Publication Details

Parallel solution of parabolic partial differential equation using higher-order method

NEČASOVÁ Gabriela and ŠÁTEK Václav. Parallel solution of parabolic partial differential equation using higher-order method. In: 20th International Conference of Numerical Analysis and Applied Mathematics. Heraklion: American Institute of Physics, 2024, pp. 1-4. ISSN 0094-243X.

Czech title

Paralelní řešení parabolické parciální diferenciální rovnice metodou vyššího řádu

Type

conference paper

Language

english

Authors

Nečasová Gabriela, Ing., Ph.D. (DITS FIT BUT)
Šátek Václav, Ing., Ph.D. (DITS FIT BUT)

Keywords

parabolic partial differential equation, method of lines, higher-order numerical method, Taylor series, parallel solution, PETSc

Abstract

The article focuses on the parallel numerical solution of parabolic partial differential equation. The method of lines is used for the discretization of the problem, which leads to the large system of ordinary differential equations. The resulting system of ordinary differential equations is solved by higher-order numerical method based on Taylor series. The numerical solution is compared with the state-of-the-art PETSc solvers. The results show that Taylor-series based methods can significantly overperform the state-of-the-art solvers.

Published

2024

Pages

1-4

Journal

AIP Conference Proceedings - American Institute of Physics, no. 3094, ISSN 0094-243X

Proceedings

20th International Conference of Numerical Analysis and Applied Mathematics

Conference

20th International Conference of Numerical Analysis and Applied Mathematics, Crete, GR

Publisher

American Institute of Physics

Place

Heraklion, GR

DOI

10.1063/5.0212373

UT WoS

001244923000289

EID Scopus

2-s2.0-85196497910

BibTeX

@INPROCEEDINGS{FITPUB12780,
   author = "Gabriela Ne\v{c}asov\'{a} and V\'{a}clav \v{S}\'{a}tek",
   title = "Parallel solution of parabolic partial differential equation using higher-order method",
   pages = "1--4",
   booktitle = "20th International Conference of Numerical Analysis and Applied Mathematics",
   journal = "AIP Conference Proceedings - American Institute of Physics",
   number = 3094,
   year = 2024,
   location = "Heraklion, GR",
   publisher = "American Institute of Physics",
   ISSN = "0094-243X",
   doi = "10.1063/5.0212373",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/12780"
}