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1. Domain Decomposition Methods in Science and Engineering XXV

Author

Ronald Haynes, Scott MacLachlan, Xiao-Chuan Cai, Laurence Halpern, Hyea Hyun Kim, Axel Klawonn, Olof Widlund, Ronald Haynes, Scott MacLachlan, Xiao-Chuan Cai, Laurence Halpern, Hyea Hyun Kim, Axel Klawonn, and Olof Widlund

Subjects
Mathematics—Data processing, Differential equations, Computer engineering, Computer networks, Computer science—Mathematics, Computer simulation, Computer-aided engineering
Abstract

These are the proceedings of the 25th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in St. John's, Newfoundland, Canada in July 2018. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2018.

Published
2020

2. Domain Decomposition Methods in Science and Engineering XXI

Author

Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, Olof Widlund, Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, and Olof Widlund

Subjects
Differential equations, Partial--Congresses, Decomposition method--Congresses
Abstract

This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.

Published
2014

3. Domain Decomposition Methods in Science and Engineering XX

Author

Randolph Bank, Michael Holst, Olof Widlund, Jinchao Xu, Randolph Bank, Michael Holst, Olof Widlund, and Jinchao Xu

Subjects
Differential equations, Partial--Congresses, Decomposition method--Congresses, Mathematics
Abstract

These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.​

Published
2013

4. Domain Decomposition Methods in Science and Engineering XIX

Author

Yunqing Huang, Ralf Kornhuber, Olof Widlund, Jinchao Xu, Yunqing Huang, Ralf Kornhuber, Olof Widlund, and Jinchao Xu

Subjects
Differential equations, Partial--Congresses, Decomposition method--Congresses
Abstract

These are the proceedings of the 19th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise in various problems in mathematics, computational science, engineering and industry. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well-developed theory which is having a direct impact on the development and improvement of these algorithms.

Published
2011

5. Domain Decomposition Methods in Science and Engineering XVIII

Author

Michel Bercovier, Martin Gander, Ralf Kornhuber, Olof Widlund, Michel Bercovier, Martin Gander, Ralf Kornhuber, and Olof Widlund

Subjects
Mathematics—Data processing, Mathematical models, Mathematical physics, Computer science—Mathematics
Abstract

th This volume contains a selection of 41 refereed papers presented at the 18 International Conference of Domain Decomposition Methods hosted by the School of ComputerScience and Engineering(CSE) of the Hebrew Universityof Jerusalem, Israel, January 12–17, 2008. 1 Background of the Conference Series The International Conference on Domain Decomposition Methods has been held in twelve countries throughout Asia, Europe, the Middle East, and North America, beginning in Paris in 1987. Originally held annually, it is now spaced at roughly 18-month intervals. A complete list of past meetings appears below. The principal technical content of the conference has always been mathematical, but the principal motivation has been to make ef cient use of distributed memory computers for complex applications arising in science and engineering. The leading 15 such computers, at the “petascale” characterized by 10 oating point operations per second of processing power and as many Bytes of application-addressablem- ory, now marshal more than 200,000 independentprocessor cores, and systems with many millions of cores are expected soon. There is essentially no alternative to - main decomposition as a stratagem for parallelization at such scales. Contributions from mathematicians, computerscientists, engineers,and scientists are together n- essary in addressing the challenge of scale, and all are important to this conference.

Published
2009

6. Domain Decomposition Methods in Science and Engineering XVII

Author

Ulrich Langer, Marco Discacciati, David E. Keyes, Olof Widlund, Walter Zulehner, Ulrich Langer, Marco Discacciati, David E. Keyes, Olof Widlund, and Walter Zulehner

Subjects
Differential equations, Partial--Congresses, Decomposition method--Congresses
Abstract

This volume contains a selection of papers presented at the 17th International Conference on Domain Decomposition Methods in Science and Engineering held at St. Wolfgang / Strobl, Austria, July 3 - 7, 2006. Domain decomposition is an active, interdisciplinary research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models. Domain decomposition techniques provide efficient tools for treating problems in all Computational Sciences. The reader will become familiar with the newest domain decomposition technologies and their use for modeling and simulating of complex problems from different fields of applications.

