129 research outputs found
Structures and waves in a nonlinear heat-conducting medium
The paper is an overview of the main contributions of a Bulgarian team of
researchers to the problem of finding the possible structures and waves in the
open nonlinear heat conducting medium, described by a reaction-diffusion
equation. Being posed and actively worked out by the Russian school of A. A.
Samarskii and S.P. Kurdyumov since the seventies of the last century, this
problem still contains open and challenging questions.Comment: 23 pages, 13 figures, the final publication will appear in Springer
Proceedings in Mathematics and Statistics, Numerical Methods for PDEs:
Theory, Algorithms and their Application
Performance Analysis of Effective Methods for Solving Band Matrix SLAEs after Parabolic Nonlinear PDEs
This paper presents an experimental performance study of implementations of
three different types of algorithms for solving band matrix systems of linear
algebraic equations (SLAEs) after parabolic nonlinear partial differential
equations -- direct, symbolic, and iterative, the former two of which were
introduced in Veneva and Ayriyan (arXiv:1710.00428v2). An iterative algorithm
is presented -- the strongly implicit procedure (SIP), also known as the Stone
method. This method uses the incomplete LU (ILU(0)) decomposition. An
application of the Hotelling-Bodewig iterative algorithm is suggested as a
replacement of the standard forward-backward substitutions. The upsides and the
downsides of the SIP method are discussed. The complexity of all the
investigated methods is presented. Performance analysis of the implementations
is done using the high-performance computing (HPC) clusters "HybriLIT" and
"Avitohol". To that purpose, the experimental setup and the results from the
conducted computations on the individual computer systems are presented and
discussed.Comment: 10 pages, 2 figure
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