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113 results on '"Descombes, Stéphane"'

1. Energy preserving methods for nonlinear Schr\'odinger equations

Author

Besse, Christophe, Descombes, Stephane, Dujardin, Guillaume, and Lacroix-Violet, Ingrid

Subjects
Mathematics - Numerical Analysis, Physics - Optics, Quantum Physics
Abstract

This paper is concerned with the numerical integration in time of nonlinear Schr\"odinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method of order 2 but is fully implicit and one may prefer a linearly implicit method like the relaxation method introduced in [10] for the cubic nonlinear Schr{\"o}dinger equation. This method is also an energy preserving method and numerical simulations have shown that its order is 2. In this paper we give a rigorous proof of the order of this relaxation method and propose a generalized version that allows to deal with general power law nonlinearites. Numerical simulations for different physical models show the efficiency of these methods.

Published
2018

4. An Explicit Hybridizable Discontinuous Galerkin Method for the 3D Time-Domain Maxwell Equations

Author

Nehmetallah, Georges, Lanteri, Stéphane, Descombes, Stéphane, Christophe, Alexandra, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Sherwin, Spencer J., editor, Moxey, David, editor, Peiró, Joaquim, editor, Vincent, Peter E., editor, and Schwab, Christoph, editor

Published
2020
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5. Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures

Author

Descombes, Stéphane, Duarte, Max, Dumont, Thierry, Guillet, Thomas, Louvet, Violaine, and Massot, Marc

Subjects
Computer Science - Numerical Analysis, Computer Science - Distributed, Parallel, and Cluster Computing, Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis
Abstract

A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational efficiency for large multidimensional computations on standard architectures such as powerful workstations. However, the data structure of the original implementation, based on trees of pointers, provides limited opportunities for efficiency enhancements, while posing serious challenges in terms of parallel programming and load balancing. The present contribution proposes a new implementation of the whole set of numerical methods including Radau5 and ROCK4, relying on a fully different data structure together with the use of a specific library, TBB, for shared-memory, task-based parallelism with work-stealing. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions on multi-core and many-core architectures, demonstrating high scalability.

Published
2015
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6. Analysis of operator splitting in the non-asymptotic regime for nonlinear reaction-diffusion equations. Application to the dynamics of premixed flames

Author

Descombes, Stéphane, Duarte, Max, Dumont, Thierry, Laurent, Frédérique, Louvet, Violaine, and Massot, Marc

Subjects
Mathematics - Numerical Analysis, Mathematics - Analysis of PDEs
Abstract

In this paper we mathematically characterize through a Lie formalism the local errors induced by operator splitting when solving nonlinear reaction-diffusion equations, especially in the non-asymptotic regime. The non-asymptotic regime is often attained in practice when the splitting time step is much larger than some of the scales associated with either source terms or the diffusion operator when large gradients are present. In a series of previous works a reduction of the asymptotic orders for a range of large splitting time steps related to very short time scales in the nonlinear source term has been studied, as well as that associated with large gradients but for linearized equations. This study provides a key theoretical step forward since it characterizes the numerical behavior of splitting errors within a more general nonlinear framework, for which new error estimates can be derived by coupling Lie formalism and regularizing effects of the heat equation. The validity of these theoretical results is then assessed in the framework of two numerical applications, a KPP-type reaction wave where the influence of stiffness on local error estimates can be thoroughly investigated; and a much more complex problem, related to premixed flame dynamics in the low Mach number regime with complex chemistry and detailed transport, for which the present theoretical study shows to provide relevant insights., Comment: SIAM Journal on Numerical Analysis (2014) 1-24

Published
2014
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7. Adaptive time splitting method for multi-scale evolutionary partial differential equations

Author

Descombes, Stéphane, Duarte, Max, Dumont, Thierry, Louvet, Violaine, and Massot, Marc

Subjects
Mathematics - Numerical Analysis, Physics - Computational Physics
Abstract

