3.1 Numerical algebra methodologies in model and data-driven scientific computing

At the core of many simulations, one has to solve a linear algebra problem that is defined in a vector space and that involves linear operators, vectors and scalars, the unknowns being usually vectors or scalars, e.g. for the solution of a linear system or an eigenvalue problem. For many years, in particular in model-driven simulations, the problems have been reformulated in classical matrix formalism possibly unfolding the spaces where the vectors naturally live (typically 3D PDEs) to end up with classical vectors in $R^n$ or $C^n$. For some problems, defined in higher dimension (e.g., time dependent 3D PDE), the other dimensions are dealt in a problem specific fashion as unfolding those dimensions would lead to too large matrices/vectors. The concace research program on numerical methodology intends to address the study of novel numerical algorithms to continue addressing the mainstream approaches relying on classical matrix formalism but also to investigate alternatives where the structure of the underlying problem is kept preserved and all dimensions are dealt with equally. This latter research activity mostly concerns linear algebra in tensor spaces. In terms of algorithmic principles, we will lay an emphasis on hierarchy as a unifying principle for the numerical algorithms, the data representation and processing (including the current hierarchy of arithmetic) and the parallel implementation towards scalability.

3.2 Composition of parallel numerical algorithms from a sequential expression

A major breakthrough for exploiting multicore machine 48 is based on a data format and computational technique originally used in an out-of-core context 62. This is itself a refinement of a broader class of numerical algorithms – namely, “updating techniques” – that were not originally developed with specific hardware considerations in mind. This historical anecdote perfectly illustrates the need to separate data representation, algorithmic and architectural concerns when developing numerical methodologies. In the recent past, we have contributed to the study of the sequential task flow (STF) programming paradigm, that enabled us to abstract the complexity of the underlying computer architecture 37, 38, 36. In the concace project, we intend to go further by abstracting the numerical algorithms and their dedicated data structures. We strongly believe that combining these two abstractions will allow us to easily compose toolbox algorithms and data representations in order to study combinatorial alternatives towards numerical and parallel computational efficiency. We have demonstrated this potential on domain decomposition methods for solving sparse linear systems arising from the discretisation of PEDs, that has been implemented in the maphys++ parallel package.

Regarding the abstraction of the target architecture in the design of numerical algorithms, the STF paradigm has been shown to significantly reduce the difficulty of programming these complex machines while ensuring high computational efficiency. However, some challenges remain. The first major difficulty is related to the scalability of the model at large scale where handling the full task graph associated with the STF model becomes a severe bottleneck. Another major difficulty is the inability (at a reasonable runtime cost) to efficiently handle fine-grained dynamic parallelism, such as numerical pivoting in the Gaussian elimination where the decision to be made depends on the outcome of the current calculation and cannot be known in advance or described in a task graph. These two challenges are the ones we intend to study first.

With respect to the second ingredient, namely the abstraction of the algorithms and data representation, we will also explore whether we can provide additional separation of concerns beyond that offered by a task-based design. As a seemingly simple example, we will investigate the possibility of abstracting the matrix-vector product, basic kernel at the core of many numerical linear algebra methods, to cover the case of the fast multipole method (FMM, at the core of the ScalFMM library). FMM is mathematically a block matrix-vector product where some of the operations involving the extra-diagonal blocks with hierachical structure would be compressed analytically. Such a methodological step forward will consequently allow the factorisation of a significant part of codes (so far completely independent because no bridge has been made upstream) including in particular the ones dealing with $\mathscr{H}\text{-matrices}$. The easy composition of these different algorithms will make it possible to explore the combinatorial nature of the possible options in order to best adapt them to the size of the problem to be treated and the characteristics of the target computer. *Offering such a continuum of numerical methods rather than a discrete set of tools is part of the team's objectives* It is a very demanding effort in terms of HPC software engineering expertise to coordinate the overall technical effort.

