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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.
Original language | English |
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Pages (from-to) | 156-170 |
Number of pages | 15 |
Journal | Computers & Mathematics with Applications |
Volume | 103 |
DOIs | |
Publication status | Published - 1 Dec 2021 |
Keywords
- Boundary element method
- Space-time
- Heat equation
- Integration
- Parallelisation
ASJC Scopus subject areas
- Numerical Analysis
Fields of Expertise
- Information, Communication & Computing
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Dive into the research topics of 'Semi-analytic integration for a parallel space-time boundary element method modelling the heat equation'. Together they form a unique fingerprint.Projects
- 1 Finished
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FWF - Besthea - Space-time boundary element methods for the heat equation
Of, G. & Watschinger, R.
1/03/19 → 30/11/22
Project: Research project