Multiscale Methods for Wave Propagation in Heterogeneous Media Over Long Time

Conference paper

DOI: 10.1007/978-3-642-21943-6_8

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 82)
Cite this paper as:
Engquist B., Holst H., Runborg O. (2012) Multiscale Methods for Wave Propagation in Heterogeneous Media Over Long Time. In: Engquist B., Runborg O., Tsai YH. (eds) Numerical Analysis of Multiscale Computations. Lecture Notes in Computational Science and Engineering, vol 82. Springer, Berlin, Heidelberg

Abstract

Multiscale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods for multiscale wave propagation in the framework of the heterogeneous multiscale method (HMM). The numerical methods couple simulations on macro- and microscales for problems with rapidly oscillating coefficients. The complexity of the new method is significantly lower than that of traditional techniques with a computational cost that is essentially independent of the smallest scale, when computing solutions at a fixed time and accuracy. We show numerical examples of the HMM applied to long time integration of wave propagation problems in both periodic and non-periodic medium. In both cases our HMM accurately captures the dispersive effects that occur. We also give a stability proof for the HMM, when it is applied to long time wave propagation problems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Numerical AnalysisCSC and Swedish e-Science Research Center (SeRC) KTHStockholmSweden
  2. 2.Department of Mathematics and Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA
  3. 3.Department of Numerical AnalysisCSC, KTHStockholmSweden

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