Numerical Upscaling for Wave Equations with Time-Dependent Multiscale Coefficients
Abstract.
In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational multiscale method in the spirit of the localized orthogonal decomposition in space with a backward Euler scheme in time. We show optimal convergence rates in space and time beyond the assumptions of spatial periodicity or scale separation of the coefficients. Further, we propose an adaptive update strategy for the time-dependent multiscale basis. Numerical experiments illustrate the theoretical results and showcase the practicability of the adaptive update strategy.
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© 2022 Society for Industrial and Applied Mathematics.
History
Submitted: 2 August 2021
Accepted: 10 May 2022
Published online: 26 October 2022
Keywords
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Funding Information
Deutsche Forschungsgemeinschaft (DFG): 258734477 - SFB 1173
Baden-Wurttemberg Ministry of Science
Klaus-Tschira Foundation
The work of the authors was supported by German Research Foundation (DFG) project 258734477 - SFB 1173, the Federal Ministry of Education and Research (BMBF), and the Baden-Württemberg Ministry of Science as part of the Excellence Strategy of the German Federal and State Governments. The work of the second author was also supported by the Klaus-Tschira Foundation.
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- A higher order multiscale method for the wave equationIMA Journal of Numerical Analysis, Vol. 9 | 19 September 2024
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