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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computational high frequency scattering from high-contrast heterogeneous media
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by Daniel Peterseim and Barbara Verfürth HTML | PDF
Math. Comp. 89 (2020), 2649-2674 Request permission

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
  • Email: daniel.peterseim@math.uni-augsburg.de
  • Barbara Verfürth
  • Affiliation: Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, D-86159 Augsburg, Germany
  • Email: barbara.verfuerth@math.uni-augsburg.de
  • 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.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 2649-2674
  • MSC (2010): Primary 35J05, 65N12, 65N15, 65N30
  • DOI: https://doi.org/10.1090/mcom/3529
  • MathSciNet review: 4136542