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady problems. The strategy considers a second order Strang method and another lower order embedded splitting scheme that takes into account potential loss of order due to the stiffness featured by time-space multi-scale phenomena. The scheme is then built upon a precise numerical analysis of the method and a complementary numerical procedure, conceived to overcome classical restrictions of adaptive time stepping schemes based on lower order embedded methods, whenever asymptotic estimates fail to predict the dynamics of the problem. The performance of the method in terms of control of integration errors is evaluated by numerical simulations of stiff propagating waves coming from nonlinear chemical dynamics models as well as highly multi-scale nanosecond repetitively pulsed gas discharges, which allow to illustrate the method capabilities to consistently describe a broad spectrum of time scales and different physical scenarios for consecutive discharge/post-discharge phases., Comment: Accepted to publication in Confluentes Mathematici. Dedication : Cet article est d\'edi\'e \`a la m\'emoire de Michelle Schatzman. Sp\'ecialiste des m\'ethodes de d\'ecomposition d'op\'erateur, sa grande clairvoyance scientifique lui a permis d'orienter plusieurs chercheurs d\'ebutants sur ce sujet \`a un moment o\`u il pouvait sembler achev\'e. Michelle aimait dire qu'il n'y a pas de fronti\`ere entre les branches des math\'ematiques et que seule une grande culture permet de naviguer dans cette for\^et et d'y trouver les bonnes techniques pour r\'esoudre un probl\`eme. Ce travail est un hommage; \`a la crois\'ee des math\'ematiques et de leurs applications effectives, il tente d'illustrer cette assertion. Michelle, ton dynamisme, ton humour et ton plaisir \`a parler math\'ematiques nous manquent

Published
2011
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8. A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

Author

Duarte, Max, Bonaventura, Zdenek, Massot, Marc, Bourdon, Anne, Descombes, Stéphane, and Dumont, Thierry

Subjects
Mathematics - Numerical Analysis, Physics - Computational Physics, Physics - Plasma Physics
Abstract

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods., Comment: Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS) for providing the basis of the multiresolution kernel of MR CHORUS, code developed for compressible Navier-Stokes equations (D\'eclaration d'Invention DI 03760-01). Accepted for publication; Journal of Computational Physics (2011) 1-28

Published
2011
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9. Operator Splitting Methods with Error Estimator and Adaptive Time-Stepping. Application to the Simulation of Combustion Phenomena

Author

Descombes, Stéphane, Duarte, Max, Massot, Marc, Chattot, Jean-Jacques, Series editor, Colella, Phillip, Series editor, Glowinski, Roland, Series editor, Joly, Patrick, Series editor, Meiron, D.I., Series editor, Pironneau, Olivier, Series editor, Quarteroni, Alfio, Series editor, Rappaz, Jacques, Series editor, Rosner, Robert, Series editor, Sagaut, P., Series editor, Seinfeld, John H., Series editor, Szepessy, Anders, Series editor, Wheeler, Mary F., Series editor, Hussaini, M. Yousuff, Series editor, Osher, Stanley J., editor, and Yin, Wotao, editor

Published
2016
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21. NiPTUNE: an automated pipeline for noninvasive prenatal testing in an accurate, integrative and flexible framework

Author

Duboc, Véronique, Pratella, David, Milanesio, Marco, Boudjarane, John, Descombes, Stéphane, Paquis-Flucklinger, Véronique, Bottini, Silvia, Hôpital Archet 2 [Nice] (CHU), Université Côte d'Azur (UCA), E-Patient : Images, données & mOdèles pour la médeciNe numériquE (EPIONE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Marseille medical genetics - Centre de génétique médicale de Marseille (MMG), Aix Marseille Université (AMU)-Institut National de la Santé et de la Recherche Médicale (INSERM), Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut de Recherche sur le Cancer et le Vieillissement (IRCAN), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015), Institut National de la Santé et de la Recherche Médicale (INSERM)-Aix Marseille Université (AMU), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), and Université Nice Sophia Antipolis (... - 2019) (UNS)

Subjects
bioinformatic pipeline, AcademicSubjects/SCI01060, Noninvasive Prenatal Testing, prenatal testing, Aneuploidy, benchmark, fetal aneuploidies prediction, fetal fraction, Pregnancy, Prenatal Diagnosis, Problem Solving Protocol, Humans, Female, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], Cell-Free Nucleic Acids, Retrospective Studies
Abstract

