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Mathematics of Computation

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Computational high frequency scattering from high-contrast heterogeneous media

Authors: Daniel Peterseim and Barbara Verfürth
Journal: Math. Comp. 89 (2020), 2649-2674
MSC (2010): Primary 35J05, 65N12, 65N15, 65N30
Published electronically: March 9, 2020
MathSciNet review: 4136542
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Abstract: This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to unusual wave scattering and absorption, which are interesting and relevant from a physical viewpoint, for instance, in the case of crystals with defects. We present a computational multiscale method in the spirit of the Localized Orthogonal Decomposition and provide its rigorous a priori error analysis for two-phase diffusion coefficients that vary between $1$ and very small values. Special attention is paid to the extreme regimes of high frequency, high contrast, and their previously unexplored coexistence. A series of numerical experiments confirms the theoretical results and demonstrates the ability of the multiscale approach to efficiently capture relevant physical phenomena.

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Additional Information

Daniel Peterseim
Affiliation: Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, D-86159 Augsburg, Germany
MR Author ID: 848711

Barbara Verfürth
Affiliation: Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, D-86159 Augsburg, Germany

Keywords: Multiscale method, wave propagation, Helmholtz equation, high contrast, photonic crystal
Received by editor(s): February 27, 2019
Received by editor(s) in revised form: October 16, 2019, and January 26, 2020
Published electronically: March 9, 2020
Additional Notes: The authors would also like to acknowledge the kind hospitality of the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), where part of this research was developed under the frame of the thematic programme Numerical Analysis of Complex PDE Models in the Sciences.
Article copyright: © Copyright 2020 American Mathematical Society