Publication Details

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

NEČASOVÁ, G.; ŠÁTEK, V. Parallel solution of parabolic partial differential equation using higher-order method. In 20th International Conference of Numerical Analysis and Applied Mathematics. AIP conference proceedings. Heraklion: American Institute of Physics, 2024. p. 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)
Šátek Václav, Ing., Ph.D. (DITS)

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, 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

DOI

10.1063/5.0212373

UT WoS

001244923000289

EID Scopus

2-s2.0-85196497910

BibTeX

@inproceedings{BUT193183,
  author="Gabriela {Nečasová} and Václav {Šátek}",
  title="Parallel solution of parabolic partial differential equation using higher-order method",
  booktitle="20th International Conference of Numerical Analysis and Applied Mathematics",
  year="2024",
  journal="AIP conference proceedings",
  number="3094",
  pages="1--4",
  publisher="American Institute of Physics",
  address="Heraklion",
  doi="10.1063/5.0212373",
  issn="0094-243X"
}