Parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditions
In this paper, three-dimensional parabolic and pseudo-parabolic equations with classical, periodic and nonlocal boundary conditions are approximated by the full approximation backward Euler method, locally one dimensional and Douglas ADI splitting schemes. The stability with respect to initial cond...
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doaj-887487729258409abe9e8462c77244032020-11-25T02:04:07ZengVilnius University PressNonlinear Analysis1392-51132335-89632014-10-0119310.15388/NA.2014.3.5Parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditionsRaimondas Čiegis0Olga Suboč1Andrej Bugajev2Vilnius Gediminas Technical University, LithuaniaVilnius Gediminas Technical University, LithuaniaVilnius Gediminas Technical University, Lithuania In this paper, three-dimensional parabolic and pseudo-parabolic equations with classical, periodic and nonlocal boundary conditions are approximated by the full approximation backward Euler method, locally one dimensional and Douglas ADI splitting schemes. The stability with respect to initial conditions is investigated. We note that the stability of the proposed numerical algorithms can be proved only if the matrix of discrete operator can be diagonalized and eigenvectors make a complete basis system. Parallel versions of all algorithms are constructed and scalability analysis is done. It is shown that discrete one-dimensional problems with periodic and nonlocal boundary conditions can be efficiently solved with similar modifications of the parallel Wang algorithm. http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13642parallel algorithmsthree-dimensional paraboloic and pseudoparabolic equationsfinite-difference method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Raimondas Čiegis Olga Suboč Andrej Bugajev |
spellingShingle |
Raimondas Čiegis Olga Suboč Andrej Bugajev Parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditions Nonlinear Analysis parallel algorithms three-dimensional paraboloic and pseudoparabolic equations finite-difference method |
author_facet |
Raimondas Čiegis Olga Suboč Andrej Bugajev |
author_sort |
Raimondas Čiegis |
title |
Parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditions |
title_short |
Parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditions |
title_full |
Parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditions |
title_fullStr |
Parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditions |
title_full_unstemmed |
Parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditions |
title_sort |
parallel algorithms for three-dimensional parabolic and pseudoparabolic problems with different boundary conditions |
publisher |
Vilnius University Press |
series |
Nonlinear Analysis |
issn |
1392-5113 2335-8963 |
publishDate |
2014-10-01 |
description |
In this paper, three-dimensional parabolic and pseudo-parabolic equations with classical, periodic and nonlocal boundary conditions are approximated by the full approximation backward Euler method, locally one dimensional and Douglas ADI splitting schemes. The stability with respect to initial conditions is investigated. We note that the stability of the proposed numerical algorithms can be proved only if the matrix of discrete operator can be diagonalized and eigenvectors make a complete basis system.
Parallel versions of all algorithms are constructed and scalability analysis is done. It is shown that discrete one-dimensional problems with periodic and nonlocal boundary conditions can be efficiently solved with similar modifications of the parallel Wang algorithm.
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topic |
parallel algorithms three-dimensional paraboloic and pseudoparabolic equations finite-difference method |
url |
http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13642 |
work_keys_str_mv |
AT raimondasciegis parallelalgorithmsforthreedimensionalparabolicandpseudoparabolicproblemswithdifferentboundaryconditions AT olgasuboc parallelalgorithmsforthreedimensionalparabolicandpseudoparabolicproblemswithdifferentboundaryconditions AT andrejbugajev parallelalgorithmsforthreedimensionalparabolicandpseudoparabolicproblemswithdifferentboundaryconditions |
_version_ |
1724944539919056896 |