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1. Multi-SPMD Programming Model with YML and XcalableMP

Author

Miwako Tsuji, Matthias S. Müller, Serge G. Petiton, Christian Terboven, Thomas Dufaud, Nahid Emad, Hitoshi Murai, Mitsuhisa Sato, Joachim Protze, Taisuke Boku, RIKEN Center for Computational Science [Kobe] (RIKEN CCS), RIKEN - Institute of Physical and Chemical Research [Japon] (RIKEN), Center for Computational Sciences [Tsukuba] (CCS), Université de Tsukuba = University of Tsukuba, Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), RWTH Aachen University, and Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH)

Subjects
020203 distributed computing, Multi-core processor, Correctness, Computer science, business.industry, 020206 networking & telecommunications, 02 engineering and technology, Parallel computing, Set (abstract data type), Software, Scalability, 0202 electrical engineering, electronic engineering, information engineering, Programming paradigm, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], business, SPMD, Implementation
Abstract

This chapter describes a multi-SPMD (mSPMD) programming model and a set of software and libraries to support the mSPMD programming model. The mSPMD programming model has been proposed to realize scalable applications on huge and hierarchical systems. It has been evident that simple SPMD programs such as MPI, XMP, or hybrid programs such as OpenMP/MPI cannot exploit the postpeta- or exascale systems efficiently due to the increasing complexity of applications and systems. The mSPMD programming model has been designed to adopt multiple programming models across different architecture levels. Instead of invoking a single parallel program on millions of processor cores, multiple SPMD programs of moderate sizes can be worked together in the mSPMD programming model. As components of the mSPMD programming model, XMP has been supported. Fault-tolerance features, correctness checks, and some numerical libraries’ implementations in the mSPMD programming model have been presented.

Published
2021
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2. Machine Learning to Design an Auto-tuning System for the Best Compressed Format Detection for Parallel Sparse Computations

Author

Olfa Hamdi-Larbi, Ichrak Mehrez, Thomas Dufaud, Université de Tunis El Manar (UTM), Taibah University, Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Maison de la Simulation (MDLS), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
Smart system, Computer science, Computation, Process (computing), 02 engineering and technology, 01 natural sciences, Theoretical Computer Science, Auto tuning, 010104 statistics & probability, Computer engineering, Work (electrical), Hardware and Architecture, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 0101 mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Software, Sparse matrix
Abstract

International audience; Many applications in scientific computing process very large sparse matrices on parallel architectures. The presented work in this paper is a part of a project where our general aim is to develop an auto-tuner system for the selection of the best matrix compression format in the context of high-performance computing. The target smart system can automatically select the best compression format for a given sparse matrix, a numerical method processing this matrix, a parallel programming model and a target architecture. Hence, this paper describes the design and implementation of the proposed concept. We consider a case study consisting of a numerical method reduced to the sparse matrix vector product (SpMV), some compression formats, the data parallel as a programming model and, a distributed multi-core platform as a target architecture. This study allows extracting a set of important novel metrics and parameters which are relative to the considered programming model. Our metrics are used as input to a machine-learning algorithm to predict the best matrix compression format. An experimental study targeting a distributed multi-core platform and processing random and real-world matrices shows that our system can improve in average up to 7% the accuracy of the machine learning.

Published
2021
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3. Shape, size, pressure and matrix effects on 2D spin crossover nanomaterials studied using density of states obtained by dynamic programming

Author

Devan Sohier, Catherine Cazelles, J. Linares, Kamel Boukheddaden, Thomas Dufaud, Pierre-Richard Dahoo, Groupe d'Etude de la Matière Condensée (GEMAC), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS), Departamento de Ciencias [Lima], Pontificia Universidad Católica del Perú (PUCP), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), PLANETO - LATMOS, Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), Sorbonne Université (SU)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS), Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Pontificia Universidad Católica del Perú = Pontifical Catholic University of Peru (PUCP), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Surface (mathematics), Phase transition, Work (thermodynamics), Materials science, General Computer Science, General Physics and Astronomy, 02 engineering and technology, 010402 general chemistry, 01 natural sciences, Spin crossover, Thermal, General Materials Science, Statistical physics, Topology (chemistry), nanomaterials, General Chemistry, 021001 nanoscience & nanotechnology, 0104 chemical sciences, dynamic programming 2, Dynamic programming, Computational Mathematics, Mechanics of Materials, Phase transitions, Density of states, [PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci], 0210 nano-technology
Abstract

