A time adaptive multirate Dirichlet–Neumann waveform relaxation method for heterogeneous coupled heat equations
(2023) In ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 103(11).- Abstract
We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler time integration, we analytically determine optimal relaxation parameters for the fully discrete scheme. We test the robustness of the relaxation parameters on the second order multirate method in 2D. DNWR is shown to be very robust and consistently yielding fast convergence rates, whereas the closely related Neumann-Neumann Waveform relaxtion (NNWR) method is slower or even diverges. The waveform approach naturally allows for different timesteps in the subproblems. In a performance comparison for DNWR,... (More)
We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler time integration, we analytically determine optimal relaxation parameters for the fully discrete scheme. We test the robustness of the relaxation parameters on the second order multirate method in 2D. DNWR is shown to be very robust and consistently yielding fast convergence rates, whereas the closely related Neumann-Neumann Waveform relaxtion (NNWR) method is slower or even diverges. The waveform approach naturally allows for different timesteps in the subproblems. In a performance comparison for DNWR, the time-adaptive method dominates the multirate method due to automatically finding suitable stepsize ratios. Overall, we obtain a fast, robust, multirate and time adaptive partitioned solver for unsteady conjugate heat transfer.
(Less)
- author
- Meisrimel, Peter LU ; Monge, Azahar LU and Birken, Philipp LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- in
- ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
- volume
- 103
- issue
- 11
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- scopus:85161055313
- ISSN
- 0044-2267
- DOI
- 10.1002/zamm.202100328
- language
- English
- LU publication?
- yes
- id
- 63bcc0de-3d6d-43d7-a53b-5d97ea4a3507
- date added to LUP
- 2023-08-30 14:07:38
- date last changed
- 2024-01-09 15:46:38
@article{63bcc0de-3d6d-43d7-a53b-5d97ea4a3507,
abstract = {{<p>We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler time integration, we analytically determine optimal relaxation parameters for the fully discrete scheme. We test the robustness of the relaxation parameters on the second order multirate method in 2D. DNWR is shown to be very robust and consistently yielding fast convergence rates, whereas the closely related Neumann-Neumann Waveform relaxtion (NNWR) method is slower or even diverges. The waveform approach naturally allows for different timesteps in the subproblems. In a performance comparison for DNWR, the time-adaptive method dominates the multirate method due to automatically finding suitable stepsize ratios. Overall, we obtain a fast, robust, multirate and time adaptive partitioned solver for unsteady conjugate heat transfer.</p>}},
author = {{Meisrimel, Peter and Monge, Azahar and Birken, Philipp}},
issn = {{0044-2267}},
language = {{eng}},
number = {{11}},
publisher = {{John Wiley & Sons Inc.}},
series = {{ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik}},
title = {{A time adaptive multirate Dirichlet–Neumann waveform relaxation method for heterogeneous coupled heat equations}},
url = {{http://dx.doi.org/10.1002/zamm.202100328}},
doi = {{10.1002/zamm.202100328}},
volume = {{103}},
year = {{2023}},
}