International audience; Abstract Noninvasive prenatal testing (NIPT) consists of determining fetal aneuploidies by quantifying copy number alteration from the sequencing of cell-free DNA (cfDNA) from maternal blood. Due to the presence of cfDNA of fetal origin in maternal blood, in silico approaches have been developed to accurately predict fetal aneuploidies. Although NIPT is becoming a new standard in prenatal screening of chromosomal abnormalities, there are no integrated pipelines available to allow rapid, accurate and standardized data analysis in any clinical setting. Several tools have been developed, however often optimized only for research purposes or requiring enormous amount of retrospective data, making hard their implementation in a clinical context. Furthermore, no guidelines have been provided on how to accomplish each step of the data analysis to achieve reliable results. Finally, there is no integrated pipeline to perform all steps of NIPT analysis. To address these needs, we tested several tools for performing NIPT data analysis. We provide extensive benchmark of tools performances but also guidelines for running them. We selected the best performing tools that we benchmarked and gathered them in a computational pipeline. NiPTUNE is an open source python package that includes methods for fetal fraction estimation, a novel method for accurate gender prediction, a principal component analysis based strategy for quality control and fetal aneuploidies prediction. NiPTUNE is constituted by seven modules allowing the user to run the entire pipeline or each module independently. Using two cohorts composed by 1439 samples with 31 confirmed aneuploidies, we demonstrated that NiPTUNE is a valuable resource for NIPT analysis.

Published
2021

24. A postprocessing technique for a discontinuous Galerkin discretization of time-dependent Maxwell's equations

Author

Nehmetallah, Georges, Chaumont-Frelet, Théophile, Descombes, Stéphane, Lanteri, Stéphane, Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée (ATLANTIS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Laboratoire Jean Alexandre Dieudonné (LJAD), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire Jean Alexandre Dieudonné (JAD)

Subjects
time-domain electromagnetics, Maxwell's equations, high-order method, FOS: Mathematics, discontinuous Galerkin method, Numerical Analysis (math.NA), Mathematics - Numerical Analysis, postprocessing, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics::Numerical Analysis
Abstract

We present a novel postprocessing technique for a discontinuous Galerkin (DG) discretization of time-dependent Maxwell's equations that we couple with an explicit Runge-Kutta time-marching scheme. The postprocessed electromagnetic field converges one order faster than the unprocessed solution in the H(curl)-norm. The proposed approach is local, in the sense that the enhanced solution is computed independently in each cell of the computational mesh, and at each time step of interest. As a result, it is inexpensive to compute, especially if the region of interest is localized, either in time or space. The key ideas behind this postprocessing technique stem from hybridizable discontinuous Galerkin (HDG) methods , which are equivalent to the analyzed DG scheme for specific choices of penalization parameters. We present several numerical experiments that highlight the superconvergence properties of the postprocessed electromagnetic field approximation.

Published
2020

30. NiPTUNE: an automated pipeline for noninvasive prenatal testing in an accurate, integrative and flexible framework.

Author

Duboc, Véronique, Pratella, David, Milanesio, Marco, Boudjarane, John, Descombes, Stéphane, Paquis-Flucklinger, Véronique, and Bottini, Silvia

Subjects
PRENATAL diagnosis, CELL-free DNA, PIPELINE inspection, PYTHON programming language, MEDICAL screening, PRINCIPAL components analysis, DATA analysis, QUALITY control
Abstract

Noninvasive prenatal testing (NIPT) consists of determining fetal aneuploidies by quantifying copy number alteration from the sequencing of cell-free DNA (cfDNA) from maternal blood. Due to the presence of cfDNA of fetal origin in maternal blood, in silico approaches have been developed to accurately predict fetal aneuploidies. Although NIPT is becoming a new standard in prenatal screening of chromosomal abnormalities, there are no integrated pipelines available to allow rapid, accurate and standardized data analysis in any clinical setting. Several tools have been developed, however often optimized only for research purposes or requiring enormous amount of retrospective data, making hard their implementation in a clinical context. Furthermore, no guidelines have been provided on how to accomplish each step of the data analysis to achieve reliable results. Finally, there is no integrated pipeline to perform all steps of NIPT analysis. To address these needs, we tested several tools for performing NIPT data analysis. We provide extensive benchmark of tools performances but also guidelines for running them. We selected the best performing tools that we benchmarked and gathered them in a computational pipeline. NiPTUNE is an open source python package that includes methods for fetal fraction estimation, a novel method for accurate gender prediction, a principal component analysis based strategy for quality control and fetal aneuploidies prediction. NiPTUNE is constituted by seven modules allowing the user to run the entire pipeline or each module independently. Using two cohorts composed by 1439 samples with 31 confirmed aneuploidies, we demonstrated that NiPTUNE is a valuable resource for NIPT analysis. [ABSTRACT FROM AUTHOR]

