Semi-analytic integration for a parallel space-time boundary element method modelling the heat equation

Jan Zapletal*, Raphael Watschinger, Günther Of, Michal Merta

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

Abstract

The presented paper concentrates on the boundary element method (BEM) for the heat equation in three spatial dimensions. In particular, we deal with tensor product space-time meshes allowing for quadrature schemes analytic in time and numerical in space. The spatial integrals can be treated by standard BEM techniques known from three dimensional stationary problems. The contribution of the paper is twofold. First, we provide temporal antiderivatives of the heat kernel necessary for the assembly of BEM matrices and the evaluation of the representation formula. Secondly, the presented approach has been implemented in a publicly available library besthea allowing researchers to reuse the formulae and BEM routines straightaway. The results are validated by numerical experiments in an HPC environment.
Originalspracheenglisch
Seiten (von - bis)156-170
Seitenumfang15
FachzeitschriftComputers & Mathematics with Applications
Jahrgang103
DOIs
PublikationsstatusVeröffentlicht - 1 Dez 2021

ASJC Scopus subject areas

  • Numerische Mathematik

Fields of Expertise

  • Information, Communication & Computing

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