Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3-D anisotropic media

Abstract

SUMMARY We present a massively parallel structured multifrontal solver for the equations describing time-harmonic elastic waves in 3-D anisotropic media. We use a multicomponent second-order finite-difference method. We extend the corresponding stencil to enhance the accuracy of the discretization without increasing the order. This accuracy is aligned with the tolerance level used for the Hierarchically SemiSeparable (HSS) low rank matrix compression underlying our solver. The interplay between the finite accuracy discretization and the finite accuracy matrix solver yields the key strategy which leads to the architecture of our algorithm. We analyse the relevant matrix structures, (numerically) estimate the rank of the dense matrices prior to the HSS compression and study the effect of anisotropy, and deduce the complexity and storage requirements of our algorithm.