We intend to strengthen our engagement in reproducible and open science. Consequently, we will continue our joint effort to ensure consistent deployment of our parallel software; this will contribute to improve its impact on academic and industrial users. The software engineering challenge is related to the increasing number of software dependencies induced by the desired capability of combining the functionality of different numerical building boxes, e.g., a domain decomposition solver (such as maphys++) that requires advanced iterative schemes (such as those provided by fabulous) as well as state-of-the-art direct methods (such as pastix, mumps, or qr_mumps), deploying the resulting software stack can become tedious 41.

In that context, we will consider the benefit of using hybridization between simulation and learning in order to reduce the complexity of classical approaches by diminishing the problem size or improving preconditioning techniques. In a longer term perspective, we will also conduct an active technological watch activity with respect to quantum computing to better understand how such a advanced computing technology can be synergized with classical scientific computing.

4.1 Aeroacoustics Simulation

This domains is in the context of a long term collaboration with Airbus Research Centers. Wave propagation phenomena intervene in many different aspects of systems design at Airbus. They drive the level of acoustic vibrations that mechanical components have to sustain, a level that one may want to diminish for comfort reason (in the case of aircraft passengers, for instance) or for safety reason (to avoid damage in the case of a payload in a rocket fairing at take-off). Numerical simulations of these phenomena plays a central part in the upstream design phase of any such project 50. Airbus Central R & T has developed over the last decades an in-depth knowledge in the field of Boundary Element Method (BEM) for the simulation of wave propagation in homogeneous media and in frequency domain. To tackle heterogeneous media (such as the jet engine flows, in the case of acoustic simulation), these BEM approaches are coupled with volumic finite elements (FEM). We end up with the need to solve large (several millions unknowns) linear systems of equations composed of a dense part (coming for the BEM domain) and a sparse part (coming from the FEM domain). Various parallel solution techniques are available today, mixing tools created by the academic world (such as the Mumps and Pastix sparse solvers) as well as parallel software tools developed in-house at Airbus (dense solver SPIDO, multipole solver, $\mathscr{H}$-matrix solver with an open sequential version available online). In the current state of knowledge and technologies, these methods do not permit to tackle the simulation of aeroacoustics problems at the highest acoustic frequencies (between 5 and 20 kHz, upper limits of human audition) while considering the whole complexity of geometries and phenomena involved (higher acoustic frequency implies smaller mesh sizes that lead to larger unknowns number, a number that grows like $f^2$ for BEM and $f^3$ for FEM, where f is the studied frequency). The purpose of the study in this domain is to develop advanced solvers able to tackle this kind of mixed dense/sparse linear systems efficiently on parallel architectures.

6.1 New software

7.1 Multifacets of lossy compression for scientific data in the Joint-Laboratory of Extreme Scale Computing

The Joint Laboratory on Extreme-Scale Computing (JLESC) was initiated at the same time lossy compression for scientific data became an important topic for the scientific communities. The teams involved in the JLESC played and are still playing an important role in developing the research, techniques, methods, and technologies making lossy compression for scientific data a key tool for scientists and engineers. In this paper, we present the evolution of lossy compression for scientific data from 2015, describing the situation before the JLESC started, the evolution of this discipline in the past 8 years (until 2023) through the prism of the JLESC collaborations on this topic and some of the remaining open research questions

For more details on this work we refer to  16.

7.2 Preconditioners based on Voronoi quantizers of random variable coefficients for stochastic elliptic partial differential equations

A preconditioning strategy is proposed for the iterative solve of large numbers of linear systems with variable matrix and right-hand side which arise during the computation of solution statistics of stochastic elliptic partial differential equations with random variable coefficients sampled by Monte Carlo. Building on the assumption that a truncated Karhunen-Loève expansion of a known transform of the random variable coefficient is known, we introduce a compact representation of the random coefficient in the form of a Voronoi quantizer. The number of Voronoi cells, each of which is represented by a centroidal variable coefficient, is set to the prescribed number P of preconditioners. Upon sampling the random variable coefficient, the linear system assembled with a given realization of the coefficient is solved with the preconditioner whose centroidal variable coefficient is the closest to the realization. We consider different ways to define and obtain the centroidal variable coefficients, and we investigate the properties of the induced preconditioning strategies in terms of average number of solver iterations for sequential simulations, and of load balancing for parallel simulations. Another approach, which is based on deterministic grids on the system of stochastic coordinates of the truncated representation of the random variable coefficient, is proposed with a stochastic dimension which increases with the number P of preconditioners. This approach allows to bypass the need for preliminary computations in order to determine the optimal stochastic dimension of the truncated approximation of the random variable coefficient for a given number of preconditioners.

