Multiscale Methods for Wave Propagation in Heterogeneous Media Over Long Time
2012 (English)In: Numerical Analysis of Multiscale Computations / [ed] Björn Engquist, Olof Runborg, Yen-Hsi R. Tsai, Springer Verlag , 2012, 167-186 p.Chapter in book (Other academic)
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.
Place, publisher, year, edition, pages
Springer Verlag , 2012. 167-186 p.
, Lecture Notes in Computational Science and Engineering, ISSN 1439-7358
IdentifiersURN: urn:nbn:se:kth:diva-48058DOI: 10.1007/978-3-642-21943-6_8ISBN: 978-3-642-21942-9OAI: oai:DiVA.org:kth-48058DiVA: diva2:456747
FunderSwedish e‐Science Research Center
QC 201111162011-11-162011-11-152013-04-09Bibliographically approved