International audience; In the present work, numerical simulations based on a new algorithm speci c for 2D con gurational topology of spin crossover nanoparticles embedded in a matrix are presented and discussed in the framework of the Ising-like model taking into account for short- (J) and long-range (G) interactions as for surface effects (L). The new al- gorithm is applied to calculate the density of states for each macro-state, which is then used to calculate exactly the thermal behavior of spin-crossover nanoparticles under an applied pressure. We nd that the pressure plays the role of a conjugate parameter of the temperature. Thus, increasing pressure is somehow equivalent to reducing the temperature.

Published
2021
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4. MYX: Runtime correctness analysis for multi-level parallel programming paradigms

Author

Christian Terboven, Matthias S. Müller, Nahid Emad, Taisuke Boku, Joachim Protze, Serge G. Petiton, Thomas Dufaud, Hitoshi Murai, Miwako Tsuji, Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH), RIKEN Center for Computational Science [Kobe] (RIKEN CCS), RIKEN - Institute of Physical and Chemical Research [Japon] (RIKEN), Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Center for Computational Sciences [Tsukuba] (CCS), Université de Tsukuba = University of Tsukuba, Hans-Joachim Bungartz, Severin Reiz, Benjamin Uekermann, Philipp Neumann, Wolfgang E. Nagel, and RWTH Aachen University

Subjects
Correctness, Exploit, Computer science, Concurrency, media_common.quotation_subject, 010103 numerical & computational mathematics, 02 engineering and technology, Parallel computing, 01 natural sciences, Workflow, Debugging, Parallel programming model, 0202 electrical engineering, electronic engineering, information engineering, Programming paradigm, 020201 artificial intelligence & image processing, Partitioned global address space, 0101 mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS, media_common
Abstract

International audience; In recent years the increasing compute power is mainly provided by rapidly increasing concurrency. Therefore, the HPC community is looking for new parallel programming paradigms to make the best use of current and upcoming machines. Under the Japanese CREST funding program, the post-petascale HPC project developed the XcalableMP programming paradigm, a pragma-based partitioned global address space (PGAS) approach. To better exploit the potential concurrency of large scale systems, the mSPMD model was proposed and implemented with the YvetteML workflow description language. When introducing a new parallel programming paradigm, good tool support for debugging and performance analysis is crucial for the productivity and therefore the acceptance in the HPC community. The subject of the MYX project is to investigate which properties of a parallel programming language specification may help tools to highlight correctness and performance issues or help to avoid common issues in parallel programming in the first place. In this paper, we exercise these investigations on the example of XcalableMP and YvetteML.

Published
2020
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5. Three Stable States Simulated for 1D Spin‐Crossover Nanoparticles Using the Ising‐Like Model

Author

Camille Harlé, Devan Sohier, Thomas Dufaud, J. Linares, Salah Eddine Allal, Pierre-Richard Dahoo, PLANETO - LATMOS, Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Groupe d'Etude de la Matière Condensée (GEMAC), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS), Pontificia Universidad Católica del Perú = Pontifical Catholic University of Peru (PUCP), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), and Pontificia Universidad Católica del Perú (PUCP)

Subjects
Surface (mathematics), Phase transition, Work (thermodynamics), Size effects, Chemistry, 02 engineering and technology, Spin crossover, 010402 general chemistry, 021001 nanoscience & nanotechnology, 01 natural sciences, 0104 chemical sciences, Inorganic Chemistry, Matrix (mathematics), Phase transitions, Computational chemistry, Ising model, Thermal, [PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci], Density of states, Nanoparticles, Statistical physics, 0210 nano-technology
Abstract

International audience; In the present work, numerical simulations for spincrossover 1D nanoparticles embedded in a matrix are presented anddiscussed in the framework of the Ising-like model taking into accountshort- (J), long-range (G) interaction as well as the interaction (L)between the surface molecules and the surroundings. Using a newalgorithm, detailed in this contribution, to calculate the density ofstates for each macro-state, we have obtained a three-state thermalbehaviour for some sets of parameters. We analyse the role of thesedifferent parameters, as well as the number of 1D SCO molecules, inthe monitoring of this particular behaviour.

