Search

Your search keyword '"Tromeur-Dervout, Damien"' showing total 150 results
Start Over Author "Tromeur-Dervout, Damien"

Refine your results

more »

more »

more »
150 results on '"Tromeur-Dervout, Damien"'

1. Co-Simulation Domain Decomposition Algorithm for Hybrid EMT-Dynamic Phasor Modeling

Author

Shourick, Hélèna, Tromeur-Dervout, Damien, Chédot, Laurent, Angrisani, Leopoldo, Series Editor, Arteaga, Marco, Series Editor, Chakraborty, Samarjit, Series Editor, Chen, Jiming, Series Editor, Chen, Shanben, Series Editor, Chen, Tan Kay, Series Editor, Dillmann, Rüdiger, Series Editor, Duan, Haibin, Series Editor, Ferrari, Gianluigi, Series Editor, Ferre, Manuel, Series Editor, Jabbari, Faryar, Series Editor, Jia, Limin, Series Editor, Kacprzyk, Janusz, Series Editor, Khamis, Alaa, Series Editor, Kroeger, Torsten, Series Editor, Li, Yong, Series Editor, Liang, Qilian, Series Editor, Martín, Ferran, Series Editor, Ming, Tan Cher, Series Editor, Minker, Wolfgang, Series Editor, Misra, Pradeep, Series Editor, Mukhopadhyay, Subhas, Series Editor, Ning, Cun-Zheng, Series Editor, Nishida, Toyoaki, Series Editor, Oneto, Luca, Series Editor, Panigrahi, Bijaya Ketan, Series Editor, Pascucci, Federica, Series Editor, Qin, Yong, Series Editor, Seng, Gan Woon, Series Editor, Speidel, Joachim, Series Editor, Veiga, Germano, Series Editor, Wu, Haitao, Series Editor, Zamboni, Walter, Series Editor, Tan, Kay Chen, Series Editor, Pierfederici, Serge, editor, and Martin, Jean-Philippe, editor

Published
2024
Full Text
View/download PDF

2. Accelerated Convergence of the Pipelined Dynamic Iteration Method for RLC Circuits

Author

Shourick, Hélèna, Tromeur-Dervout, Damien, Chédot, Laurent, 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, Dostál, Zdeněk, editor, Kozubek, Tomáš, editor, Klawonn, Axel, editor, Langer, Ulrich, editor, Pavarino, Luca F., editor, Šístek, Jakub, editor, and Widlund, Olof B., editor

Published
2024
Full Text
View/download PDF

3. Co-simulation domain decomposition algorithm for hybrid EMT-Dynamic Phasor modeling

Author

Shourick, Héléna, Tromeur-Dervout, Damien, and Chédot, Laurent

Subjects
Mathematics - Numerical Analysis, 65, 65B05, 65L80, 65M55, 68U20
Abstract

An iterative coupling algorithm based on restricted additive Schwarz domain decomposition is investigated to co-simulate electrical circuits with hybrid electromagnetic (EMT) and transient stability (TS) modeled using dynamic phasors. This co-simulation algorithm does not introduce any delay between the data exchanged at the co-simulation step. The pure linear convergence property of the iterative method allows it to be accelerated towards the true solution by a non-intrusive Aitken's acceleration of the convergence post-processing, even if the domain decomposition interface conditions make the iterative method divergent. This provides a method less sensitive to the splitting. Numerical tests on a linear RLC circuit combining EMT and TS modeling are provided., Comment: 30 pages, 18 figures, 2 tables

Published
2022

4. COSTARICA estimator for rollback-less systems handling in iterative co-simulation algorithms

Author

Eguillon, Yohan, Lacabanne, Bruno, and Tromeur-Dervout, Damien

Subjects
Electrical Engineering and Systems Science - Systems and Control, Computer Science - Computational Engineering, Finance, and Science, Mathematics - Dynamical Systems, Mathematics - Numerical Analysis, 65, 65L05, 68U20
Abstract