For more details on this work we refer to  31.

7.3 Robustness and reliability of state-space, frame-based modeling for thermoacoustics

The Galerkin modal expansion is a well-known method used to develop reduced order models for thermoacoustics. A known issue is the appearance of Gibbs-type oscillations on velocity fluctuations at the interface between subdomains and at boundary conditions. Recent work of Laurent et al. (2019) and Laurent et al. (2021) have shown that it is possible to overcome this issue by using an over-completed frame, instead of a Galerkin modal basis. However, the low-order modeling based on this frame modal expansion may generate spurious modes, that are spirious eigenpairs. In this paper, the origin of these non-physical modes is identified and a method is proposed to automatically remove them from the outcome. By preventing any interaction between the physical and non-physical components, the proposed methodology drastically improves the robustness and reliability of the frame modal expansion modeling for thermoacoustics. The main numerical methodology relies on perturbation theory of symmetric eigenproblem and numerical approximation of the range of linear operators.

For more details on this work we refer to  15.

7.4 Computing WSBM marginals with Tensor-Train decomposition

The Weighted Stochastic Block Model (WSBM) is a statistical model for unsupervised clustering of individuals based on a pairwise distance matrix. The probabilities of group membership are computed as unary marginals of the joint conditional distribution of the WSBM, whose exact evaluation with brute force is out of reach beyond a few individuals. We propose to build an exact Tensor- Train (TT) decomposition of the multivariate joint distribution, from the SVD of each binary factor of a WSBM, which leads to variables separation. We present how to exploit this decomposition to compute unary and binary marginals. They are expressed without approximation as products of matrices involved in the TT decomposition. However, the implementation of the procedure faces sev- eral numerical challenges. First, the dimensions of the matrices involved grow faster than exponentially with the number of variables. We bypass this difficulty by using the format of TT-matrices. Second, the TT-rank of the products grows exponentially. Then, we use a numerical approximation of matrices product that guarantees a low TT-rank, the rounding. We compare the TT approach with two classical inference methods, the Mean-Field approximation and the Gibbs Sampler, on the problem of binary marginal inference for WSBM with various distances structures and up to fifty variables. The results lead to recommend the TT approach for its accuracy and reasonable computing time. Further researches should be devoted to the numerical difficulties for controlling the rank in rounding, to be able to deal with larger problems.

For more details on this work we refer to 22

7.5 A filtered multilevel Monte Carlo method for estimating the expectation of cell-centered discretized random fields

In this work, we investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of numerical simulators have inconsistent dimensions across the multilevel hier- archy. This requires the introduction of grid transfer operators borrowed from multigrid methods. By adapting mathematical tools from multigrid methods, we perform a theoretical spectral analysis of the MLMC estimator of the expectation of discretized random fields, in the specific case of linear, symmetric and circulant simulators. We then propose filtered MLMC (F-MLMC) estimators based on a filtering mechanism similar to the smoothing process of multigrid methods, and we show that the filtering operators improve the estimation of both the small- and large-scale components of the variance, resulting in a reduction of the total variance of the estimator. Next, the conclusions of the spectral analysis are experimentally verified with a one-dimensional illustration. Finally, the pro- posed F-MLMC estimator is applied to the problem of estimating the discretized variance field of a diffusion-based covariance operator, which amounts to estimating the expectation of a discretized random field. The numerical experiments support the conclusions of the theoretical analysis even with non-linear simulators, and demonstrate the improvements brought by the F-MLMC estimator compared to both a crude MC and an unfiltered MLMC estimator.

For more details on this work we refer to 47.

