained from the simple model problem leads to remarkable identities for Calderón projectors and related operators, and the convergence results and optimal choice of the relaxation parameter we obtained is independent of the geometry, the space dimension of the problem, and the precise form of the spatial elliptic operator, like for optimal Schwarz methods. We confirmed this analysis with numerical experiments.

Finally, in connection with boundary integral formulations, we extended the past work of
*Integral equations on multi-screens.* Integral Equations and Operator Theory,
77(2):167–197, 2013

Viewing tangential multi-traces of vector fields from the perspective of quotient spaces we introduced the notion of single-traces and spaces of jumps. We also derived representation formulas and established key properties of the involved potentials and related boundary operators. Their coercivity were proved using a splitting of jump fields. Another new aspect emerged in the form of surface differential operators linking various trace spaces.

Asymptotic models oriented toward more efficient numerical simulation methods have been investigated in three different directions.

In we investigated the eigenvalue problem *A curious instability phenomenon for a rounded corner in presence of a
negative material*. Asymp. Anal., 88(1):43–74, 2014

Contract with Total, February 2015 - February 2018, that funds the PhD of Hussam Al Daas on enlarged Krylov subspace methods for oil reservoir and seismic imaging applications. Supervisor, L. Grigori.

ANR-MN (Modèles Numériques) October 2013 - September 2017

The main goal is the methodological and numerical development of a new robust inversion tool, associated with the numerical solution of the electromagnetic forward problem, including the benchmarking of different other existing approaches (Time Reverse Absorbing Condition, Method of Small-Volume Expansions, Level Set Method). This project involves the development of a general parallel open source simulation code, based on the high-level integrated development environment of FreeFem++, for modeling an electromagnetic direct problem, the scattering of arbitrary electromagnetic waves in highly heterogeneous media, over a wide frequency range in the microwave domain. The first applications considered here will be medical applications: microwave tomographic images of brain stroke, brain injuries, from both synthetic and experimental data in collaboration with EMTensor GmbH, Vienna (Austria), an Electromagnetic Medical Imaging company.

ANR appel à projet générique October 2015 - September 2020

This project in scientific computing aims at developing new domain decomposition methods for massively parallel simulation of electromagnetic waves in harmonic regime. The specificity of the approach that we propose lies in the use of integral operators not only for solutions local to each subdomain, but for coupling subdomains as well. The novelty of this project consists, on the one hand, in exploiting multi-trace formalism for domain decomposition and, on the other hand, considering optimized Schwarz methods relying on Robin type transmission conditions involving quasi-local integral operators.

ANR appel à projet générique October 2015 - September 2020

In spite of decades of work on the modeling of greenhouse gas emission such as CO2 and N2O and on the feedback effects of temperature and water content on soil carbon and nitrogen transformations, there is no agreement on how these processes should be described, and models are widely conflicting in their predictions. Models need improvements to obtain more accurate and robust predictions), especially in the context of climate change, which will affect soil moisture regime.

The goal of this new project is now to go further using the models developed in MEPSOM to upscale heterogeneities identified at the scale of microbial habitats and to produce macroscopic factors for biogeochemical models running at the field scale.

To achieve this aim, it will be necessary to work at different scales: the micro-scale of pores (μm) where the microbial habitats are localized, the meso-scale of cores at which laboratory measurements on CO2 and N2O fluxes can be performed, and the macro-scale of the soil profile at which outputs are expected to predict greenhouse gas emission. The aims of the project are to (i) develop new descriptors of the micro-scale 3D soil architecture that explain the fluxes measured at the macro-scale, (ii) Improve the performance of our 3D pore scale models to simulate both micro-and meso- scales at the same time. Upscaling methods like “homogeneization” would help to simulate centimeter samples which cannot be achieved now. The reduction of the computational time used to solve the diffusion equations and increase the number of computational units, (iii) develop new macro-functions describing the soil micro-heterogeneity and integrate these features into the field scale models.