Co-simulation is widely used in the industry due to the emergence of modular dynamical models made up of interconnected, black-boxed systems. Several co-simulation algorithms have been developed, each with different properties and different levels of accuracy and robustness. Among them, the most accurate and reliable ones are the iterative ones, although they have a main drawback in common: the involved systems are required to be capable of rollback. The latter denotes the ability of a system to integrate over a co-simulation time step that has already been simulated. Non-rollback-capable system can only go forward in time and every integrated step is definitive. In practice, the industrial modelling and simulation platforms rarely produce rollback-capable systems. This paper proposes a solution that slightly changes the co-simulation methodology and that enables to use iterative co-simulation methods on a modular model which contains non-rollback-capable systems in case the latter represent ordinary differential equations. The idea is to replace such a system by a simplified version, which is used to estimate the results of the integrations instead of integrating the real system. Once the co-simulation method's surrogate iterations on these estimators predict the convergence on the co-simulation step, the non-rollback-capable systems genuinely integrate the step using the estimated solution on the other systems before moving forward, transforming the iterative co-simulation method into a non-iterative one.

Published
2022

5. MISSILES: an Efficient Resolution of the Co-simulation Coupling Constraint on Nearly Linear Differential Systems through a Global Linear Formulation

Author

Eguillon, Yohan, Lacabanne, Bruno, and Tromeur-Dervout, Damien

Subjects
Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, Computer Science - Performance, 65, 65L05, 68U20
Abstract

In a co-simulation context, interconnected systems of differential equations are solved separately but they regularly communicate data to one another during these resolutions. Iterative co-simulation methods have been developed in order to enhance both stability and accuracy. Such methods imply that the systems must integrate one or more times per co-simulation step (the interval between two consecutive communications) in order to find the best satisfying interface values for exchanged data (according to a given coupling constraint). This requires that every system involved in the modular model is capable of rollback: the ability to re-integrate a time interval that has already been integrated with different input commands. In a paper previously introduced by Eguillon et al. in 2022, the COSTARICA process is presented and consists in replacing the non-rollback-capable systems by an estimator on the non-last integrations of the iterative process. The MISSILES algorithm, introduced in this paper, consists in applying the COSTARICA process on every system of a modular model simulated with the IFOSMONDI-JFM iterative co-simulation method (introduced by Eguillon et al. in 2021). Indeed, in this case, the iterative part on the estimators of each system can be avoided as the global resolution on a co-simulation step can be written as a single global linear system to solve. Consequently, MISSILES is a non-iterative method that leads to the same solution than the IFOSMONDI-JFM iterative co-simulation method applied to systems using the COSTARICA process to emulate the rollback.

Published
2022

6. Accelerating the convergence of Dynamic Iteration method with Restricted Additive Schwarz splitting for the solution of RLC circuits

Author

Shourick, Helena, Tromeur-Dervout, Damien, and Chedot, Laurent

Subjects
Mathematics - Numerical Analysis, 65, 65B05, 65L80, 65M55, 68U20
Abstract

The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear convergence or divergence of the method with respect to the linear operator belonging to the restricted additive Schwarz interface. It allows us to accelerate it toward the true solution with the Aitken's technique for accelerating convergence. This provides a dynamic iteration method less sensitive to the splitting. Numerical examples with convergent and divergent splitting show the efficiency of the proposed approach. We also test it on a linear RLC circuit combining different types of circuit modeling (Transient Stability model and Electro-Magnetic Transient model) with overlapping partitions. Finally, some results for a weakly nonlinear differential algebraic equations system are also provided., Comment: 16 pages, 7 figures, 1 table

Published
2022

7. Aitken-Schwarz heterogeneous Domain Decomposition for EMT-TS Simulation

Author

Schourick, Héléna, Tromeur-Dervout, Damien, and Chedot, Laurent

Subjects
Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, 65B05, 65L80, 65F10, G.1.7, I.6.5
Abstract