Published
2017
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6. Size effect on the three state thermal hysteresis of a 2D spin crossover nanoparticles

Author

Camille Harlé, Thomas Dufaud, Devan Sohier, Salah Eddine Allal, J. Linares, Pierre-Richard Dahoo, Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), PLANETO - LATMOS, Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Groupe d'Etude de la Matière Condensée (GEMAC), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS), Pontificia Universidad Católica del Perú = Pontifical Catholic University of Peru (PUCP), Sorbonne Université (SU)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS), and Pontificia Universidad Católica del Perú (PUCP)

Subjects
History, Materials science, Condensed matter physics, Computer simulation, 010405 organic chemistry, 02 engineering and technology, Atmospheric temperature range, 021001 nanoscience & nanotechnology, 01 natural sciences, Stability (probability), Square lattice, Square (algebra), 0104 chemical sciences, Computer Science Applications, Education, Hysteresis, Spin crossover, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], 0210 nano-technology, Spin-½
Abstract

In this report first we show, in a framework of the Ising-like model, a numerical simulation of a typical two step thermal transition obtained for a square lattice 12x12: a "first-step hysteresis" for a high spin fraction Nhs between 0 - 0,5 and at a higher temperature a "second-step hysteresis" with Nhs between 0.5 and 1. As long as we decrease the number of molecules the temperature range of the "second-step hysteresis" moves to a lower temperature, until is obtained, for a square of 4x4, a clear overlapped case with a three state behaviour. A detailed analys is on the role of the size system (4x4, 5x5, 6x6, 8x8 and 12x12) on the stability of this "Three state behaviour" is presented in this contribution. We study the influence of the surrounding environment for this specific thermal hysteresis. To solve the self-consistent equation related to the average value of the spin-operator , we use the density of the states calculated using a dynamic programming algorithm that will be presented in this paper.

Published
2018
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7. Design of Data Management for Multi SPMD Workflow Programming Model

Author

Miwako Tsuji, Thomas Dufaud, Mitsuhisa Sato, Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), RIKEN Center for Computational Science [Kobe] (RIKEN CCS), RIKEN - Institute of Physical and Chemical Research [Japon] (RIKEN), Center for Computational Sciences [Tsukuba] (CCS), Université de Tsukuba = University of Tsukuba, and Dufaud, Thomas

Subjects
020203 distributed computing, Speedup, business.industry, Computer science, Data management, Distributed computing, Message passing, 010103 numerical & computational mathematics, 02 engineering and technology, computer.software_genre, 01 natural sciences, Data modeling, Workflow, Middleware (distributed applications), 0202 electrical engineering, electronic engineering, information engineering, Programming paradigm, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], 0101 mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], business, SPMD, computer, ComputingMilieux_MISCELLANEOUS
Abstract

As both the complexity of algorithms and architecture increase, development of scientific software becomes a challenge. In order to exploit future architecture, we consider a Multi-SPMD workflow programing model. Then, data transfer between tasks during computation highly depends on the architecture and middleware used. In this study we design an adaptive system for data management in a parallel programming environment which can express two level of parallelism. We show how the consideration of multiple strategies based on I/O and direct message passing can improve performances and fault tolerance in the YML-XMP environment. On a real application with a sufficiently large amount of local data, speedup of 1.36 for a mixed strategy to 1.73 for a direct message passing method are obtained compared to our original design.

Published
2018

8. Machine Learning for Optimal Compression Format Prediction on Multiprocessor Platform

Author

Olfa Hamdi-Larbi, Nahid Emad, Ichrak Mehrez, Thomas Dufaud, Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Université de Tunis El Manar (UTM), Maison de la Simulation (MDLS), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
020203 distributed computing, business.industry, Computer science, Multiprocessing, 010103 numerical & computational mathematics, 02 engineering and technology, Numerical models, Machine learning, computer.software_genre, 01 natural sciences, Data modeling, Kernel (image processing), 0202 electrical engineering, electronic engineering, information engineering, Artificial intelligence, 0101 mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], business, computer, Large size, Sparse matrix
Abstract

International audience; Many scientific applications handle large size sparse matrices which can be stored using special compression formats to reduce memory space and processing time. The choice of the Optimal Compression Format (OCF) is a critical process that involves several criteria. In this paper, we propose to use machine learning approach to predict the OCF (among CSR, CSC, ELL and COO) for SMVP kernel on multiprocessor platform. Our goal is not only to reach high accuracy values but also to minimize the LUBS (Loss Under Best Selection). Our main contribution consists in using data parallel model to extract features dataset. Experimental results show that we achieve more than 95% accuracy.

