Semi-analytic integration for a parallel space-time boundary element method modelling the heat equation. (1st December 2021)

• Record Type: Journal Article
• Authors: Zapletal, Jan; Watschinger, Raphael; Of, Günther; Merta, Michal
• Is Part Of: Computers & mathematics with applications. Volume 103(2021)
• Page Start: 156
• Page End: 170
• Publication Date: 2021-12-01
• Subjects: Boundary element method -- Space-time -- Heat equation -- Integration -- Parallelisation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.10.025
• Languages: English
• ISSNs: 0898-1221

Abstract

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.