In this paper, a Schwarz heterogeneous domain decomposition method (DDM) is used to co-simulate an RLC electrical circuit where a part of the domain is modeled with Electro-Magnetic Transients (EMT) modeling and the other part with dynamic phasor (TS) modeling. Domain partitioning is not based on cutting at transmission lines which introduces a physical delay on the dynamics of the solution, as is usually done, but only on connectivity considerations. We show the convergence property of the homogeneous DDM EMT-EMT and TS-TS and of the heterogeneous DDM TS-EMT, with and without overlap and we use the pure linear divergence/convergence of the method to accelerate it toward the searched solution with the Aitken's acceleration of the convergence technique., Comment: 8 pages, 4 Figures, 1 Table, conference

Published
2021

8. F3ORNITS: A Flexible Variable Step Size Non-Iterative Co-simulation Method handling Subsystems with Hybrid Advanced Capabilities

Author

Eguillon, Yohan, Lacabanne, Bruno, and Tromeur-Dervout, Damien

Subjects
Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, Computer Science - Performance
Abstract

This paper introduces the F3ORNITS non-iterative co-simulation algorithm in which F3 stands for the 3 flexible aspects of the method: flexible polynomial order representation of coupling variables, flexible time-stepper applying variable co-simulation step size rules on subsystems allowing it and flexible scheduler orchestrating the meeting times among the subsystems and capable of asynchronousness when subsystems constraints requires it. The motivation of the F3ORNITS method is to accept any kind of co-simulation model, including any kind of subsystem, regardless on their available capabilities. Indeed, one the major problems in industry is that the subsystems usually have constraints or lack of advanced capabilities making it impossible to implement most of the advanced co-simulation algorithms on them. The method makes it possible to preserve the dynamics of the coupling constraints when necessary as well as to avoid breaking C1 smoothness at communication times, and also to adapt the co-simulation step size in a way that is robust both to zero-crossing variables (contrary to classical relative error-based criteria) and to jumps. Two test cases are presented to illustrate the robustness of the F3ORNITS method as well as its higher accuracy than the non-iterative Jacobi coupling algorithm (the most commonly used method in industry) for a smaller number of co-simulation steps.

Published
2021

9. IFOSMONDI Co-simulation Algorithm with Jacobian-Free Methods in PETSc

Author

Eguillon, Yohan, Lacabanne, Bruno, and Tromeur-Dervout, Damien

Subjects
Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, Computer Science - Performance
Abstract

IFOSMONDI iterative algorithm for implicit co-simulation of coupled physical systems (introduced by the authors in july 2019 during the Simultech conference, p.176-186) enables us to solve the nonlinear coupling function while keeping the smoothness of interfaces without introducing a delay. Moreover, it automatically adapts the size of the steps between data exchanges among the systems according to the difficulty of the solving of the coupling constraint. The latter was solved by a fixed-point algorithm in the original implementation whereas this paper introduces the JFM version (standing for Jacobian-Free Methods). Most implementations of Newton-like methods require a jacobian matrix which can be difficult to compute in the co-simulation context, except in the case where the interfaces are represented by a Zero-Order-Hold (ZOH). As far as IFOSMONDI coupling algorithm uses Hermite interpolation for smoothness enhancement (up to Third-Order-Hold), we propose hereafter a new formulation of the non-linear coupling function including both the values and the time-derivatives of the coupling variables. This formulation is well designed for solving the coupling through jacobian-free Newton type methods. Consequently, successive function evaluations consist in multiple simulations of the systems on a co-simulation time step using rollback. The orchestrator-workers structure of the algorithm enables us to combine the PETSc framework on the orchestrator side for the non-linear Newton-type solvers with the parallel integrations of the systems on the workers side thanks to MPI processes. Different nonlinear methods will be compared to one another and to the original fixed-point implementation on a newly proposed 2-systems academic test-case (mass-spring-damper type) with direct feedthrough on both sides.

