A parallel space–time boundary element method for the heat equation

Stefan Dohr, Jan Zapletal, Günther Of, Michal Merta, Michal Kravcenko

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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.

Originalspracheenglisch
FachzeitschriftComputers & mathematics with applications
Frühes Online-Datum2019
DOIs
PublikationsstatusElektronische Veröffentlichung vor Drucklegung. - 2019

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Boundary integral equations
Boundary element method
Heat Equation
Boundary Elements
Program processors
Scalability
Space-time
Decomposition
Data storage equipment
Vectorization
Load Balance
Boundary Integral Equations
Vertex of a graph
Shared Memory
Complete Graph
Parallelization
Parallelism
Speedup
Experiments
Mesh

Schlagwörter

    ASJC Scopus subject areas

    • Numerische Mathematik
    • !!Computational Mathematics
    • !!Computational Theory and Mathematics
    • !!Modelling and Simulation

    Fields of Expertise

    • Information, Communication & Computing

    Treatment code (Nähere Zuordnung)

    • Basic - Fundamental (Grundlagenforschung)

    Dies zitieren

    A parallel space–time boundary element method for the heat equation. / Dohr, Stefan; Zapletal, Jan; Of, Günther; Merta, Michal; Kravcenko, Michal.

    in: Computers & mathematics with applications, 2019.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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    AB - 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.

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