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

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

Research output: Contribution to journalArticleResearchpeer-review

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.

Original languageEnglish
JournalComputers & mathematics with applications
Early online date2019
DOIs
Publication statusE-pub ahead of print - 2019

Fingerprint

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

Keywords

  • Heat equation
  • Parallelization
  • Space–time boundary element method
  • Vectorization

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Modelling and Simulation

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

Cite this

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.

Research output: Contribution to journalArticleResearchpeer-review

@article{94173dcb2ed34099a4929f5e18e82457,
title = "A parallel space–time boundary element method for the heat equation",
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.",
keywords = "Heat equation, Parallelization, Space–time boundary element method, Vectorization",
author = "Stefan Dohr and Jan Zapletal and G{\"u}nther Of and Michal Merta and Michal Kravcenko",
year = "2019",
doi = "10.1016/j.camwa.2018.12.031",
language = "English",
journal = "Computers & mathematics with applications",
issn = "0898-1221",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - A parallel space–time boundary element method for the heat equation

AU - Dohr, Stefan

AU - Zapletal, Jan

AU - Of, Günther

AU - Merta, Michal

AU - Kravcenko, Michal

PY - 2019

Y1 - 2019

N2 - 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.

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.

KW - Heat equation

KW - Parallelization

KW - Space–time boundary element method

KW - Vectorization

UR - http://www.scopus.com/inward/record.url?scp=85059669009&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2018.12.031

DO - 10.1016/j.camwa.2018.12.031

M3 - Article

JO - Computers & mathematics with applications

JF - Computers & mathematics with applications

SN - 0898-1221

ER -