Published
2018
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9. Numerical Investigations of the Thermal, Pressure and Size Effects on 2D Spin Crossover Nanoparticles

Author

Thomas Dufaud, R. Caballero, Salah Eddine Allal, Kamel Boukheddaden, Camille Harlé, J. Linares, Devan Sohier, F. De Zela, Pierre-Richard Dahoo, PLANETO - LATMOS, Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Pontificia Universidad Católica del Perú = Pontifical Catholic University of Peru (PUCP), Groupe d'Etude de la Matière Condensée (GEMAC), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), and Pontificia Universidad Católica del Perú (PUCP)

Subjects
Physics, History, Monte Carlo method, 02 engineering and technology, State (functional analysis), 010402 general chemistry, 021001 nanoscience & nanotechnology, 01 natural sciences, Molecular physics, 0104 chemical sciences, Computer Science Applications, Education, Matrix (mathematics), Magnetization, Spin crossover, Thermal, [PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci], 0210 nano-technology, Eigenvalues and eigenvectors, Spin-½
Abstract

6th International Conference on Mathematical Modelling in Physical Sciences (IC-MSQUARE 2017)28–31 August 2017, Pafos, Cyprus; International audience; In the framework of the Ising-like model, the thermal and pressure effects on the spin crossover systems are evaluated through two-states fictitious spin operators σ with eigenvalues and respectively associated with the low-spin (LS) and high-spin (HS) states of each spin-crossover (SCO) molecule. Based on each configurational state, the macroscopic SCO system, is described by the following variables: m=Σ σi , s=Σ σi σj and c=Σ σk standing respectively for the total magnetization, the short-range correlations and surface magnetization. To solve this problem, we first determine the density of macrostates d[m][s][c], giving the number of microscopic configurations with the same m, s and c values. In this contribution, two different ways have been performed to calculate this important quantity: (i) the entropic sampling method, based on Monte Carlo simulations and (ii) a new algorithm based on specific dynamic programming. These two methods were tested on the 2D SCO nanoparticles for which, we calculated the average magnetization < σ> taking into account for short-, long-range interactions as well as for the interaction between surface molecules with their surrounding matrix. We monitored the effect of the pressure, temperature and size on the properties of the SCO nanoparticles

Published
2017
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10. Understanding the Performances of Sparse Compression Formats Using Data Parallel Programming Model

Author

Ichrak Mehrez, Olfa Hamdi-Larbi, Nahid Emad, Thomas Dufaud, Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Université de Tunis El Manar (UTM), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)

Subjects
020203 distributed computing, Matrix-free methods, Computer science, MathematicsofComputing_NUMERICALANALYSIS, Parallel algorithm, Context (language use), 010103 numerical & computational mathematics, 02 engineering and technology, Parallel computing, Sparse approximation, 01 natural sciences, Kernel (linear algebra), Sparse array, Parallel programming model, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Algorithm, ComputingMilieux_MISCELLANEOUS, Sparse matrix
Abstract

International audience; Several applications in numerical scientific computing involve very large sparse matrices with a regular or irregular sparse structure. These matrices can be stored using special compression formats (storing only non-zero elements) to reduce memory space and processing time. The choice of the optimal format is a critical process that involves several criteria. The general context of this work is to propose an auto-tuner system that, given a sparse matrix, a numerical method, a parallel programming model and an architecture, can automatically select the Optimal Compression Format (OCF). In this paper we study the performance of two different sparse compression formats namely CSR (Compressed Sparse Row) and CSC (Compressed Sparse Column). Thus, we propose data parallel algorithms for Sparse Matrix Vector Product in the case of each format. We extract a set of parameters that can help us to select the more suitable compression format for a given sparse matrix.

