Optimized Schwarz Waveform Relaxation method for a parabolic interface problem with quadratic jump (Jing Lyu)

16.12.2025 14:00 – 15:00

We focus on the heterogeneous optimized Schwarz waveform relaxation (OSWR) algorithm for solving a parabolic interface problem coupled with nonlinear (quadratic) interface jump conditions. This mathematical model problems was introduced to describe the concentration of an ion between the aqueous solution and the adjoining polymeric membrane. To handle the nonlinearity, we establish flexible linear transmission conditions used in the heterogeneous OSWR, including the standard Robin, the scaled Robin, and the two-sided Robin conditions. The free parameters involved are then optimized in a Fourier analysis framework, and the corresponding convergence rate estimates are obtained in an asymptotic sense. Our study reveals that the stronger the heterogeneity contrast is, the faster the algorithm converges, where the new heterogeneity parameter consists not only of the diffusion coefficient and the width of the media, but also the interface parameters. Particularly, the two-sided Robin condition is time mesh independent. Finally, we illustrate our theoretical results using several numerical experiments. Our OSWR algorithm can also be extended to many other multi-physics problems that are non-linearly coupled along the interface.

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

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