Published
2021

13. Preconditioning of the Reduced System Associated with the Restricted Additive Schwarz Method

Author

Pacull, François, Tromeur-Dervout, Damien, 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, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
Full Text
View/download PDF

14. Partially Updated Restricted Additive Schwarz Preconditioner

Author

Berenguer, Laurent, Tromeur-Dervout, Damien, 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, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
Full Text
View/download PDF

15. Electromagnetic Transient Analysis of Transmission Line Based on Rational Krylov Approximation

Author

Tromeur DERVOUT, Damien, Mouhaidali, Amjad, Tromeur-Dervout, Damien, Chadebec, Olivier, Guichon, Jean-Michel, Silvant, Sebastien, 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), SuperGrid Institute SAS, Laboratoire de Génie Electrique de Grenoble (G2ELab ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)

Subjects
Admittance, Computer science, [SPI.NRJ]Engineering Sciences [physics]/Electric power, 020208 electrical & electronic engineering, Line model, Energy Engineering and Power Technology, Approximation algorithm, 020302 automobile design & engineering, 02 engineering and technology, Transmission system, transmission line model, Transient analysis, rational krylov approximation, Electric power transmission, 0203 mechanical engineering, Transmission line, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Convergence (routing), Electromagnetic transient, 0202 electrical engineering, electronic engineering, information engineering, frequency depen- dency, Applied mathematics, passivity, Vector fitting, Electrical and Electronic Engineering
Abstract

International audience; This paper shows a comparison between Vector fitting and rational Krylov fitting techniques for the determination of rational models concerning the fitting accuracy, the computational performances and the model order. Primarily, the mathematics behind the second technique are presented. It should be noted that rational Krylov fitting have never been used in transmission line modeling. A new procedure is proposed to use rational Krylov fitting instead of vector fitting in the universal line model (ULM). Furthermore, it is demonstrated that this procedure has several advantages over the traditional one. Two illustrative examples involving a transmission system are presented for validation of the new procedure.

Published
2021

18. Low-Rank Update of the Restricted Additive Schwarz Preconditioner for Nonlinear Systems

Author

Berenguer, Laurent, Tromeur-Dervout, Damien, 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, Erhel, Jocelyne, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Pichot, Géraldine, editor, Sassi, Taoufik, editor, and Widlund, Olof, editor

Published
2014
Full Text
View/download PDF

21. Adaptive Parareal for Systems of ODEs

Author

Guibert, David, Tromeur-Dervout, Damien, Barth, Timothy J., editor, Griebel, Michael, editor, Keyes, David E., editor, Nieminen, Risto M., editor, Roose, Dirk, editor, Schlick, Tamar, editor, and Widlund, Olof B., editor

Published
2007
Full Text
View/download PDF

22. Non-Overlapping DDMs to Solve Flow in Heterogeneous Porous Media

Author

Calugaru, Dan-Gabriel, Tromeur-Dervout, Damien, Barth, Timothy J., editor, Griebel, Michael, editor, Keyes, David E., editor, Nieminen, Risto M., editor, Roose, Dirk, editor, Schlick, Tamar, editor, Kornhuber, Ralf, editor, Hoppe, Ronald, editor, Périaux, Jacques, editor, Pironneau, Olivier, editor, Widlund, Olof, editor, and Xu, Jinchao, editor

Published
2005
Full Text
View/download PDF

25. Acceleration of the convergence of the Asynchronous RAS method

Author

Tromeur-Dervout, Damien, Tromeur-Dervout, Damien, 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), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Aitken acceleration of the convergence, asynchronous Schwarz, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

This paper focuses on the Aitken's acceleration of the convergence of the asynchronous Restricted Additive Schwarz (RAS) iterates for which transmission conditions on some artificial interfaces generated by the domain decomposition may not have not been updated for some iterates. We show that despite the error operator depends of the iterate, the low-rank approximation of this operator using singular value decomposition of the iterated interface solutions allows to still accelerate. We develop a modeling of the asynchronous RAS allowing to set the level of asynchronism and show how it deteriorates its convergence and its convergence's acceleration. Finaly, some regularization techniques on the iterated interface solutions allow to enhance the acceleration of the convergence .

