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arXiv · 1811.05224

A parallel solver for a preconditioned space-time boundary element method for the heat equation

Stefan Dohr·Michal Merta·Günther Of·Olaf Steinbach·Jan Zapletal
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Abstract

We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel scalability in distributed memory systems in contrast to time-stepping methods where the parallelization is usually limited to spatial dimensions. We present a parallelization technique which is based on a decomposition of the input mesh into submeshes and a distribution of the corresponding blocks of the system matrices among processors. To ensure load balancing, the distribution is based on a cylic decomposition of complete graphs. In addition, the solution of the global linear system requires the use of an efficient preconditioner. We present a robust preconditioning strategy which is based on boundary integral operators of opposite order, and extend the introduced parallel solver to the preconditioned system.

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Stefan Dohr, Michal Merta, Günther Of, Olaf Steinbach, Jan Zapletal. 2018-11-13. A parallel solver for a preconditioned space-time boundary element method for the heat equation. https://doi.org/10.1007/978-3-030-56750-7_11

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