Volume 6, Issue 3
Parallel Solution of Linear Systems

Sidi-Mahmoud Kaber, Amine Loumi & Philippe Parnaudeau

East Asian J. Appl. Math., 6 (2016), pp. 278-289.

Published online: 2018-02

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  • Abstract

Computational scientists generally seekmore accurate results in shorter times, and to achieve this a knowledge of evolving programming paradigms and hardware is important. In particular, optimising solvers for linear systems is a major challenge in scientific computation, and numerical algorithms must be modified or new ones created to fully use the parallel architecture of new computers. Parallel space discretisation solvers for Partial Differential Equations (PDE) such as Domain Decomposition Methods (DDM) are efficient and well documented. At first glance, parallelisation seems to be inconsistent with inherently sequential time evolution, but parallelisation is not limited to space directions. In this article, we present a new and simple method for time parallelisation, based on partial fraction decomposition of the inverse of some special matrices. We discuss its application to the heat equation and some limitations, in associated numerical experiments.

  • Keywords

Parallel computation, numerical linear algebra.

  • AMS Subject Headings

65Y05, 65F05, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-278, author = {}, title = {Parallel Solution of Linear Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {3}, pages = {278--289}, abstract = {

Computational scientists generally seekmore accurate results in shorter times, and to achieve this a knowledge of evolving programming paradigms and hardware is important. In particular, optimising solvers for linear systems is a major challenge in scientific computation, and numerical algorithms must be modified or new ones created to fully use the parallel architecture of new computers. Parallel space discretisation solvers for Partial Differential Equations (PDE) such as Domain Decomposition Methods (DDM) are efficient and well documented. At first glance, parallelisation seems to be inconsistent with inherently sequential time evolution, but parallelisation is not limited to space directions. In this article, we present a new and simple method for time parallelisation, based on partial fraction decomposition of the inverse of some special matrices. We discuss its application to the heat equation and some limitations, in associated numerical experiments.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.210715.250316a}, url = {http://global-sci.org/intro/article_detail/eajam/10798.html} }
TY - JOUR T1 - Parallel Solution of Linear Systems JO - East Asian Journal on Applied Mathematics VL - 3 SP - 278 EP - 289 PY - 2018 DA - 2018/02 SN - 6 DO - http://dor.org/10.4208/eajam.210715.250316a UR - https://global-sci.org/intro/eajam/10798.html KW - Parallel computation, numerical linear algebra. AB -

Computational scientists generally seekmore accurate results in shorter times, and to achieve this a knowledge of evolving programming paradigms and hardware is important. In particular, optimising solvers for linear systems is a major challenge in scientific computation, and numerical algorithms must be modified or new ones created to fully use the parallel architecture of new computers. Parallel space discretisation solvers for Partial Differential Equations (PDE) such as Domain Decomposition Methods (DDM) are efficient and well documented. At first glance, parallelisation seems to be inconsistent with inherently sequential time evolution, but parallelisation is not limited to space directions. In this article, we present a new and simple method for time parallelisation, based on partial fraction decomposition of the inverse of some special matrices. We discuss its application to the heat equation and some limitations, in associated numerical experiments.

Sidi-Mahmoud Kaber, Amine Loumi & Philippe Parnaudeau. (2020). Parallel Solution of Linear Systems. East Asian Journal on Applied Mathematics. 6 (3). 278-289. doi:10.4208/eajam.210715.250316a
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