Published
2020

26. Proceedings of the 32nd International conference on Parallel Computational Fluid Dynamics

Author

Mesri, Youssef, Tromeur-Dervout, Damien, MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL), Centre de Mise en Forme des Matériaux (CEMEF), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021

30. TIME DISCRETIZATION STRATEGIES FOR A 3D LID-DRIVEN CAVITY BENCHMARK WITH PETSc

Author

Tromeur-Dervout, Damien, Tromeur-Dervout, Damien, Modélisation mathématique, calcul scientifique (MMCS), 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)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics::Fluid Dynamics, Navier-Stokes system, [INFO.INFO-CE]Computer Science [cs]/Computational Engineering, Finance, and Science [cs.CE], lid-driven cavity problem, Navier-Stokes, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [INFO.INFO-CE] Computer Science [cs]/Computational Engineering, Finance, and Science [cs.CE], [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], velocity-vorticity formulation, High performance computing, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], ComputingMethodologies_COMPUTERGRAPHICS
Abstract

We present parallel implementations in PETSc of three time discretization strategies to solve the 3D incompressible Navier-Stokes equations in velocity-vorticity formulation applied to the lid-driven cavity with aspect ratio 3:1 with second order finite differences discretization in space. Different features of the PETSC software are investigated allowing fast prototyping of parallel numerical methods adapted to the proposed strategies. Comparisons on parallel efficiency, numerical accuracy, and flow behavior are given

Published
2018

31. Electromagnetic Transient Analysis of Transmission Line Based on Rational Krylov Approximation.

Author

Mouhaidali, Amjad, Tromeur-Dervout, Damien, Chadebec, Olivier, Guichon, Jean-Michel, and Silvant, Sebastien

Subjects
*ELECTRIC transients, *ELECTRIC lines, *KRYLOV subspace, *TRANSIENT analysis, *TRANSMISSION line matrix methods
Abstract

This paper shows a comparison between Vector fitting and rational Krylov fitting techniques for the determination of rational models concerning the fitting accuracy, the computational performances and the model order. Primarily, the mathematics behind the second technique are presented. It should be noted that rational Krylov fitting have never been used in transmission line modeling. A new procedure is proposed to use rational Krylov fitting instead of vector fitting in the universal line model (ULM). Furthermore, it is demonstrated that this procedure has several advantages over the traditional one. Two illustrative examples involving a transmission system are presented for validation of the new procedure. [ABSTRACT FROM AUTHOR]

Published
2021
Full Text
View/download PDF

33. SPARSE AITKEN-SCHWARZ WITH APPLICATION TO DARCY FLOW

Author

Berenguer, Laurent, Tromeur-Dervout, Damien, 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), ANR, and Tromeur-Dervout, Damien

Subjects
Mathematics::Complex Variables, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Restricted Additive Schwarz, Domain Decomposition Methods, [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Darcy flow, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], GeneralLiterature_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], acceleration of convergence, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
Abstract

This paper focuses on the acceleration of the Schwarz method by the Aitken’s acceleration of the convergence technique by considering the special structure of the Schwarz’s error operator between two consecutive iterates on the domain decomposition’s interfaces. The new proposed method, called Sparse Aitken-Schwarz method, builds a low-rank space for each subdomain to approximate the true solution on its interfaces instead of building a low-rank space associated to the gathered subdomains’ interfaces solution as the Aitken-Schwarz technique does. Weshow that the resulting method is better than the full GMRES method applied to the global interface problem as the low-rank space generated is a space whose dimension is larger than the size of Krylov space for the same number of local solving. The Sparse Aitken-Schwarz has better robustness to noise than the AitkenSchwarz. Weak and strong scaling results on a two-level parallel implementation show the improvements of the Sparse Aitken-Schwarz over the Aitken-Schwarz on a 3D Darcy flow application with randomly distributed permeability fields with high contrast values (Berenguer & Al, Aitken’s acceleration of the Schwarz process using singular value decomposition for heterogeneous 3D groundwater flowproblems, Computers & Fluids 80:320-326, 2013)

