Time adaptive waveform methods for dynamic multiphysics problems (Philipp Birken, University of Lund)

27.02.2024 14:00

We discuss partitioned time-integration of dynamic multiphysics problems, which commonly exhibit a multiscale behavior, requiring independent time-grids. The ideal method for solving these problems allows independent and adaptive time-grids, higher order time-discretizations, is fast and robust, and allows the coupling of existing subsolvers, executed in parallel.

Waveform relaxation (WR) methods can potentially have all of these properties. These iterate on continuous-in-time interface functions, obtained via suitable interpolation. This way, one can allow for time adaptivity in the subsolvers. We present a fast and highly robust, second order in time, adaptive WR method. Basis is a Dirichlet-Neumann coupling at the interface, combined with an acceleration technique based on Quasi-Newton methods. As a leading example, we use coupled heat equations and discuss existing convergence results.

Numerical results demonstrate the robustness and efficiency of the method for different multiphysics problems.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

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