Title: Parallel Numerical Linear Algebra for Future Extreme-Scale Systems

Programm: H2020

Duration: November 2015 - November 2018

Coordinator: UMEÅUniversitet

Partners:

Science and Technology Facilities Council (United Kingdom)

Computer Science Department, UmeåUniversitet (Sweden)

Mathematics Department, The University of Manchester (United Kingdom)

Inria contact: Laura Grigori

The NLAFET proposal is a direct response to the demands for new mathematical and algorithmic approaches for applications on extreme scale systems, as identified in the FETHPC work programme and call. This project will enable a radical improvement in the performance and scalability of a wide range of real-world applications relying on linear algebra software, by developing novel architecture-aware algorithms and software libraries, and the supporting runtime capabilities to achieve scalable performance and resilience on heterogeneous architectures. The focus is on a critical set of fundamental linear algebra operations including direct and iterative solvers for dense and sparse linear systems of equations and eigenvalue problems. Achieving this requires a co-design effort due to the characteristics and overwhelming complexity and immense scale of such systems. Recognized experts in algorithm design and theory, parallelism, and auto-tuning will work together to explore and negotiate the necessary tradeoffs. The main research objectives are: (i) development of novel algorithms that expose as much parallelism as possible, exploit heterogeneity, avoid communication bottlenecks, respond to escalating fault rates, and help meet emerging power constraints; (ii) exploration of advanced scheduling strategies and runtime systems focusing on the extreme scale and strong scalability in multi/many-core and hybrid environments; (iii) design and evaluation of novel strategies and software support for both offline and online auto-tuning. The validation and dissemination of results will be done by integrating new software solutions into challenging scientific applications in materials science, power systems, study of energy solutions, and data analysis in astrophysics. The deliverables also include a sustainable set of methods and tools for cross-cutting issues such as scheduling, auto-tuning, and algorithm-based fault tolerance packaged into open-source library modules.

Title: EXascale Algorithms and Advanced Computational Techniques

Programm: FP7

Duration: September 2013 - August 2016

Coordinator: IMEC

Partners:

Fraunhofer-Gesellschaft Zur Foerderung Der Angewandten Forschung E.V (Germany)

Interuniversitair Micro-Electronica Centrum Vzw (Belgium)

Intel Corporations (France)

Numerical Algorithms Group Ltd (United Kingdom)

T-Systems Solutions for Research (Germany)

Universiteit Antwerpen (Belgium)

Universita della Svizzera italiana (Switzerland)

Université de Versailles Saint-Quentin-En-Yvelines. (France)

Vysoka Skola Banska - Technicka Univerzita Ostrava (Czech Republic)

Inria contact: Luc Giraud

Numerical simulation is a crucial part of science and industry in Europe. The advancement of simulation as a discipline relies on increasingly compute intensive models that require more computational resources to run. This is the driver for the evolution to exascale. Due to limits in the increase in single processor performance, exascale machines will rely on massive parallelism on and off chip, with a complex hierarchy of resources. The large number of components and the machine complexity introduce severe problems for reliability and programmability. The former of these will require novel fault-aware algorithms and support software. In addition, the scale of the numerical models exacerbates the difficulties by making the use of more complex simulation algorithms necessary, for numerical stability reasons. A key example of this is increased reliance on solvers. Such solvers require global communication, which impacts scalability, and are often used with preconditioners, increasing complexity again. Unless there is a major rethink of the design of solver algorithms, their components and software structure, a large class of important numerical simulations will not scale beyond petascale. This in turn will hold back the development of European science and industry which will fail to reap the benefits from exascale. The EXA2CT project brings together experts at the cutting edge of the development of solvers, related algorithmic techniques, and HPC software architects for programming models and communication. It will take a revolutionary approach to exascale solvers and programming models, rather than the incremental approach of other projects. We will produce modular open source proto-applications that demonstrate the algorithms and programming techniques developed in the project, to help boot-strap the creation of genuine exascale codes.

**Inria@SiliconValley**

Associate Team involved in the International Lab:

Title: Communication Optimal Algoritms for Linear Algebra

International Partner (Institution - Laboratory - Researcher):

University of California Berkeley (United States) - Electrical Engineering and Computer Science (EECS) - James Demmel

Start year: 2010

See also: https://

Our goal is to continue COALA associated team that focuses on the design and implementation of numerical algorithms for today's large supercomputers formed by thousands of multicore processors, possibly with accelerators. We focus on operations that are at the heart of many scientific applications as solving linear systems of equations or least squares problems. The algorithms belong to a new class referred to as communication avoiding that provably minimize communication, where communication means the data transferred between levels of memory hierarchy or between processors in a parallel computer. This research is motivated by studies showing that communication costs can already exceed arithmetic costs by orders of magnitude, and the gap is growing exponentially over time. An important aspect that we consider here is the validation of the algorithms in real applications through our collaborations. COALA is an Inria associate team that focuses on the design and implementation of numerical algorithms for today's large supercomputers formed by thousands of multicore processors, possibly with accelerators. We focus on operations that are at the heart of many scientific applications as solving linear systems of equations or least squares problems. The algorithms belong to a new class referred to as communication avoiding that provably minimize communication, where communication means the data transferred between levels of memory hierarchy or between processors in a parallel computer. This research is motivated by studies showing that communication costs can already exceed arithmetic costs by orders of magnitude, and the gap is growing exponentially over time. An important aspect that we consider here is the validation of the algorithms in real applications through our collaborations.