Published
2022
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31. An explicit hybridizable discontinuous Galerkin method for the 3D time-domain Maxwell equations

Author

Nehmetallah, Georges, Lanteri, Stephane, Descombes, Stéphane, Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)

Subjects
Maxwell's equations, time-domain, hybridized discontinuous Galerkin, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics::Numerical Analysis, discontinuous Galerkin
Abstract

We present an explicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. The method is fully explicit similarly to classical so-called DGTD (Discontinuous Galerkin Time-Domain) methods that have been extensively studied during the last 15 years for the simulation of time-domain electromagnetic wave propagation. This HDGTD (Hybridizable Discontinuous Galerkin Time-Domain) method is also high-order accurate in both space and time and can be seen as a generalization of the classical DGTD scheme based on upwind fluxes. In particular, it coincides with the latter scheme for a particular choice of the stabilization parameter introduced in the definition of numerical traces in the HDG framework. It posseses a superconvergence property that allows, by means of local postprocessing, to obtain new improved approximations of the variables at any time levels. In particular, the new approximation converge with order k + 1 instead of k in the H curl-norm for k ≥ 1 .The proposed method has been implemented for dealing with general 3D problems. We provide numerical results aiming at assessing its numerical convergence properties by considering first a model problem. Then, this HDGTD method is applied to a classical scattering problem.

Published
2019

32. Energy-preserving methods for nonlinear Schrödinger equations.

Author

Besse, Christophe, Descombes, Stéphane, Dujardin, Guillaume, and Lacroix-Violet, Ingrid

Subjects
NONLINEAR Schrodinger equation, SCHRODINGER equation, CRANK-nicolson method, NUMERICAL integration, COMPUTER simulation
Abstract

This paper is concerned with the numerical integration in time of nonlinear Schrödinger equations using different methods preserving the energy or a discrete analogue of it. The Crank–Nicolson method is a well-known method of order |$2$| but is fully implicit and one may prefer a linearly implicit method like the relaxation method introduced in Besse (1998, Analyse numérique des systèmes de Davey-Stewartson. Ph.D. Thesis , Université Bordeaux) for the cubic nonlinear Schrödinger equation. This method is also an energy-preserving method and numerical simulations have shown that its order is |$2$|⁠. In this paper we give a rigorous proof of the order of this relaxation method and propose a generalized version that allows one to deal with general power law nonlinearites. Numerical simulations for different physical models show the efficiency of these methods. [ABSTRACT FROM AUTHOR]

Published
2021
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33. A new family of exponential-based high order DGTD methods for modelling 3D transient multiscale electromagnetic problems

Author

Wang, Hao, Xu, Li, Li, Bin, Descombes, Stéphane, Lantéri, Stéphane, Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), University of Electronic Science and Technology of China (UESTC), Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), National Natural Science Foundation of China, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), University of Electronic Science and Technology of China [Chengdu] (UESTC), and Laboratoire Jean Alexandre Dieudonné (LJAD)

Subjects
time-domain Maxwell's equations, time integration, Discontinuous Galerkin Time-Domain method, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Multiscale problems, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