7.6 Multilevel Surrogate-based Control Variates

Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC estimator for the outputs of computationally expensive solvers. The control variates (CV) method corrects the MC estimator with a term derived from auxiliary random variables that are highly correlated with the original random variable. These auxiliary variables may come from surrogate models. Such a surrogate-based CV strategy is extended here to the multilevel Monte Carlo (MLMC) framework, which relies on a sequence of levels corresponding to numerical simulators with increasing accuracy and computational cost. MLMC combines output samples obtained across levels, into a telescopic sum of differences between MC estimators for successive fidelities. In this paper, we introduce three multilevel variance reduction strategies that rely on surrogate-based CV and MLMC. MLCV is presented as an extension of CV where the correction terms devised from surrogate models for simulators of different levels add up. MLMC-CV improves the MLMC estimator by using a CV based on a surrogate of the correction term at each level. Further variance reduction is achieved by using the surrogate-based CVs of all the levels in the MLMC-MLCV strategy. Alternative solutions that reduce the subset of surrogates used for the multilevel estimation are also introduced. The proposed methods are tested on a test case from the literature consisting of a spectral discretization of an uncertain 1D heat equation, where the statistic of interest is the expected value of the integrated temperature along the domain at a given time. The results are assessed in terms of the accuracy and computational cost of the multilevel estimators, depending on whether the construction of the surrogates, and the associated computational cost, precede the evaluation of the estimator. It was shown that when the lower fidelity outputs are strongly correlated with the high-fidelity outputs, a significant variance reduction is obtained when using surrogate models for the coarser levels only. It was also shown that taking advantage of pre-existing surrogate models proves to be an even more efficient strategy.

For more details on this work we refer to 26

7.7 Quadrature Rules in General Continuous Bayesian Networks : Discrete Inference without Discretization

Probabilistic inference in high-dimensional continuous or hybrid domains poses significant challenges, commonly addressed through discretization, sampling, or reliance on parametric assumptions. The drawbacks of these methods are well-known: inaccuracy, slow computa- tional speeds or overly constrained models. This paper introduces a novel general inference algorithm designed for Bayesian networks featuring both discrete and continuous variables. The algorithm avoids the discretization of continuous densities into histograms by employ- ing quadrature rules to compute continuous integrals and avoids the use of a parametric model by using orthogonal polynomials to represent the posterior density. Additionally, it preserves the computational efficiency of classical sum-product algorithms by using an auxiliary discrete Bayesian networks appropriately constructed to make continuous inference. Numerous experiments are conducted using either the conditional linear Gaussian model as a benchmark, or non-Gaussian models for greater generality. Our algorithm demonstrates significant improvements both in speed and accuracy when compared with existing methods

For more details on this work we refer to 29

7.8 Material Parameter Estimation for a Viscoelastic Stenosis Model Using a Variational Autoencoder Inverse Mapper

Coronary artery disease, a prevalent condition often leading to heart attacks, may cause abnormal wall shear stresses near stenosed regions generating high frequent acoustic shear waves. In a previous study, a viscoelastic agarose gel was used to model the human tissue and it was shown that two material parameters of the gel could be estimated with a high certainty using a classical inverse problem. Given the high computational cost of traditional methods, this paper explores machine learning (ML) alternatives, particularly a Variational Autoencoder Inverse Mapper (VAIM). VAIM, previously successful in nuclear physics, uses neural networks to approximate forward and backward mappings and learn posterior parameter distributions. This paper validates previous research by generating data around ground truth values, demonstrating VAIM’s ability to estimate two material parameters effectively. Further, it addresses realistic applications by training and testing on noisy data and generalizing findings across different intervals of signal damping.

For more details on this work we refer to 28

7.9 Abstracting hierarchical methods for accelerating matrix-vector products on heterogeneous machine clusters: A unified framework for Fast Multipole Methods, $\mathscr{H}$-Matrices, and beyond

The Fast Multipole Method (FMM) is a renowned algorithm for accelerating the computation of interactions in N-body simulations and is recognized as one of the most influential algorithms of the 21st century. While commonly depicted as a tree-based approach, the FMM mathematically represents a block matrix-vector product, where hierarchical extra-diagonal block operations are compressed analytically, echoing the literature on $\mathscr{H}$-matrices 46 where those are compressed algebraically. However, few attempts have been made to bridge the gap between FMM and $\mathscr{H}$ matrices (61, 63). The goal of the PhD aims to abstract and unify hierarchical methods, including the FMM, $\mathscr{H}$-matrices, and their flat counterparts (Block Low-Rank matrices 71 for instance), especially for computing fast matrix-vector products.

