Detail publikačního výsledku

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

NEČASOVÁ, G.; ŠÁTEK, V.

Original Title

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

English Title

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

Type

Paper in proceedings (conference paper)

Original 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.

English 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.

Keywords

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

Key words in English

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

Authors

NEČASOVÁ, G.; ŠÁTEK, V.

RIV year

2025

Released

07.06.2024

Publisher

American Institute of Physics

Location

Heraklion

Book

20th International Conference of Numerical Analysis and Applied Mathematics

ISBN

0094-243X

Periodical

AIP conference proceedings

Number

3094

State

United States of America

Pages from

1

Pages to

4

Pages count

4

Full text in the Digital Library

http://hdl.handle.net/

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"
}