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.
@article{arxiv.1811.05224,
title = {A parallel solver for a preconditioned space-time boundary element method for the heat equation},
author = {Stefan Dohr and Michal Merta and Günther Of and Olaf Steinbach and Jan Zapletal},
journal= {arXiv preprint arXiv:1811.05224},
year = {2021}
}
Comments
Submitted for publication in the proceedings of the 25th International Conference on Domain Decomposition Methods