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.

翻译：提交的论文侧重于三个空间层面热方程式的边界要素方法(BEM),特别是,我们处理的是在空间时间和数值方面允许等离子体分析方法的气压产品时空介质,空间构件可以通过三个维静止问题中已知的标准BEM技术处理,论文的贡献是双重的。首先,我们提供BEM矩阵组装和评估代表公式所需的热内核的时间抗降解剂。第二,在公开开放的图书馆Besthea实施了所介绍的方法,允许研究人员直接再利用公式和BEM常规。结果通过HPC环境中的数值实验得到验证。