—The accurate and efficient simulation of 3D transient multiscale electromagnetic problems is extremely challenging for conventional numerical methods. Assuming a splitting of the underlying tetrahedral mesh in coarse and fine parts and using the Lawson procedure, we derive a family of exponential-based time integration methods for the time-domain Maxwell's equations discretized by a high order discontinuous Galerkin (DG) scheme formulated on locally refined unstructured meshes. These methods remove the stiffness on the time explicit integration of the semi-discrete operator associated to the fine part of the mesh, and allow for the use of high order time explicit scheme for the coarse part operator. They combine excellent stability properties with the ability to obtain very accurate solutions even for very large time step sizes. Here, the explicit time integration of the Lawson-transformed semi-discrete system relies on a Low-Storage Runge-Kutta (LSRK) scheme, leading to a combined Lawson-LSRK scheme. In addition, efficient techniques are also presented to further improve the efficiency of this exponential-based time integration. For the efficient calculation of matrix exponential, we employ the Krylov subspace method. Numerical experiments are presented to assess the stability, verify the accuracy and numerical convergence of the Lawson-LSRK scheme. They also demonstrate that the DGTD methods based on the proposed time integration scheme can be much faster than those based on classical fully explicit time stepping schemes, with the same accuracy and moderate memory usage increase on locally refined unstructured meshes, and are thus very promising for modelling three-dimensional multiscale electromagnetic problems.

Published
2017

38. Operator splitting methods with error estimator and adaptive time-stepping. Application to the simulation of combustion phenomena

Author

Descombes, Stéphane, Duarte, Max, Massot, Marc, Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Center for Computational Sciences and Engineering [LBNL Berkeley] (CCSE), Lawrence Berkeley National Laboratory [Berkeley] (LBNL), CD-adapco [London], Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, Fédération de Mathématiques de l'Ecole Centrale Paris (FR3487), Centre National de la Recherche Scientifique (CNRS)-Ecole Centrale Paris-CentraleSupélec, CentraleSupélec, Roland Glowinski, Stanley Osher, Wotao Yin, ANR-09-BLAN-0075,Séchelles,Simulation et comparaison avec l'expérience pour la validation de modèles de problèmes multi-échelles.(2009), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris Saclay (COmUE), and Ecole Centrale Paris-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; Operator splitting techniques were originally introduced with the main objective of saving computational costs. A multi-physics problem is thus split in subproblems of different nature with a significant reduction of the algorithmic complexity and computational requirements of the numerical solvers. Nevertheless, splitting errors are introduced in the numerical approximations due to the separate evolution of the split subproblems and can compromise a reliable reproduction of the coupled dynamics. In this chapter we present a numerical technique to estimate such splitting errors on the fly and dynamically adapt the splitting time steps according to a user-defined accuracy tolerance. The method applies to the numerical solution of time-dependent stiff PDEs, illustrated here by propagating laminar flames investigated in combustion applications.

Published
2015

39. The Lie–Trotter splitting method for nonlinear evolutionary problems involving critical parameters. An exact local error representation and application to nonlinear Schrödinger equations in the semi-classical regime

Author

Descombes, Stéphane, Thalhammer, Mechthild, Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Faculty of Mathematics, Computer Science and Physics, University of Innsbruck, and Descombes, Stéphane

Subjects
Convergence, Local error representation, Exponential operator splitting methods, Semi-classical regime, Time-dependent nonlinear Schrödinger equations, Nonlinear evolutionary problems, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In the present work, we investigate the error behaviour of exponential operator splitting methods for nonlinear evolutionary problems. In particular, our concern is to deduce an exact local error representation that is suitable in the presence of critical parameters. Essential tools in the theoretical analysis including time-dependent nonlinear Schrödinger equations in the semi-classical regime as well as parabolic initial-boundary value problems with high spatial gradients are an abstract formulation of differential equations on function spaces and the formal calculus of Lie-derivatives. We expose the general mechanism on the basis of the least technical example method, the first-order Lie–Trotter splitting

Published
2013

41. Méthodes numériques adaptatives pour la simulation de la dynamique de fronts de réaction multi-échelles en temps et en espace

Author

Massot, Marc, Duarte, Max, Descombes, Stéphane, Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, Ecole Centrale Paris, Fédération de Mathématiques de l'Ecole Centrale Paris (FR3487), Ecole Centrale Paris-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