Published
2017

41. Parallel Preconditioners for 3D Global Reactive Transport

Author

Pacull, François, Sabit, Souhila, Erhel, Jocelyne, Tromeur-Dervout, Damien, Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), 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)-École Centrale de Lyon (ECL), 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), ANR-12-MONU-0012,H2MNO4,Hydrogéologie Hétérogène avec un Modèle Numérique Original, Optimisé et Orienté Objets(2012), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan [Villeurbanne] (ICJ), 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)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Erhel, Jocelyne, and Modèles Numériques - Hydrogéologie Hétérogène avec un Modèle Numérique Original, Optimisé et Orienté Objets - - H2MNO42012 - ANR-12-MONU-0012 - MN - VALID

Subjects
[SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [SDU.STU.GP] Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience

Published
2014

42. Nonlinear Transmission Conditions for Schwarz and Dual Schur Complement Time Domain Decomposition

Author

Linel, Patrice, Tromeur-Dervout, Damien, Computational Biomedicine Laboratory [Rochester], Rochester Institute of Technology, 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-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), B.H.V. Topping, P. Iványi, and ANR-12-MONU-0012,H2MNO4,Hydrogéologie Hétérogène avec un Modèle Numérique Original, Optimisé et Orienté Objets(2012)

Subjects
[INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In this paper, we propose a right transmission condition for the time decomposition that consists to transform the initial boundary value problem into a time boundary values problem. This allows us to use the classical multiplicative Schwarz algorithm using non-overlapping time slices. It also avoids the symmetrizing of the time interval needed to set the unknown value of the solution at the end time boundary of the last time slice. We show that, for nonlinear scalar problems, we must imposed some invariant of the problem as transmission conditions between time slices. We derive a Robin transmission condition in order to break the sequentiality of the propagating of the exact solution from the first time slice to the time slices that follow. We show the purely linear behaviour of this multiplicative Schwarz and its extrapolation to the right transmission conditions using Aitken's technique to accelerate convergence. Then a dual Schur complement technique is used on the nonlinear problem. We derive a method where the nonlinear transmission conditions are used to solve on each time slice while imposing the constraint of the solution continuity between time slices.

Published
2013

43. Acceleration of Convergence for Domain Decomposition Methods

Author

Berenguer, Laurent, Dufaud, Thomas, Tromeur-Dervout, Damien, 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), Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Topping, B.H.V. and Iványi, P., 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), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; The Schwarz domain decomposition method [1] is a very attractive numerical method for parallel computing as it needs only to update the boundary conditions on the artificial interfaces generated by domain decomposition. Thus only local communications between the neighbouring sub-domains are required. Nevertheless, the main drawback of this method is its slow rate of convergence which depends of the partial differential problem, the geometry of the sub-domains, and the size of the overlap when overlap is present. The idea of using Aitken acceleration [2] on the classical additive Schwarz DD method was introduced in [3]. These authors have called the corresponding method the Aitken-Schwarz (AS) method. This review paper is on the Aitken's acceleration of the convergence technique applied to the Schwarz domain decomposition method. It gives the two salient features of the methodology: first the pure linear convergence of the Schwarz domain decomposition method when it applies to a linear system of equations. Second, the building of an approximation space in order to represent the Schwarz iterate solution at the artificial interfaces generated by the domain decomposition. Some properties such as the decrease in absolute value of the solution's coefficients in the approximation space are searched in order to approximate the error operator and to apply the acceleration on a reduced space for saving computing.In [4] the author extends the methodology with an Aitken acceleration based on the singular value decomposition of the solution at the artificial boundary. Then this method becomes totally mesh non dependant, on some a priori criterion based on the singular values decreasing and gives a tool to select the singular vectors involved in the Aitken operator approximation. This allows three-dimensional computation on the linear Darcy equation to be achieved where the permeability field follows a random log normal distribution law [5].

