Jari Toivanen
Department of Mathematical Information Technology
University of Jyväskylä
Jyväskylä, Finland
We study time-harmonic acoustics scattering in layered media with a piecewise constant speed of sound. This leads to the solution of the Helmholtz equation with jumps in wavenumber. The problems can include sound-hard, sound-soft, or elastic scatterers. A finite element discretization is performed using a orthogonal meshes which can be locally adapted to the interfaces. For the iterative solution of resulting large indefinite linear systems, domain decomposition preconditioners are constructed using a fast direct solver. The iterations can be carried out in small subspaces related to interfaces. The numerical experiments demonstrate the capability to solve very large scale two-dimensional and three-dimensional problems with up to billions of unknowns.