INTEGRAL-EQUATION METHOD VIA DOMAIN DECOMPOSITION AND COLLOCATION FORSCATTERING PROBLEMS

In this paper an exterior domain decomposition (DD) method based on th e boundary element (BE) formulation for the solutions of two or three- dimensional time-harmonic scattering problems in acoustic media is des cribed It is known that the requirement of large memory and intensive computation has been one of the major obstacles for solving large scal e high-frequency acoustic systems using the traditional nonlocal BE fo rmulations due to the fully populated resultant matrix generated from the BE discretization. The essence of this study is to decouple throug h DD of the problem-defined exterior region, the original problem into arbitrary subproblems with data sharing only at the interfaces. By de composing the exterior infinite domain into appropriate number of infi nite subdomains, this method not only ensures the validity of the form ulation for all frequencies but also leads to a diagonalized, blockwis e-banded system of discretized equations, for which the solution requi res only O(N) multiplications, where N is the number of unknowns on th e scatterer surface. The size of an individual submatrix that is assoc iated with a subdomain may be determined by the user, and may be selec ted such that the restriction due to the memory limitation of a given computer may be accommodated. In addition, the method may suit for par allel processing since the data associated with each subdomain (impeda nce matrices, load vectors, etc.) may be generated in parallel, and th e communication needed will be only for the interface values. Most sig nificantly, unlike the existing boundary integral-based formulations v alid for all frequencies, our method avoids the use of both the hypers ingular operators and the double integrals, therefore reducing the com putational effort. Numerical experiments have been conducted for rigid cylindrical scatterers subjected to a plane incident wave. The result s have demonstrated the accuracy of the method for wave numbers rangin g from 0 to 30, both directly on the scatterer and in the far-field, a nd have confirmed that the procedure is valid for critical frequencies .