Application of multigrid approach to the subsurface imaging problem

摘要

In this paper, the multigrid technique was considered for the solution of two dimensional Helmholtz equation with radiation boundary conditions. To achieve h-independent convergence of the iterative method, the original Helmholtz equation was transformed by using so-called "regularizing" plane wave. The recently developed "black-box" type multigrid method was adopted as a solver. This multigrid approach uses matrix dependent prolongation operator. The convergence of proposed algorithm was investigated on several test problems. Numerical results for realistic ranges of parameters in soil and mine-like targets are presented.