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A Time-Adaptive Multirate Quasi-Newton Waveform Iteration for Coupled Problems

Kotarsky, Niklas LU and Birken, Philipp LU (2025) In International Journal for Numerical Methods in Engineering 126(12).
Abstract
We consider waveform iterations for dynamical coupled problems, or more specifically, PDEs that interact through a lower-dimensional interface. We want to allow for the reuse of existing codes for the subproblems, called a partitioned approach. To improve computational efficiency, different and adaptive time steps in the subsolvers are advisable. Using so-called waveform iterations in combination with relaxation, this has been achieved for heat transfer problems earlier. Alternatively, one can use a black box method like Quasi-Newton to improve the convergence behavior. These methods have recently been combined with waveform iterations for fixed time steps. Here, we suggest an extension of the Quasi-Newton method to the time-adaptive... (More)
We consider waveform iterations for dynamical coupled problems, or more specifically, PDEs that interact through a lower-dimensional interface. We want to allow for the reuse of existing codes for the subproblems, called a partitioned approach. To improve computational efficiency, different and adaptive time steps in the subsolvers are advisable. Using so-called waveform iterations in combination with relaxation, this has been achieved for heat transfer problems earlier. Alternatively, one can use a black box method like Quasi-Newton to improve the convergence behavior. These methods have recently been combined with waveform iterations for fixed time steps. Here, we suggest an extension of the Quasi-Newton method to the time-adaptive setting and analyze its properties. We compare the proposed Quasi-Newton method with state-of-the-art solvers on a heat transfer test case and a complex mechanical Fluid-Structure interaction case, demonstrating the method's efficiency.
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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal for Numerical Methods in Engineering
volume
126
issue
12
article number
e70063
pages
11 pages
publisher
John Wiley & Sons Inc.
external identifiers
  • scopus:105008276761
ISSN
0029-5981
DOI
10.1002/nme.70063
language
English
LU publication?
yes
id
c8f47b55-91e3-44ff-81e1-074f8caa1787
date added to LUP
2025-07-18 10:52:22
date last changed
2025-11-08 14:20:07
@article{c8f47b55-91e3-44ff-81e1-074f8caa1787,
  abstract     = {{We consider waveform iterations for dynamical coupled problems, or more specifically, PDEs that interact through a lower-dimensional interface. We want to allow for the reuse of existing codes for the subproblems, called a partitioned approach. To improve computational efficiency, different and adaptive time steps in the subsolvers are advisable. Using so-called waveform iterations in combination with relaxation, this has been achieved for heat transfer problems earlier. Alternatively, one can use a black box method like Quasi-Newton to improve the convergence behavior. These methods have recently been combined with waveform iterations for fixed time steps. Here, we suggest an extension of the Quasi-Newton method to the time-adaptive setting and analyze its properties. We compare the proposed Quasi-Newton method with state-of-the-art solvers on a heat transfer test case and a complex mechanical Fluid-Structure interaction case, demonstrating the method's efficiency.<br/>}},
  author       = {{Kotarsky, Niklas and Birken, Philipp}},
  issn         = {{0029-5981}},
  language     = {{eng}},
  month        = {{06}},
  number       = {{12}},
  publisher    = {{John Wiley & Sons Inc.}},
  series       = {{International Journal for Numerical Methods in Engineering}},
  title        = {{A Time-Adaptive Multirate Quasi-Newton Waveform Iteration for Coupled Problems}},
  url          = {{http://dx.doi.org/10.1002/nme.70063}},
  doi          = {{10.1002/nme.70063}},
  volume       = {{126}},
  year         = {{2025}},
}