Grigori Laura

Date: Aug 2014 - June 2015

Institution: University of California Berkeley (United States)

Laura Grigori: long term mission at UC Berkeley, Computer Science Department, from September 2015 to June 2016.

Xavier Claeys: Seminar of Applied Mathematics, ETH Zürich, Switzerland, June. 7th - 20th, 2015.

Frédéric Hecht: Cours FreeFem++, Maths departement, Universty of Oxford, England, march 16th - 20th, 2015.

Frédéric Hecht: FreeFem++, Cimpa Summer School on Current Research in FEM at IIT Bombay, India 6-17 July , 2015.

Frédéric Hecht: Organizing the 7th FreeFem++ days (December 2015, Paris)

Frédéric Hecht: Organizing Contributions to PDE for Applications, September 2015, Paris

Laura Grigori: Member of Scientific Committee of Ecole CEA-EDF-Inria on Efficacité Énergétique dans le Calcul Haute Performance / Green HPC, 2015.

Laura Grigori: Member of Program Committee of IEEE International Parallel and Distributed Processing Symposium, IPDPS 2015.

Laura Grigori: Member of Program Committee of IEEE/ACM SuperComputing SC15 Conference, November 2015.

Laura Grigori: Member of Program Committee of HiPC 2015, IEEE Int'l Conference on High Performance Computing.

Laura Grigori: Member of Program Committee of International Conference on Parallel Processing and Applied Mathematics PPAM15, 2015.

Laura Grigori: Member of Program Committee of Workshop on Parallel Symbolic Computation (PASCO 2015), University of Bath, UK, 2015.

Laura Grigori: Area editor for Parallel Computing Journal, Elsevier, since June 2013.

Laura Grigori: Member of the editorial board for the SIAM book series Software, Environments and Tools. See
http://

Frédéric Nataf: Member of the editorial board of Journal of Numerical Mathematics

Laura Grigori: Invited speaker (plenary), ACM/IEEE Supercomputing'15,
International Conference for High Performance Computing, Networking,
Storage, and Analysis, Austin, November 2015,
http://

Laura Grigori: Invited plenary speaker, Emerging Technology Conference, June
2015, University of Manchester, http://

Frédéric Nataf: Invited plenary speaker, XXIII International Conference on Domain Decomposition Methods, 6-10 July 2015, South Korea.

Frédéric Nataf: Invited plenary speaker, International Conference on Preconditioning Techniques for Large Sparse Matrix Problems, 17-19 June 2015, at the University of Technology, Eindhoven, Netherlands.

Xavier Claeys: invited talk in the Seminar on PDE, LMV, Univ. Versailles, 15th of Jan. 2015.

Xavier Claeys: invited talk in the Seminar on Applied Math., CMAP, École Polytechnique, 8th of Dec. 2015.

Laura Grigori: Program Director of the SIAM SIAG on Supercomputing (SIAM special interest group on supercomputing), January 2014 - December 2015. Nominated by a Committee and elected by the members of this SIAG. One of the roles is to Co-Chair the SIAM Conference on Parallel Processing and Scientific Computing 2016.

Laura Grigori: November 2015 - current, expert to the Scientific Commission of IFPEN (French Petroleum Institute). Evaluation of research programs, PhD theses, work representing a total of 5 days per year.

Frédéric Hecht: President of the selection committee of the opening 0254 MCF 26, Université de Technologie de Compiègne.

Master: Laura Grigori, Guest lecture in a class on Randomized Linear Algebra
taught by Ravi Kanan, UC Berkeley, November 2015. The slides of the
lecture on *Algorithms for computing low rank approximations*
can be found on Laura Grigori's webpage.

Master: Laura Grigori, Spring 2015, UC Berkeley, Creation of a reading group and
lectures on randomized linear algebra that gathers together students
and experts interested in learning more and working on fast linear
algebra algorithms for machine learning applications. More details
are available at
https://

Master: Laura Grigori, Spring 2015, UC Berkeley, Guest lecturer in CS267 Class of
J. Demmel on *Applications of Parallel Computing* (lectures
13 to 16). The slides are available on L. Grigori's website, videos can be
found here https://

Lecture 13 on Communication Avoiding Algorithms in Linear Algebra

Lecture 14 on Graph partitioning

Lecture 15 on Sparse Direct Solvers

Lecture 16 on Iterative Solvers

Master : Frederic Nataf, Course on Domain Decomposition Methods, 30 hours, Master 2, UPMC, France.