In a paper currently being drafted, we propose an abstraction of hierarchical methods that consists of four main components: (1) a partitioning scheme to decompose degrees of freedom and organize the matrix into a block structure, (2) an admissibility criterion to predict which blocks to compress and which to leave intact, (3) a method for compressing admissible blocks (analytical, algebraic, or arithmetic...), and (4) a strategy to manage bases. The objective is to develop a single algorithm that could accommodate all hierarchical methods and adapt to various physical problem sizes and target computer characteristics.

This work is part of Antoine Gicquel's PhD thesis and is carried out in the context of the Diwina ANR project.

7.10 Using the Fast Multipole Method to Accelerate Matrix-Vector Products

In electrical engineering, solving low-frequency Maxwell's equations is crucial for modeling devices with ferromagnetic materials and large air volumes, typically due to voids and gaps. The Magnetostatic Moment Method (MMM), based on volume integral equations, offers an efficient alternative to the Finite Element Method (FEM) in such cases. The MMM's advantage lies in not requiring the meshing of air regions, significantly reducing the number of unknowns. However, the MMM results in linear systems with dense matrices, leading to computational challenges in terms of memory and execution time for large problems. To address this issue, we consider a low-rank approximation of the matrix using the Fast Multipole Method (FMM). This hierarchical algorithm, which uses a tree-based domain partitioning, can reduce the complexity of matrix-vector product calculations from O(N2) to O(N). Our work focuses on adapting a black-box FMM variant, available in the C++ ScalFMM library, to accelerate matrix-vector products within the MMM framework. Additionally, we developed a parallel, shared memory-based version to further enhance computational efficiency. Our numerical results demonstrate the effectiveness of this enhanced FMM-based matrix-vector product in a simplified application modeling a low-frequency antenna.

For more details on this work we refer to 33

7.11 Optimizing multigrid efficiency using machine learning techniques

Our research explores the integration of machine learning into multigrid solvers, focusing on the similarities between UNet architectures and multigrid cycles. While traditional geometric multigrid methods rely on fixed stencils for smoothing and prolongation/restriction steps, these operations can be reinterpreted as trainable parameters within a neural network framework. During the project, we developed a flexible multigrid cycle implementation in PyTorch, where we replace matrix-vector multiplications with stencils by 2D convolutions. This approach enables us to train stencil values using gradient-based optimization techniques. The multigrid solver is thus effectively transformed into a hybrid learning-based solver. Our work investigates various optimization strategies to improve performance and generalization of the multigrid cycle, where we train one or more components at the same time. We aim to identify which parameters and methods have the greatest impact on efficiency, both in terms of computational cost and solution quality.

7.12 Comparison of multigrid and machine learning-based Poisson solvers

We present a comprehensive comparison of the multigrid method and the UNet architecture for solving Poisson’s equation. Those two methods show a lot of similarity and also have the very interesting characteristic that their solving time should scale linearly with the number of mesh nodes. Nevertheless, for Poisson’s equation, an analysis of the number of floating-point operations demonstrates that the multi-grid V-Cycle should be faster than the UNet. We have realized a practical comparison of the two methods solving time for different number of mesh nodes on the same computation nodes using GPU.

For more details on this work we refer to 27

7.13 Statistical machine learning techniques to predict the rank in $\mathscr{H}$-matrix computation

The efficient solution of large, dense linear systems arising from the Boundary Element Method (BEM) for integral equations on complex geometries is nowadays often addressed using Hierarchical matrix ($\mathscr{H}$-matrix) techniques. The main challenges are twofold: first, determining the hierarchical block low-rank structure of the matrix—i.e., identifying which blocks have low rank and can be advantageously stored as the product of rectangular matrices; second, estimating the actual ranks of these blocks. In this work, we explore supervised statistical machine learning techniques to tackle these challenges. More specifically, we train models based on decision trees (specifically, random forests or gradient-boosted trees) on synthetic datasets generated from simple geometries and validate their generalization capabilities on 3D aircraft meshes.