National audience; Nous abordons le développement d'une nouvelle génération de méthodes numériques pour la résolution des EDP évolutives qui modélisent des phénomènes multi-échelles en temps et en espace issus de divers domaines applicatifs. La raideur associée à ce type de problème, que ce soit via le terme source chimique qui présente un large spectre d'échelles de temps caractéristiques ou encore via la présence de fort gradients très localisés associés aux fronts de réaction, implique en général de sévères difficultés numériques. En conséquence, il s'agit de développer des méthodes qui garantissent la précision des résultats en présence de forte raideur en s'appuyant sur des outils théoriques solides, tout en permettant une implémentation efficace. Même si nous étendons ces idées à des systèmes plus généraux par la suite, ce travail se focalise sur les systèmes de réaction-diffusion raides. La base de la stratégie numérique s'appuie sur une décomposition d'opérateur spécifique, dont le pas de temps est choisi de manière à respecter un niveau de précision donné par la physique du problème, et pour laquelle chaque sous-pas utilise un intégrateur temporel d'ordre élevé dédié. Ce schéma numérique est ensuite couplé à une approche de multirésolution spatiale adaptative permettant une représentation de la solution sur un maillage dynamique adapté. L'ensemble de cette stratégie a conduit au développement du code de simulation générique 1D/2D/3D académique MBARETE de manière à évaluer les développements théoriques et numériques dans le contexte de configurations pratiques raides issues de plusieurs domaines d'application. L'efficacité algorithmique de la méthode est démontrée par la simulation d'ondes de réaction raides dans le domaine de la dynamique chimique non-linéaire et dans celui de l'ingénierie biomédicale pour la simulation des accidents vasculaires cérébraux caractérisée par un terme source "chimique" complexe. Pour étendre l'approche à des applications plus complexes et plus fortement instationnaires, nous introduisons pour la première fois une technique de séparation d'opérateur avec pas de temps adaptatif qui permet d'atteindre une précision donnée garantie malgré la raideur des EDP.

Published
2012

42. Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations

Author

Descombes, Stéphane, Lanteri, Stéphane, Moya, Ludovic, Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), INRIA, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)

Subjects
locally implicit time integration methods, discontinuous Galerkin spatial discretization, time-domain Maxwell equations, ACM: G.: Mathematics of Computing, ACM: G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, locally refined meshes lead to severe stability constraints on explicit integration methods to numerically solve a time-dependent partial differential equation. If the ratio of fine to coarse elements is small, the time step size restriction can be overcome by blending an implicit and an explicit scheme where only the solution variables living at fine elements are treated implicitly. The counterpart of this approach is having to solve a linear system per time step. But due to the assumed small fine to coarse elements ratio, the overhead will also be small while the solution can be advanced in time with step sizes determined by the coarse elements. In this paper, we present two locally implicit time integration methods for solving the time-domain Maxwell equations spatially discretized with a DG method. Numerical experiments for two-dimensional problems illustrate the theory and the usefulness of the implicit-explicit approaches in presence of local refinements.; Les méthodes Galerkin discontinues sont particulièrement bien adaptées à la prise en compte de maillages localement raffinés, permettant de considérer avec précision des géométries complexes. Cependant, l'utilisation d'un schéma d'intégration en temps explicite conduit à une restriction importante du pas de temps admissible, ce dernier étant déterminé par les plus petits éléments du maillage considéré pour assurer la stabilité de la méthode. Si le rapport entre le nombre d'éléments fins et grossiers est petit, les restrictions de taille du pas de temps les plus contraignantes peuvent être évitées par l'utilisation d'un schéma d'intégration en temps localement implicite. La contre-partie est de devoir résoudre un système linéaire à chaque itération en temps. Cependant, le rapport entre le nombre d'éléments fins et grossiers étant petit alors le surcoût issu de la résolution du système linéaire sera faible, tandis que la solution peut être avancée avec un pas de temps déterminé par les éléments grossiers du maillage global. Dans ce papier, nous présentons deux méthodes d'intégration en temps localement implicites pour la résolution des équations de Maxwell en domaine temporel, discrétisées en espace par une méthode Galerkin discontinue. Des tests numériques sur des problèmes en dimension deux illustrent la théorie et l'utilité des approches implicite-explicite en présence de raffinements locaux.

