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

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 stand...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 103; pp. 156 - 170
Main Authors Zapletal, Jan, Watschinger, Raphael, Of, Günther, Merta, Michal
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.12.2021
Elsevier BV
Subjects
Boundary element method
Heat equation
Integration
Mathematical analysis
Parallelisation
Space-time
Spacetime
Tensors
Thermodynamics
Space-time
Integration
Heat equation
Parallelisation
Boundary element method
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2021.10.025