This work is part of Théo Briquet's PhD.

7.14 Convergence analysis of overlapping domain decomposition preconditioners for nonlinear problems

Numerical simulations of nonlinear partial differential equations often involve solving large nonlinear systems, for which Newton's method is widely employed due to its rapid convergence near the solution. However, its performance can deteriorate in the presence of strong nonlinearities or poor initial guesses. Nonlinear overlapping domain decomposition methods, such as RASPEN  55 and Substructured RASPEN (SRASPEN) 51, have shown to address these challenges effectively. While SRASPEN reduces the problem size by restricting computations to a substructure, it suffers from a loss of information outside the substructure, leading to additional inner subdomain iterations.

In this work, we analyze the convergence of RASPEN, demonstrating how domain decomposition improves the convergence rate of Newton's method by highlighting the impact of substructuring on the global domain error contraction. Furthermore, we propose an inexpensive adjustment to SRASPEN to mitigate the loss of global information, thereby reducing computational cost and improving overall efficiency. Numerical experiments show the computational performance of the improved SRASPEN, establishing it as a robust approach for solving large-scale nonlinear systems.

This work is part of Ettaouchi El Mehdi's PhD thesis and is carried out in collaboration with Nicolas Tardieu (EDF).

7.15 Low-rank tensor solver for magnetostatic problems for electric power applications

The development of electrical and electromechanical devices requires solving Maxwell's equations, which is challenging due to their complexity. Volumetric integral methods (VIM) are advantageous for low-frequency problems as they eliminate the need to mesh air regions. However, they result in dense matrices, leading to high computational costs. Compression techniques, such as fast multipole methods (FMM) and $\mathscr{H}$-Matrix, have mitigated these issues by reducing complexity.

This thesis introduces low-rank tensors, specifically Tensor-Train, to further compress systems and accelerate computations by transforming problems into a tensor framework without constructing full tensors. We focused on two VIM methods: the Magnetic Moment Method and the Scalar Potential Method, both of which were adapted to a tensor format. Additionally, we conducted comparisons of these tensor-based methods with $\mathscr{H}$H-Matrix and FMM approaches on simple test cases to evaluate their performance and efficiency.

To solve the compressed linear systems, two approaches were explored: solvers based on optimization techniques and classical iterative solvers, such as Krylov subspace methods. The Tensor-Train approach demonstrated better performance in terms of both compression and solver computation time, making it particularly efficient for large-scale problems. While the methods have been tested on simple problems to validate their effectiveness, future work will focus on applying them to more complex geometries to further evaluate their scalability and robustness.

This work is part of Amine Zekri's PhD thesis and is carried out in the context of the TensoVim ANR project.

7.16 Intra-node performance

As part of the EoCoE III project, this work aims to enable robust and high-performance solutions for large sparse linear systems on modern platforms characterized by increasing complexity and resource heterogeneity. The focus is on optimizing the parallelization of domain decomposition algorithms within the Composyx software framework, employing both direct and iterative methods to enhance scalability and accuracy. These algorithms rely on several state-of-the-art libraries, including BLAS/LAPACK for dense linear algebra operations, direct sparse solvers for exact subproblem resolution, and partitioners for efficient domain decomposition. Achieving seamless integration and optimal utilization of these libraries is critical for ensuring computational efficiency. Our current efforts target homogeneous multi-core architectures, aiming to optimize all algorithmic stages for maximal performance. For heterogeneous platforms, particularly CPU+GPU nodes, we propose a task-based approach that decomposes the computational workflow into fine-grained tasks. This strategy facilitates load balancing and efficient resource allocation, leveraging the complementary strengths of CPUs and GPUs. In this context, we are developing innovative techniques to express and exploit parallelism, enabling the algorithms to scale effectively on exascale systems. By addressing challenges related to increasing platform heterogeneity and algorithmic complexity, this work seeks to ensure that domain decomposition methods remain robust, scalable, and well-suited to the computational demands of large-scale simulations in the exascale era.

