@Article{EAJAM-6-278,
author = {Sidi-Mahmoud Kaber, Amine Loumi and Philippe Parnaudeau},
title = {Parallel Solution of Linear Systems},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {6},
number = {3},
pages = {278--289},
abstract = {<p style="text-align: justify;">Computational scientists generally seek more 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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.210715.250316a},
url = {http://global-sci.org/intro/article_detail/eajam/10798.html}
}