Multiscale Methods for One Dimensional Wave Propagation with High Frequency Initial Data
2011 (English)Report (Other academic)
High frequency wave propagation problems are computationally costly to solve by traditional techniques because the short wavelength must be well represented over a domain determined by the largest scales of the problem. We have developed and analyzed a new numerical method for high frequency wave propagation in the framework of heterogeneous multiscale methods, closely related to the analytical method of geometrical optics. The numerical method couples simulations on macro- and micro-scales for problems with highly oscillatory initial data. The method has a computational complexity essentially independent of the wavelength. We give one numerical example with a sharp but regular jump in velocity on the microscopic scale for which geometrical optics fails but our HMM gives correct results. We briefly discuss how the method can be extended to higher dimensional problems.
Place, publisher, year, edition, pages
KTH Royal Institute of Technology , 2011. , 24 p.
Trita-NA, ISSN 0348-2952 ; 2011:6
IdentifiersURN: urn:nbn:se:kth:diva-48068OAI: oai:DiVA.org:kth-48068DiVA: diva2:456758
QC 201111172011-11-172011-11-152011-11-17Bibliographically approved