This work is conducted in collaboration with IRIT.

8.1 European initiatives

8.2 National initiatives

9.1 Promoting scientific activities

9.2 Teaching - Supervision - Juries

10.1 Major publications

• 1 articleE.Emmanuel Agullo, B.Bérenger Bramas, O.Olivier Coulaud, E.Eric Darve, M.Matthias Messner and T.Toru Takahashi. Task-Based FMM for Multicore Architectures.SIAM Journal on Scientific Computing3612014, 66-93HALDOI
• 2 articleE.Emmanuel Agullo, A.Alfredo Buttari, A.Abdou Guermouche, J.Julien Herrmann and A.Antoine Jego. Task-based parallel programming for scalable matrix product algorithms.ACM Transactions on Mathematical Software2023HAL
• 3 articleE.Emmanuel Agullo, L.Luc Giraud and L.Louis Poirel. Robust preconditioners via generalized eigenproblems for hybrid sparse linear solvers.SIAM Journal on Matrix Analysis and Applications4022019, 417–439HALDOI
• 4 miscE.Emily Bourne, P.Philippe Leleux, K.Katharina Kormann, C.Carola Kruse, V.Virginie Grandgirard, Y.Yaman Güçlü, M. J.Martin J Kühn, U.Ulrich Rüde, E.Eric Sonnendrücker and E.Edoardo Zoni. Solver comparison for Poisson-like equations on tokamak geometries.September 2022HAL
• 5 articleB.Bérenger Bramas, O.Olivier Coulaud and G.Guillaume Sylvand. Time-domain BEM for the wave equation on distributed-heterogeneous architectures: A blocking approach.Parallel Computing49July 2015, 66-82HALDOI
• 6 articleF.Fabien Casenave, A.Alexandre Ern and G.Guillaume Sylvand. Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain.Journal of Computational Physics257AJanuary 2014, 627-644HALDOI
• 7 articleS.Siegfried Cools, E. F.Emrullah Fatih Yetkin, E.Emmanuel Agullo, L.Luc Giraud and W.Wim Vanroose. Analyzing the Effect of Local Rounding Error Propagation on the Maximal Attainable Accuracy of the Pipelined Conjugate Gradient Method.SIAM Journal on Matrix Analysis and Applications391March 2018, 426 - 450HALDOI
• 8 articleV.Vincent Darrigrand, A.Andrei Dumitrasc, C.Carola Kruse and U.Ulrich Rüde. Inexact inner–outer Golub–Kahan bidiagonalization method: A relaxation strategy.Numerical Linear Algebra with ApplicationsDecember 2022HALDOI
• 9 articleD. A.Daniele Antonio Di Pietro, P.Pierre Matalon, P.Paul Mycek and U.Ulrich Rüde. High-order multigrid strategies for HHO discretizations of elliptic equations.Numerical Linear Algebra with ApplicationsJune 2022HALDOI
• 10 articleA.Alain Franc, P.Pierre Blanchard and O.Olivier Coulaud. Nonlinear mapping and distance geometry.Optimization Letters1422020, 453-467HALDOI
• 11 articleL.Luc Giraud, Y.-F.Yan-Fei Jing and Y.Yanfei Xiang. A block minimum residual norm subspace solver with partial convergence management for sequences of linear systems.SIAM Journal on Matrix Analysis and Applications4322022, 710-739HALDOI
• 12 miscY.Yongseok Jang, J.Jerome Bonelle, C.Carola Kruse, F.Frank Hülsemann and U.Ulrich Ruede. Fast Linear Solvers for Incompressible CFD Simulations with Compatible Discrete Operator Schemes.April 2023HAL
• 13 articleM.Marc Odunlami, V.Vincent Le Bris, D.Didier Bégué, I.Isabelle Baraille and O.Olivier Coulaud. A-VCI: A flexible method to efficiently compute vibrational spectra.Journal of Chemical Physics14621June 2017HALDOI

