Solving Helmholtz Equation by Means of Domain Decomposition Using Discontinuous Galerkin and Pseudospectral Methods

In this work we introduce and study numerically a new method for solving two-dimensional Helmholtz equation in complex media with high-contrast velocity variations. The proposed method is based on coupling the IPDG method for solving the problem in the surface neighbourhood with fast pseudospectral method applied in the lower part of the domain. The coupling is implemented using overlapping domain decomposition with Robin transmission conditions. Results of numerical experiments with both analytical solutions and point-like sources are presented for Gullfaks benchmark.