Published
2017
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11. Aitken’s acceleration of the Schwarz process using singular value decomposition for heterogeneous 3D groundwater flow problems

Author

Thomas Dufaud, Laurent Berenguer, Damien Tromeur-Dervout, 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
Darcy's law, General Computer Science, Discretization, Groundwater flow, Mathematical analysis, Singular value decomposition, General Engineering, Aitken's delta-squared process, Domain decomposition methods, 010103 numerical & computational mathematics, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 01 natural sciences, Darcy–Weisbach equation, 010101 applied mathematics, Schwarz domain decomposition, Permeability (earth sciences), Aitken's acceleration of convergence, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], 0101 mathematics, Schwarz alternating method, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; This paper is devoted to the acceleration by Aitken's technique of the convergence of the Schwarz domain decomposition method applied to large scale 3D problems with non-separable linear operators. These operators come from the discretization of groundwater flow problems modeled by the linear Darcy equation, where the permeability field is highly heterogeneous and randomly generated. To be computationally efficient, a low-rank approximation of the Aitken's formula is computed from the singular value decomposition of successive iterated solutions on subdomains interfaces. Numerical results explore the efficiency of the solver with respect to the random distribution parameters, and specific implementations of the acceleration are compared for large scale 3D problems. These results confirm the numerical behavior of the methodology obtained on 2D Darcy problems (Tromeur-Dervout D. Meshfree adaptive Aitken-Schwarz domain decomposition with application to Darcy flow. Comput Sci Eng Technol 2009;21:217-50).

Published
2013
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12. Reprint of Efficient parallel implementation of the fully algebraic multiplicative Aitken-RAS preconditioning technique

Author

Thomas Dufaud and Damien Tromeur-Dervout

Subjects
Algebra, Singular value, Operator (computer programming), Interface (Java), Multiplicative function, General Engineering, Domain decomposition methods, Acceleration (differential geometry), Parallel computing, Algebraic number, Software, Software implementation, Mathematics
Abstract

This paper details the software implementation of the ARAS preconditioning technique (Dufaud T, Tromeur-Dervout D. Aitken's acceleration of the Restricted Additive Schwarz preconditioning using coarse approximations on the interface. CR Math Acad Sci Paris 2010;348(13-14):821-4), in the PETSc framework. Especially, the PETSc implementation of interface operators involved in ARAS and the introduction of a two level of parallelism in PETSc for the RAS are described. The numerical and parallel implementation performances are studied on academic and industrial problems, and compared with the RAS preconditioning. For saving computational time on industrial problems, the Aitken's acceleration operator is approximated from the singular values decomposition technique of the RAS iterate solutions.

Published
2013
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13. Acceleration of Convergence for Domain Decomposition Methods

Author

Damien Tromeur-Dervout, Laurent Berenguer, and Thomas Dufaud

Subjects
Rate of convergence, Numerical analysis, Additive Schwarz method, Mathematical analysis, Singular value decomposition, Aitken's delta-squared process, Domain decomposition methods, General Medicine, Schwarz alternating method, System of linear equations, Mathematics
Abstract

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
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14. Towards an auto-tuning system design for optimal sparse compression format selection with user expertise

Author

Nahid Emad, Ichrak Mehrez, Thomas Dufaud, Olfa Hamdi-Larbi, Parallélisme, Réseaux, Systèmes, Modélisation (PRISM), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Maison de la Simulation (MDLS), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
Hardware architecture, 020203 distributed computing, Multi-core processor, Theoretical computer science, Job shop scheduling, Computer science, Horner's method, 010103 numerical & computational mathematics, 02 engineering and technology, computer.software_genre, 01 natural sciences, Expert system, Computer engineering, Parallel programming model, 0202 electrical engineering, electronic engineering, information engineering, Systems design, 0101 mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], computer, ComputingMilieux_MISCELLANEOUS, Sparse matrix
Abstract

Several applications in numerical scientific computing process sparse matrices with either a regular or irregular structure. The very large size of these matrices requires to use compressing formats and target parallel/distributed architectures in order to reduce both space complexity and processing time. The optimal compression format (OCF) of such matrices may in fact vary according to both the application context of the numerical method and the target hardware architecture. In this paper, we propose a design of a system that automatically selects the OCF according to the two above cited parameters. The expert system obtained from our model targets dynamic integration of the user expertise thus allowing better performances. The optimal format selection is based on the makespan criterion. As a first validation test of our system, we studied the representative case of Horner scheme in the context of data parallel programming model and multicore cluster. Our experiments focus on the four compression formats CSR, CSC, COO and ELLPACK and their complexities in a data parallel programming model context.

