Use of Discontinuous Grids for Solving Helmholtz Equation in Complex Models

In this paper, we consider 2D Helmholtz equation with complex shift and assume it to be solved using domain decomposition technique where finite-difference method on fine and coarce meshes applied in the upper and lower parts of the model respectively. We proved that the use of different grids leads to nonsymmetrical perturbation of the original operator, thus causes the irreducible error in the solution – artificial reflections from the boundaries of the subdomains, even though the residual tends to zero exponentially with respect to the number of iteration.