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Computational scattering in complex multiscale media

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MWSW03 - Computational methods for multiple scattering

Scattering in spatially varying media can lead to a plethora of interesting phenomena and their numerical simulation still poses severe challenges. At the example of the Helmholtz equation, we present the Localized Orthogonal Decomposition (LOD), a computational multiscale method able to cope with rather unstructured coefficients and high-frequency regimes. The talk focuses on strategies for two additional challenges, namely high-contrast and nonlinear media. For the high-contrast case, we present a suitable adaption of the LOD , discuss error estimates and show numerical examples illustrating resonance effects from the high contrast. For the nonlinear Helmholtz equation, we propose an adaptive iterative multiscale approximation inspired by the LOD and present its a priori error analysis.

This talk is part of the Isaac Newton Institute Seminar Series series.

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