### 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.

Language | English |
---|---|

Journal | Computers & mathematics with applications |

Early online date | 2019 |

DOIs | |

Status | E-pub ahead of print - 2019 |

### Fingerprint

### 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

*Computers & mathematics with applications*. https://doi.org/10.1016/j.camwa.2018.12.031

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

Research output: Contribution to journal › Article › Research › peer-review

*Computers & mathematics with applications*. https://doi.org/10.1016/j.camwa.2018.12.031

}

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

T2 - Computers & mathematics with applications

JF - Computers & mathematics with applications

SN - 0898-1221

ER -