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.

中文翻译：

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并行时空边界元法对热方程建模的半解析积分

本文针对三个空间维度的热力方程着重于边界元方法（BEM）。特别地，我们处理张量积时空网格，从而允许在时间上解析和在空间上数值解析的正交方案。可以通过从三维固定问题中获知的标准BEM技术来处理空间积分。论文的贡献是双重的。首先，我们提供了BEM矩阵的组装和表示公式的评估所必需的热核的时间反导数。其次，在公开可用的Bestesta库中实现了所提出的方法，使研究人员可以立即重复使用公式和BEM例程。通过在HPC环境中进行的数值实验验证了结果。