Published
2013

44. Proper Orthogonal Decomposition in Decoupling Dynamical Systems

Author

Pham, Duc Toan, Tromeur-Dervout, Damien, 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), P. Iványi, B.H.V. Topping, and ANR-06-TLOG-0026,PARADE,Algorithmes Numériques/Symboliques Parallèles de Résolution de Systèmes d'Equations Algébro-Differentielles(2006)

Subjects
[INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; POD is well known for model reduction for different applications. It uses snapshots of the solution at previous time steps to generate a low dimensional approximation space for the solution. Here we focus on the potential of this method in order to decouple a dynamical system into dynamical subsystems split on a multiprocessors architecture. Each processor is in charge of a subsystem in a non-reduced form while it keeps a representation of the other subsystems managed by the other processors under a reduced form. The analysis of the behavior of the error on the decoupling of the dynamical system using the POD, allows us to define a mathematical criterion for updating the basis of the reduced model. Moreover, we enhance a technique to update the POD basis on the fly in order to retrieve most part of dynamics of the solution on the simulation's time interval. Some parallelism results on nonlinear large dynamical systems show the efficiency of wall clock times for the method.

Published
2011

45. Parallel Computational Fluid Dynamics 2008 Lecture Notes in Computational Science and Engineering

Author

Tromeur-Dervout, Damien, Brenner, Gunther, Emerson, David, Erhel, Jocelyne, 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), Institut für Technische Mechanik [Clausthal], Clausthal University of Technology (TU Clausthal), Computational Science and Engineering Department [Daresbury] (STFC), Science & Technologie Facilities Council, Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), 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), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)

Subjects
computer science, [SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph], numerical analysis, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, computational fluid dynamics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], parallel computation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [PHYS.MECA.ACOU]Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph], [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
Abstract

International audience; This book collects the proceedings of the Parallel Computational Fluid Dynamics 2008 conference held in Lyon, France. Contributed papers by over 40 researchers representing the state of the art in parallel CFD and architecture from Asia, Europe, and North America examine major developments in (1) block-structured grid and boundary methods to simulate flows over moving bodies, (2) specific methods for optimization in Aerodynamics Design, (3) innovative parallel algorithms and numerical solvers, such as scalable algebraic multilevel preconditioners and the acceleration of iterative solutions, (4) software frameworks and component architectures for parallelism, (5) large scale computing and parallel efficiencies in the industrial context, (6) lattice Boltzmann and SPH methods, and (7) applications in the environment, biofluids, and nuclear engineering.

Published
2010

46. Meshfree Adaptative Aitken-Schwarz Domain Decomposition with application to Darcy Flow

Author

Tromeur-Dervout, Damien, 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), and ANR-07-CIS7-0004,MICAS,Modelling and Intensive Computation for Aquifer Simulations(2007)

Subjects
Schwarz domain decomposition, parallel computing, Stokes, Aitken acceleration of convergence, Darcy, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, partial differential equation of elliptic type, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; This chapter is devoted to the numerical development of the Schwarz domain decomposition for non separable operators where the convergence is accelerated by the Aitken process which is not based on the mesh property. We demonstrate the linear divergence/convergence of the Schwarz method on the coupling of Darcy equation and Stokes vectorial equation. We derive explicit formula for the coefficient of amplification of the error. Then we recall the good property of this two-level domain decomposition especially in a metacomputing context. When the operator is non separable and/or the mesh is not regular, the technique for the acceleration cannot take advantage of a decomposition of the solution in "Fourier" or "sinus" basis leading to a diagonal or block diagonal acceleration. We propose three algorithms based on the singular value decomposition of the iterates produced by iterative methods exhibiting a pure linear convergence. Evidence of numerically efficient acceleration of convergence, based on a posteriori estimates provided by the singular value decomposition (SVD), are given for the Jacobi and Schwarz methods on Darcy problem where the permeability exhibits strong contrasts.

Published
2009

Catalog

Books, media, physical & digital resources
See catalog results