Communications in Mathematical Sciences
Volume 9 (2011)
Multi-scale methods for wave propagation in heterogeneous media
Pages: 33 – 56
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 couple 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.
multi-scale, wave propagation, HMM, homogenization
2010 Mathematics Subject Classification
35B27, 35L05, 65N06