10.2 Publications of the year

10.3 Cited publications

• 36 articleE.E. Agullo, O.O. Aumage, B.B. Bramas, O.O. Coulaud and S.S. Pitoiset. Bridging the gap between openMP and task-based runtime systems for the fast multipole method.IEEE Transactions on Parallel and Distributed Systems28102017DOIback to text
• 37 articleE.Emmanuel Agullo, B.Bérenger Bramas, O.Olivier Coulaud, E.Eric Darve, M.Matthias Messner and T.Toru Takahashi. Task-Based FMM for Multicore Architectures.SIAM Journal on Scientific Computing3612014, 66-93HALDOIback to text
• 38 articleE.Emmanuel Agullo, B.Berenger Bramas, O.Olivier Coulaud, E.Eric Darve, M.Matthias Messner and T.Toru Takahashi. Task-based FMM for heterogeneous architectures.Concurrency and Computation: Practice and Experience289jun 2016, 2608--2629URL: http://doi.wiley.com/10.1002/cpe.3723DOIback to text
• 39 articleE.Emmanuel Agullo, S.Siegfried Cools, E.Emrullah Fatih-Yetkin, L.Luc Giraud, N.Nick Schenkels and W.Wim Vanroose. On soft errors in the conjugate gradient method: sensitivity and robust numerical detection.SIAM Journal on Scientific Computing426November 2020HALDOIback to text
• 40 articleE.Emmanuel Agullo, E.Eric Darve, L.Luc Giraud and Y.Yuval Harness. Low-Rank Factorizations in Data Sparse Hierarchical Algorithms for Preconditioning Symmetric Positive Definite Matrices.SIAM Journal on Matrix Analysis and Applications394October 2018, 1701-1725HALback to text
• 41 techreportE.Emmanuel Agullo, M.Marek Felšöci and G.Guillaume Sylvand. A comparison of selected solvers for coupled FEM/BEM linear systems arising from discretization of aeroacoustic problems: literate and reproducible environment.RT-0513Inria Bordeaux Sud-OuestJune 2021, 100HALback to text
• 42 articleE.Emmanuel Agullo, L.Luc Giraud and Y.-F.Y-F Jing. Block GMRES method with inexact breakdowns and deflated restarting.SIAM Journal on Matrix Analysis and Applications3542014, 1625--1651back to text
• 43 articleE.Emmanuel Agullo, L.Luc Giraud and L.Louis Poirel. Robust preconditioners via generalized eigenproblems for hybrid sparse linear solvers.SIAM Journal on Matrix Analysis and Applications4022019, 417--439HALDOIback to text
• 44 techreportP.Pierre Blanchard, O.Olivier Coulaud and E.Eric Darve. Fast hierarchical algorithms for generating Gaussian random fields.8811Inria Bordeaux Sud-OuestDecember 2015HALback to textback to text
• 45 phdthesisP.Pierre Blanchard. Fast hierarchical algorithms for the low-rank approximation of matrices, with applications to materials physics, geostatistics and data analysis.Bordeaux2017, URL: https://tel.archives-ouvertes.fr/tel-01534930back to text
• 46 techreportS.Steffen Börm, L.Lars Grasedyck and W.Wolfgang Hackbusch. Hierarchical Matrices.2003, 1--173back to textback to text
• 47 unpublishedJ.Jérémy Briant, P.Paul Mycek, M.Mayeul Destouches, O.Olivier Goux, S.Serge Gratton, S.Selime Gürol, E.Ehouarn Simon and A. T.Anthony T. Weaver. A filtered multilevel Monte Carlo method for estimating the expectation of discretized random fields.November 2023, working paper or preprintHALDOIback to text
• 48 articleA.Alfredo Buttari, J.Julien Langou, J.Jakub Kurzak and J.Jack Dongarra. Parallel tiled QR factorization for multicore architectures.Concurrency and Computation: Practice and Experience20132008, 1573--1590back to text
• 49 articleE.Erin Carson, N. J.Nicholas J. Higham and S.Srikara Pranesh. Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems.SIAM Journal on Scientific Computing426January 2020, A4063--A4083DOIback to text
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