Master : Frederic Nataf, Course on Domain Decomposition Methods, 15 hours, Master 2, ENSTA, France.

Textbook published by SIAM: AN INTRODUCTION TO DOMAIN DECOMPOSITION METHODS: ALGORITHMS, THEORY, AND PARALLEL IMPLEMENTATION, V. Dolean, P. Jolivet and F. Nataf, 2015.

Licence : Xavier Claeys, Calculus, 12hrs, L1, Université Pierre-et-Marie Curie Paris 6, France

Licence : Xavier Claeys, Orientation et Insertion Professionnelle, 40hrs, L2, Université Pierre-et-Marie Curie Paris 6, France

Master : Xavier Claeys, Informatique de base, 72hrs, M1, Université Pierre-et-Marie Curie Paris 6, France

Master : Xavier Claeys, Informatique Scientifique, 44hrs M1, Université Pierre-et-Marie Curie Paris 6, France

Master : Xavier Claeys, Résolution des EDP par éléments finis, 18hrs M2, Université Pierre-et-Marie Curie Paris 6, France

Master : Frédéric Hecht , Informatique de base, 24hrs, M1, Université Pierre-et-Marie Curie Paris 6, France

Master : Frédéric Hecht , Des EDP à leur résolution par la méthode des éléments finis (MEF), 24hrs, M2, Université Pierre-et-Marie Curie Paris 6, France

Master : Frédéric Hecht , Numerical methods for fluid mechanics, 10hrs, M2, Université Pierre-et-Marie Curie Paris 6, France

Master : Frédéric Hecht , Calcul scientifique 3 / projet industriel Freefem++, 28hrs, M2, Université Pierre-et-Marie Curie Paris 6, France

Master : Frédéric Hecht , Ingénierie 1 / Logiciel pour la simulation (Freefem++), 21hrs, M2, Université Pierre-et-Marie Curie Paris 6, France

Master : Frédéric Hecht , Ingénierie 2 / Projet collaboratif, 21hrs, M2, Université Pierre-et-Marie Curie Paris 6, France

PhD: Pierre-Henri Tournier, Absorption de l'eau et des nutriments par les racines des plantes : modélisation, analyse et simulation, Univ. Paris VI, February 2015, co-advisors M. Compte and F. Hecht.

PhD in progress: Alan Ayala, since October 2015 (funded by NLAFET H2020 project), co-advisors Xavier Claeys and Laura Grigori.

PhD in progress : Sebastien Cayrols, since October 2013 (funded by Maison de la simulation), adivsor Laura Grigori.

PhD in progress: Hussam Al Daas, since February 2015 (funded by contract with Total), advisor Laura Grigori.

PhD in progress: Olivier Tissot, since October 2015 (funded by NLAFET H2020 project), advisor Laura Grigori.

PhD in progress : Ryadh Haferssas, since October 2013 (funded by Ecole Doctorale, UPMC), advisor F. Nataf

PhD in progress : Mireille El-HAddad, since March 2014 (Cotuelle l’Université Saint-Joseph de Beyrouth, Liban et UPMC) , advisors F. Hecht and T. Sayah.

PhD in progress : Gillaume Verger El-HAddad, since Sept. 2013 (funded by ANR Becasim, Université de Rouen), advisors F. Hecht and I. Danaila.

Laura Grigori: PhD thesis of Florian Dang, Examiner, president of the jury, Université de Versailles, July 2015.

Laura Grigori: PhD thesis of Hamza Jeljeli, Examinateur, Université de Lorraine, Juillet 2015.

Xavier Claeys: PhD thesis of Mathieu Lecouvez, Examinateur, École Polytechnique, Juillet 2015

Xavier Claeys: PhD thesis of Simon Marmorat, Examinateur, École Polytechnique, Novembre 2015

Frédéric Hecht: HDR of Laurence Moreau , Rapporteur, UTT, Troyes, june 2015

Frédéric Hecht: PhD thesis of Arnaud BERTRAND , Rapporteur, Université de Strasbourg, November 2015

Frédéric Hecht: PhD thesis of Moussa Diédhiou , Examinateur, Université de la Rochelle, December 2015