Published
2012

43. Time-space adaptive numerical methods for the simulation of combustion fronts

Author

Duarte, Max, Massot, Marc, Descombes, Stéphane, Tenaud, Christian, Candel, Sebastien, Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, Center for Turbulence Research [Stanford] (CTR), Stanford University, Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université - UFR d'Ingénierie (UFR 919), Sorbonne Université (SU)-Sorbonne Université (SU)-Université Paris-Saclay-Université Paris-Sud - Paris 11 (UP11), and The authors wish to thank Parviz Moin and the Center for Turbulence Research at Stanford University for their hospitality and financial support. Support from the RTRA DIGITEO (Project MUSE, PI M. Massot) and Ecole Centrale Paris fellowship for M. Duarte are gratefully acknowledged. This research was supported by a fundamental project grant from ANR (French National Research Agency - ANR Blancs): Séchelles} (project leader S. Descombes). The support of a Ph.D. grant from Mathematics (INSMI) and Engineering (INSIS) Institutes of CNRS is gratefully acknowledged ad well as the the support by INCA project (National Initiative for Advanced Combustion - CNRS - ONERA - SAFRAN).

Subjects
adaptive multiresolution, diffusion flames, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, ignition, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Physics::Chemical Physics, Adaptive operator splitting, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], combustion, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
Abstract

http://www.stanford.edu/group/ctr/ResBriefs/2011/; International audience; In this work we are concerned with the the numerical simulation of flames issued from combustion applications with a time-space adaptive technique. This study is carried out in a classical context of laminar flames interacting with vortex structures including self-ignition processes of reactive mixtures. Hydrodynamics are decoupled from transport equations by adopting a standard thermo-diffusive approach. In this context and for the considered application, adaptive space meshing is advantageous because of the presence of localized fronts, whereas the important transient phases owing to the imposed velocity fields, as well as sudden physical variations given by the ignition of the mixture, require an adequate time adaptation in order to efficiently describe these phenomena. The coupling of an adaptive splitting technique with adaptive multiresolution in space allows a very efficient approach and leads to detailed numerical simulations in 2D and 3D with standard computer ressources.

Published
2012

44. New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke

Author

Duarte, Max, Massot, Marc, Descombes, Stéphane, Tenaud, Christian, Dumont, Thierry, Louvet, Violaine, Laurent, Frédérique, Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université - UFR d'Ingénierie (UFR 919), Sorbonne Université (SU)-Sorbonne Université (SU)-Université Paris-Saclay-Université Paris-Sud - Paris 11 (UP11), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Numerical Medicine (NUMED), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Projet RTRA DIGITEO MUSE (PI - M. Massot), E. Cancès, V. Louvet, M. Massot, PEPS Maths-ST2I project MIPAC, CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris Saclay (COmUE), Université Nice Sophia Antipolis (1965 - 2019) (UNS), Université Paris-Sud - Paris 11 (UP11)-Sorbonne Université - UFR d'Ingénierie (UFR 919), Sorbonne Université (SU)-Sorbonne Université (SU)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université Paris Saclay (COmUE), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), and École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes

Subjects
Adaptive multiresolution, Parallel computing, Ischemic stroke, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Operator splitting, Reaction-diffusion, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts, spatially very localized. In this paper, we introduce a new resolution strategy based on time operator splitting and space adaptive multiresolution in the context of very localized and stiff reaction fronts. Based on recent theoretical studies of numerical analysis, such a strategy leads to a splitting time step which is not restricted neither by the fastest scales in the source term nor by restrictive diffusive step stability limits, but only by the physics of the phenomenon. We aim thus at solving accurately complete models including all time and space scales of the phenomenon, considering large simulation domains with conventional computing resources. The efficiency of the method is evaluated through 2D and 3D numerical simulations of a human ischemic stroke model, conducted on a simplified brain geometry, for which a simple parallelization strategy for shared memory architectures was implemented, in order to reduce computing costs related to "detailed chemistry" features of the model.

Published
2011

45. Numerical simulation of a stroke: numerical problems and methodology

Author

Descombes, Stéphane, Dumont, Thierry, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Dumont, Thierry, École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SDV.SP.PHARMA] Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, Quantitative Biology::Tissues and Organs, [SDV.SP.PHARMA]Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

The numerical simulation of an ischemic stroke is a challenging problem: a complicated geometry, and a very stiff large system of reaction-diffusion equations. This paper, intended for mathematicians as well as for biologist, gives a survey and an introduction to the numerical methods used and some results.

Published
2007

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