Published
2016
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15. Efficient parallel implementation of the fully algebraic multiplicative Aitken-RAS preconditioning technique

Author

Thomas Dufaud, Damien Tromeur-Dervout, 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), région Rhône-Alpes through the project CHPID of the cluster ISLE, and ANR-07-TLOG-0011,LIBRAERO,Large Information Base for the Research in AEROdynamics(2007)

Subjects
Parallel computing, 010101 applied mathematics, Aitken-Schwarz method, General Engineering, Restricted Additive Schwarz preconditioner, Domain decomposition, 010103 numerical & computational mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], 0101 mathematics, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 01 natural sciences, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Software
Abstract

International audience; This paper details the software implementation of the ARAS preconditioning technique (Dufaud T, Tromeur- Dervout D. Aitken's acceleration of the Resctricted Additive Schwarz preconditioning using coarse approximations on the interface. CR Math Acad Sci Paris 2010;348(13-14):821-4), in the PETSc framework. Especially, the PETSc implementation of interface operators involved in ARAS and the introduction of a two level of parallelism in PETSc for the RAS are described. The numerical and parallel implementation performances are studied on academic and industrial problems, and compared with the RAS preconditioning. For saving computational time on industrial problems, the Aitken's acceleration operator is approximated from the singular values decomposition technique of the RAS iterate solutions.

Published
2012
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16. A two-level preconditioning framework based on a Richardson iterative process

Author

Thomas Dufaud, Pichot, Géraldine, Jocelyne Erhel and Martin Gander and Laurence Halpern and Géraldine Pichot and Taoufik Sassi and Olof Widlund, 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), GEOFRAC, SAGE team, Inria Rennes and LMNO, Caen, 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), and 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)

Subjects
Mathematical optimization, Iterative and incremental development, Preconditioner, 010102 general mathematics, Linear system, MathematicsofComputing_NUMERICALANALYSIS, 010103 numerical & computational mathematics, Krylov subspace, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Space (mathematics), 01 natural sciences, Computer Science::Numerical Analysis, Mathematics::Numerical Analysis, Iterated function, Singular value decomposition, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Applied mathematics, 0101 mathematics, Algebraic number, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; A fully algebraic framework for constructing coarse spaces for multilevel preconditioning techniques is proposed. An issue of multilevel techniques is their application to linear system encountered in industrial applications which can be derived from non-elliptic PDEs. Drawing our inspiration from the Aitken-SVD methodology, dedicated to Schwarz methods, we proposed to construct an approximation space by computing the Singular Value Decomposition of a set of iterated solutions of the Richardson process associated to a given preconditioner.

Published
2014

17. ARAS2 preconditioning technique for CFD industrial cases

Author

Thomas Dufaud, Damien Tromeur-Dervout, 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), 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), Randolph Bank and Michael Holst and Olof Widlund and Jinchao Xu, 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), and Pichot, Géraldine

Subjects
010101 applied mathematics, Combinatorics, Matrix (mathematics), Non singular, 010103 numerical & computational mathematics, 0101 mathematics, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 01 natural sciences, Condition number, Algorithm, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; A two-level preconditioning technique based on the Aitken’s acceleration of the convergence of the Restricted Additive Schwarz (RAS) domain decomposition method is derived. When it is applied to linear problems, the RAS has a pure linear rate of convergence/divergence that can be enhanced with optimized boundary conditions giving the ORAS method based on the underlying PDE. The RAS method’s linear convergence allows its acceleration of the convergence by the Aitken’s process. In this new two level algebraic preconditioner technique named ARAS2, the coarse grid operator uses only parts of the artificial interfaces contrary to the patch substructuring method. In this way, it can be seen as similar as the SchurRAS method but it differs because the discrete Steklov-Poincar operator connects the coarse artificial interfaces of all the subdomains. Numerical results of the good properties of the ARAS2 preconditioning are provided on industrial problems with no knowledge of the underlying equations.

