Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Waveform Relaxation with Asynchronous Time-integration

Meisrimel, Peter LU and Birken, Philipp LU (2022) In ACM Transactions on Mathematical Software 48(4).
Abstract

We consider Waveform Relaxation (WR) methods for parallel and partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high time-integration orders. Classical WR methods such as Jacobi or Gauss-Seidel WR are typically either parallel or converge quickly.We present a novel parallel WR method utilizing asynchronous communication techniques to get both properties. Classical WR methods exchange discrete functions after time-integration of a subproblem. We instead asynchronously exchange time-point solutions during time-integration and directly incorporate all new information in the interpolants. We show both continuous and... (More)

We consider Waveform Relaxation (WR) methods for parallel and partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high time-integration orders. Classical WR methods such as Jacobi or Gauss-Seidel WR are typically either parallel or converge quickly.We present a novel parallel WR method utilizing asynchronous communication techniques to get both properties. Classical WR methods exchange discrete functions after time-integration of a subproblem. We instead asynchronously exchange time-point solutions during time-integration and directly incorporate all new information in the interpolants. We show both continuous and time-discrete convergence in a framework that generalizes existing linear WR convergence theory. An algorithm for choosing optimal relaxation in our new WR method is presented. Convergence is demonstrated in two conjugate heat transfer examples. Our new method shows an improved performance over classical WR methods. In one example, we show a partitioned coupling of the compressible Euler equations with a nonlinear heat equation, with subproblems implemented using the open source libraries DUNE and FEniCS.

(Less)
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Asynchronous iteration, coupled problems, dynamic iteration, thermal fluid-structure interaction, waveform relaxation
in
ACM Transactions on Mathematical Software
volume
48
issue
4
article number
45
publisher
Association for Computing Machinery (ACM)
external identifiers
  • scopus:85151556116
ISSN
0098-3500
DOI
10.1145/3569578
language
English
LU publication?
yes
id
a21c8194-762b-49ca-a854-be4f82564f10
date added to LUP
2023-05-29 14:38:28
date last changed
2023-05-29 14:38:28
@article{a21c8194-762b-49ca-a854-be4f82564f10,
  abstract     = {{<p>We consider Waveform Relaxation (WR) methods for parallel and partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high time-integration orders. Classical WR methods such as Jacobi or Gauss-Seidel WR are typically either parallel or converge quickly.We present a novel parallel WR method utilizing asynchronous communication techniques to get both properties. Classical WR methods exchange discrete functions after time-integration of a subproblem. We instead asynchronously exchange time-point solutions during time-integration and directly incorporate all new information in the interpolants. We show both continuous and time-discrete convergence in a framework that generalizes existing linear WR convergence theory. An algorithm for choosing optimal relaxation in our new WR method is presented. Convergence is demonstrated in two conjugate heat transfer examples. Our new method shows an improved performance over classical WR methods. In one example, we show a partitioned coupling of the compressible Euler equations with a nonlinear heat equation, with subproblems implemented using the open source libraries DUNE and FEniCS.</p>}},
  author       = {{Meisrimel, Peter and Birken, Philipp}},
  issn         = {{0098-3500}},
  keywords     = {{Asynchronous iteration; coupled problems; dynamic iteration; thermal fluid-structure interaction; waveform relaxation}},
  language     = {{eng}},
  number       = {{4}},
  publisher    = {{Association for Computing Machinery (ACM)}},
  series       = {{ACM Transactions on Mathematical Software}},
  title        = {{Waveform Relaxation with Asynchronous Time-integration}},
  url          = {{http://dx.doi.org/10.1145/3569578}},
  doi          = {{10.1145/3569578}},
  volume       = {{48}},
  year         = {{2022}},
}