Multiscale Finite Element Method for Computing Wave Propagation and Scattering in Heterogeneous Media

摘要

The objective of this study is to develop a multiscale/ multiresolution method for computing wave propagation and scattering in strongly heterogeneous media. The important feature of this method is that does not require resolving the small scale details, yet it can capture their effect on the large scales. The central idea is to incorporate the small scale information into the finite element base functions, so that the effect of small scales on the large scales is correctly captured. This feature allows us to break a large scale computation into many small and independent pieces, which can be carried out in perfect parallel. As a consequence, the size of the computation is drastically reduced. This gives us the possibility to attack problems with many spatial and time scales.