Cell{centered Finite Diierence Modeling for the 3-d Helmholtz Problem

The Helmholtz problem in the 3{dimensional space is hard to solve numerically due to its huge problem size and poorly{conditioned algebraic system obtained by discretization schemes. In this paper, we suggest a nonoverlapping domain decomposition iterative procedure for solving the problem by the cell{centered nite diierence (CCFD) methods. We introduce a modiied Robin interface boundary operator, incorporating relaxation parameters, on the subdomain interfaces to match the continuity of the normal components of the ux on the interfaces and to accelerate the convergence speed. The ux variables are replaced by adjacent values of the discrete solution in order to minimize the computer storage. The convergence of the algorithm is analyzed and a heuristic strategy for nding computationally eecient relaxation parameters is addressed. Numerical results are given to show the eeectiveness of the method.