Multi-scale methods for wave propagation in heterogeneous media
Abstract
Multi-scale 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 multi-scale wave propagation in the framework of heterogeneous multi-scale method. The numerical methods couples simulations on macro- and micro-scales for problems with rapidly oscillating coefficients. We show that the complexity of the new method is significantly lower than that of traditional techniques with a computational cost that is essentially independent of the micro-scale. A convergence proof is given and numerical results are presented for periodic problems in one, two and three dimensions. The method is also successfully applied to non-periodic problems and for long time integration where dispersive effects occur.
Cite
@article{arxiv.0911.2638,
title = {Multi-scale methods for wave propagation in heterogeneous media},
author = {Bjorn Engquist and Henrik Holst and Olof Runborg},
journal= {arXiv preprint arXiv:0911.2638},
year = {2009}
}