Published
2013

18. On-the-fly Singular Value Decomposition for Aitken's Acceleration of the Schwarz Domain Decomposition Method

Author

Laurent Berenguer, Thomas Dufaud, Duc Toan Pham, Damien Tromeur-Dervout, 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), Koen De Bosschere, Erik H. D'Hollander, Gerhard R. Joubert, David Padua, Frans Peters, Mark Sawyer, ANR-07-CIS7-0004,MICAS,Modelling and Intensive Computation for Aquifer Simulations(2007), Tromeur-Dervout, Damien, Calcul intensif et simulation - Modelling and Intensive Computation for Aquifer Simulations - - MICAS2007 - ANR-07-CIS7-0004 - CIS - VALID, and Koen De Bosschere, Erik H. D'Hollander, Gerhard R. Joubert, David Padua, Frans Peters, Mark Sawyer

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], [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; This paper discusses the low-rank approximation of the Aitken's acceleration of the convergence of the Schwarz domain decomposition method. The singular value decomposition (SVD) of the solution on interfaces at successive Schwarz iterations gives a basis of a low-dimensional space. The error operator of the Schwarz process, involved in the Aitken's formula, is approximated in this space. The efficiency of the Aitken's acceleration depends on the quality of this basis to approximate the exact solution, which is related to the number of iterations involved in the SVD. We use an iterative procedure to compute the SVD simultaneously with the Schwarz process in order to perform the Aitken's acceleration when the SVD satisfies a mathematical criterion.

Published
2011

19. Une méthode de décomposition de domaine pour résoudre l'équation de Darcy 3D dans les milieux poreux fortement hétérogènes

Author

Laurent Berenguer, Thomas Dufaud, Damien Tromeur-Dervout, Association Française de Mécanique, and Service irevues, irevues

Subjects
[PHYS.MECA]Physics [physics]/Mechanics [physics], [PHYS.MECA] Physics [physics]/Mechanics [physics]
Abstract

Colloque avec actes et comité de lecture. Internationale.; International audience; Nous présentons une méthode parallèle pour résoudre l'équation de Darcy 3D où le champ de perméabilité varie aléatoirement suivant une distribution log normale et avec de fortes amplitudes dans des domaines discrétisés de 10^8 à 10^9 inconnues. Cette technique de décomposition de domaine de type Aitken-Schwarz conduit à un parallélisme à deux niveaux où les problèmes locaux sont résolus par multigrille algébrique parallèle (AGMG de Y. Notay). L'influence sur la construction de l'accélération d' Aitken de l'espace d'approximation pour représenter la solution sur les interfaces sera discuté.

Published
2011

20. Numerical Investigations and Parallel Implementation of the ARAS2 Preconditioning Technique

Author

Damien Tromeur-Dervout, Thomas Dufaud, 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-07-TLOG-0011,LIBRAERO,Large Information Base for the Research in AEROdynamics(2007)

Subjects
Singular value, Computer science, Decomposition (computer science), Applied mathematics, [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], Orthogonal basis
Abstract

International audience; The RAS preconditioning on academic and industrial problems. To build the Aitken's acceleration, a choice of an orthogonal basis defined on the subdomains interfaces must be made. For saving computational time, an orthogonal basis dependent of the problem is made using the singular values decomposition technique. The parallel implementation of the method in the Petsc framework is described.

Published
2011
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21. Adaptive Aitken-Schwarz Method for Non Separable Operator on Multiprocessor Systems

Author

Thomas Dufaud, Damien Tromeur-Dervout, Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués (LI-PaRAD), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dufaud, Thomas, Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués ( LI-PaRAD ), Université de Versailles Saint-Quentin-en-Yvelines ( UVSQ ), Maison de la Simulation ( MDLS ), and Université de Versailles Saint-Quentin-en-Yvelines ( UVSQ ) -Université Paris-Sud - Paris 11 ( UP11 ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS )

Subjects
[ INFO.INFO-DC ] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2010

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