A parallel space–time boundary element method for the heat equation. (1st November 2019)

• Record Type: Journal Article
• Authors: Dohr, Stefan; Zapletal, Jan; Of, Günther; Merta, Michal; Kravčenko, Michal
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 9(2019)
• Page Start: 2852
• Page End: 2866
• Publication Date: 2019-11-01
• Subjects: Space–time boundary element method -- Heat equation -- Parallelization -- Vectorization; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.12.031
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper we introduce a new parallel solver for the weakly singular space–time boundary integral equation for the heat equation. The space–time boundary mesh is decomposed into a given number of submeshes. Pairs of the submeshes represent dense blocks in the system matrices, which are distributed among computational nodes by an algorithm based on a cyclic decomposition of complete graphs ensuring load balance. In addition, we employ vectorization and threading in shared memory to ensure intra-node efficiency. We present scalability experiments on different CPU architectures to evaluate the performance of the proposed parallelization techniques. All levels of parallelism allow us to tackle large problems and lead to an almost optimal speedup.