Published
2008

7. Domain Decomposition Methods in Science and Engineering XVI

Author

Olof Widlund, David E. Keyes, Olof Widlund, and David E. Keyes

Subjects
Differential equations, Partial--Congresses, Decomposition method--Congresses
Abstract

Domain decomposition is an active, interdisciplinary research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. Since the advent of hierarchical distributed memory computers, it has been motivated by considerations of concurrency and locality in a wide variety of large-scale problems, continuous and discrete. Historically, it emerged from the analysis of partial differential equations, beginning with the work of Schwarz in 1870. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.

Published
2007

8. Domain Decomposition Methods - Algorithms and Theory

Author

Andrea Toselli, Olof Widlund, Andrea Toselli, and Olof Widlund

Subjects
Decomposition method, Differential equations, Partial, Differential equations, Partial--Numerical solutions
Abstract

This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.

Published
2005

9. Domain Decomposition Methods in Science and Engineering

Author

Ralf Kornhuber, Ronald W. Hoppe, Jacques Periaux, Olivier Pironneau, Olof Widlund, Jinchao Xu, Ralf Kornhuber, Ronald W. Hoppe, Jacques Periaux, Olivier Pironneau, Olof Widlund, and Jinchao Xu

Subjects
Physics, Decomposition method--Congresses, Computer science, Computer science--Mathematics, Differential equations, Partial--Congresses
Abstract

Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

Published
2005

11. Capacitance matrix methods for the Helmholtz equation on general three-dimensional regions

Author

Dianne P. O'Leary and Olof Widlund

Subjects
Computational Mathematics, Algebra and Number Theory, Applied Mathematics
Abstract

Capacitance matrix methods provide techniques for extending the use of fast Poisson solvers to arbitrary bounded regions. These techniques are further studied and developed with a focus on the three-dimensional case. A discrete analogue of classical potential theory is used as a guide in the design of rapidly convergent iterative methods. Algorithmic and programming aspects of the methods are also explored in detail. Several conjugate gradient methods are discussed for the solution of the capacitance matrix equation. A fast Poisson solver is developed which is numerically very stable even for indefinite Helmholtz equations. Variants thereof allow substantial savings in primary storage for problems on very fine meshes. Numerical results show that accurate solutions can be obtained at a cost which is proportional to that of the fast Helmholtz solver in use.

Published
1979

12. High order fast Laplace solvers for the Dirichlet problem on general regions

Author

Victor Pereyra, Wlodzimierz Proskurowski, and Olof Widlund

Subjects
Computational Mathematics, Algebra and Number Theory, Applied Mathematics
Abstract

Highly accurate finite difference schemes are developed for Laplace’s equation with the Dirichlet boundary condition on general bounded regions in R n {R^n} . A second order accurate scheme is combined with a deferred correction or Richardson extrapolation method to increase the accuracy. The Dirichlet condition is approximated by a method suggested by Heinz-Otto Kreiss. A convergence proof of his, previously not published, is given which shows that, for the interval size h, one of the methods has an accuracy of at least O ( h 5.5 ) O({h^{5.5}}) in L 2 {L_2} . The linear systems of algebraic equations are solved by a capacitance matrix method. The results of our numerical experiments show that highly accurate solutions are obtained with only a slight additional use of computer time when compared to the results obtained by second order accurate methods.

Published
1977

14. Numerical Analysis

Author

Olof Widlund and Roger Teman

Subjects
Computational Mathematics, Algebra and Number Theory, Applied Mathematics
Published
1975

20. Distributed Nonsmooth Contact Domain Decomposition (NSCDD): Algorithmic Structure and Scalability

Author

Vincent Visseq, David Dureisseix, Alexandre Martin, Frédéric Dubois, Pierre Alart, Laboratoire de Mécanique et Génie Civil (LMGC), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique des Structures Industrielles Durables (LAMSID - UMR 8193), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Réseaux, Moyens Informatiques, Calcul Scientifique (Remics), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Modélisation Mathématique en Mécanique (M3), This work was partly supported by OSEO, FEDER and the region of Languedoc-Roussillon (Degrip project), Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, Olof Widlund, Laboratoire de Mécanique et Génie Civil ( LMGC ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mécanique des Structures Industrielles Durables ( LAMSID - UMR 8193 ), EDF R&D ( EDF R&D ), EDF ( EDF ) -EDF ( EDF ) -Centre National de la Recherche Scientifique ( CNRS ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] ( LaMCoS ), Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Réseaux, Moyens Informatiques, Calcul Scientifique ( Remics ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Modélisation Mathématique en Mécanique ( M3 ), Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, Olof Widlund, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-EDF R&D (EDF R&D), and EDF (EDF)-EDF (EDF)

