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PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING
Edited by: P. Iványi, B.H.V. Topping and G. Várady
Using Discrete Mathematics to Optimize Parallelism in Boundary Element Method
M. Kravčenko1,2, M. Merta1 and J. Zapletal1,2
1 IT4Innovations, VSB-Technical University of Ostrava, Czech Republic
M. Kravcenko, M. Merta, J. Zapletal, "Using Discrete Mathematics to Optimize Parallelism in Boundary Element Method", in P. Iványi, B.H.V. Topping, G. Várady, (Editors), "Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 2, 2017. doi:10.4203/ccp.111.2
Keywords: distributed parallelism, cyclic decomposition of complete graphs, boundary element method, high performance computing, adaptive cross approximation.
In this work we present an approach for distribution of system matrices occurring in the fast boundary element method (BEM) among computational nodes in order to accelerate their assembly. An underlying mesh is decomposed into a given number of submeshes, pairs of which represent blocks in a system matrix. The aim is to distribute the submeshes among computational nodes in a way which minimizes the amount of mesh parts owned by a single process and which inherently defines the distribution of the system matrix. Additionally, each process owns exactly one diagonal block since their assembly is typically the most time consuming in the fast BEM. The distribution of submeshes is based on a cyclic decomposition of complete graphs into dense subgraphs. We briefly present the method, a boundary element environment it is implemented in and provide results of numerical experiments.
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