Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 103, Issue -, Pages 156-170Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2021.10.025
Keywords
Boundary element method; Space-time; Heat equation; Integration; Parallelisation
Categories
Funding
- Czech Science Foundation [19-29698L]
- Austrian Science Fund (FWF) [I 4033-N32]
- Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development, and Innovations project e-INFRA [CZ - LM2018140]
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The paper introduces the application of the boundary element method for the heat equation in three spatial dimensions, with results validated through numerical experiments in an HPC environment.
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.
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