Subjects
Mathematical optimization, Computer science, Interface (Java), Computation, Structure (category theory), [ SPI.MECA.STRU ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph], Domain decomposition methods, Granular media, 02 engineering and technology, [ PHYS.MECA.STRU ] Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph], 01 natural sciences, Discrete element method, Computational science, 010101 applied mathematics, [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], Scalability, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Parallel detection, 0101 mathematics
Abstract

A draft (preprint) version of the publication is available at http://dd21.inria.fr/pdf/visseqv_contrib.pdf; International audience; Numerical simulations of the dynamics of discrete structures in presence of numerous impacts with frictional contacts leads to CPU-intensive large time computations. To deal with these problems, numerical tools have been developed, such as the nonsmooth contact domain decomposition (NSCDD). We present further a distributed version of its algorithm with parallel detection of fine contacts and discuss two possible communication schemes to solve the interface problem. Those improvements allow to study scalability and numerical performances of the method for 2D and 3D granular media.

Published
2012

21. An Adaptive Parallel-in-Time Method with application to a membrane problem

Author

Jocelyne Erhel, Noha Makhoul Karam, Nabil Nassif, 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), Department of mathematics [Beirut], American University of Beirut [Beyrouth] (AUB), 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 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), Jocelyne Erhel and Martin Gander and Laurence Halpern and Géraldine Pichot and Taoufik Sassi and Olof Widlund, 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), 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), and SAGE team, Inria Rennes and LMNO, Caen

Subjects
Discrete mathematics, Sequence, Work (thermodynamics), [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Value (computer science), 010103 numerical & computational mathematics, 02 engineering and technology, Function (mathematics), Grid, 01 natural sciences, Data model, Feature (computer vision), 020204 information systems, 0202 electrical engineering, electronic engineering, information engineering, Initial value problem, 0101 mathematics, [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

In a previous work (Nassif et al., In: V.A. al (ed.) ICCS 06. Computer Science, pp. 148–155. Springer, New York, 2006), we introduced an approach for solving the initial value problem \(\frac{\mathit{dY}} {\mathit{dt}} = F(t,Y ),\,Y (0) = Y _{0}\) in a time-parallel way. The main feature of the method is its capacity to automatically generate a non-regular time grid, adapted to the behavior of the solution. Parallel integration is made possible by introducing a “shooting function” that partitions the problem into a sequence of shooting value problems, each defined on a time slice of the coarse grid. After rescaling the variables on each slice, a prediction data model that permits accurate predictions of the solution at the beginning of every slice, leads to an Adaptive Parallel Time Integration (APTI) algorithm. In this paper, the method is applied to a membrane problem having oscillatory and unbounded solutions on (0, ∞).

Published
2014

22. Domain Decomposition Methods in Science and Engineering XXI

Author

Olof B. Widlund, Taoufik Sassi, Jocelyne Erhel, Martin J. Gander, Géraldine Pichot, Laurence Halpern, 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), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-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)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-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), Section de mathématiques [Genève], Université de Genève (UNIGE), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Jocelyne Erhel and Martin Gander and Laurence Halpern and Géraldine Pichot and Taoufik Sassi and Olof Widlund, 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), Université de Genève = University of Geneva (UNIGE), Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), 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
Computer science, Scale (chemistry), Numerical analysis, Domain decomposition methods, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Field (computer science), Computational science, Development (topology), Scalability, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Domain analysis, 0101 mathematics, Massively parallel, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.

Published
2014

23. 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

24. Symbolic techniques for domain decomposition methods

Author

Frédéric Nataf, Victorita Dolean, Alban Quadrat, Thomas Cluzeau, DMI (XLIM-DMI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Randolph Bank and Michael Holst and Olof Widlund and Jinchao Xu, Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), DMI, and Université Nice Sophia Antipolis (... - 2019) (UNS)

Subjects
Mathematical optimization, Partial differential equation, MathematicsofComputing_NUMERICALANALYSIS, Computational mathematics, Domain decomposition methods, 010103 numerical & computational mathematics, Symbolic computation, 01 natural sciences, 010101 applied mathematics, Algebra, Scalability, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

International audience; Some algorithmic aspects of systems of PDEs based simulations can be better clarified by means of symbolic computation techniques. This is very important since numerical simulations heavily rely on solving systems of PDEs. For the large-scale problems we deal with in today's standard applications, it is necessary to rely on iterative Krylov methods that are scalable (i.e., weakly dependent on the number of degrees on freedom and number of subdomains) and have limited memory requirements.

Published
2013

25. 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

26. Parallel Adaptive Deflated GMRES

Author

Jocelyne Erhel, Désiré Nuentsa Wakam, William Gropp, 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), Department of Computer Science [UIUC] (UIUC), University of Illinois at Urbana-Champaign [Urbana], University of Illinois System-University of Illinois System, Randolph Bank and Michael Holst and Olof Widlund and Jinchao Xu, INRIA-Illinois-ANL Joint Laboratory for Petascale computing, ANR-07-TLOG-0011,LIBRAERO,Large Information Base for the Research in AEROdynamics(2007), 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
Iterative and incremental development, Iterative method, Computer science, Linear system, MathematicsofComputing_NUMERICALANALYSIS, 020206 networking & telecommunications, 010103 numerical & computational mathematics, 02 engineering and technology, Krylov subspace, Solver, 01 natural sciences, Generalized minimal residual method, Rate of convergence, 0202 electrical engineering, electronic engineering, information engineering, Slow convergence, Applied mathematics, 0101 mathematics, [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

Many scientific libraries are currently based on the GMRES method as a Krylov subspace iterative method for solving large linear systems. The restarted formulation known as GMRES(m) has been extensively studied and several approaches have been proposed to reduce the negative effects due to the restarting procedure. A common effect in GMRES(m) is a slow convergence rate or a stagnation in the iterative process. In this situation, it is less attractive as a general solver in industrial applications. In this work, we propose an adaptive deflation strategy which retains useful information at time of restart to avoid stagnation in GMRES(m) and improve its convergence rate. We give a parallel implementation in the PETSc package. The provided numerical results show that this approach can be effectively used in the hybrid direct/iterative methods to solve large-scale systems.

Published
2013

27. Domain Decomposition Methods for Electromagnetic Wave Propagation Problems in Heterogeneous Media and Complex Domains

Author

Stéphane Lanteri, Ronan Perrussel, Victorita Dolean, Martin J. Gander, Mohamed El Bouajaji, Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Section de mathématiques [Genève], Université de Genève = University of Geneva (UNIGE), Ampère (AMPERE), 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)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Yunqing Huang, Ralf Kornhuber, Olof Widlund and Jinchao Xu, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Nice Sophia Antipolis (... - 2019) (UNS), and Université de Genève (UNIGE)

Subjects
Discretization, Mathematical analysis, Domain decomposition methods, 010103 numerical & computational mathematics, Mixed finite element method, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 01 natural sciences, Finite element method, 010101 applied mathematics, Discontinuous Galerkin method, 0101 mathematics, Spectral method, Boundary element method, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Extended finite element method, Mathematics
Abstract

International audience; We are interested here in the numerical modeling of time-harmonic electromagnetic wave propagation problems in irregularly shaped domains and heterogeneous media. In this context, we are naturally led to consider volume discretization methods (i.e. finite element method) as opposed to surface discretization methods (i.e. boundary element method). Most of the related existing work deals with the second order form of the time-harmonic Maxwell equations discretized by a conforming finite element method [14]. More recently, discontinuous Galerkin (DG) methods have also been considered for this purpose. While the DG method keeps almost all the advantages of a conforming finite element method (large spectrum of applications, complex geometries, etc.), the DG method has other nice properties which explain the renewed interest it gains in various domains in scientific computing: easy extension to higher order interpolation (one may increase the degree of the polynomials in the whole mesh as easily as for spectral methods and this can also be done locally), no global mass matrix to invert when solving time-domain systems of partial differential equations using an explicit time discretization scheme, easy handling of complex meshes (the mesh may be a classical conforming finite element mesh, a non-conforming one or even a mesh made of various types of elements), natural treatment of discontinuous solutions and coefficient heterogeneities and nice parallelization properties.

Published
2010

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