Wave scattering with UV multilevel partitioning method: 2. Three-dimensional problem of nonpenetrable surface scattering

A UV multilevel partitioning method (UV-MLP) is developed to solve scalar wave three-dimensional (3-D) scattering problem. The method consists of setting up a table of transmitting and receiving block size and their separation using fast coarse-coarse sampling. For a specific scattering problem with given geometry, the scattering structure is partitioned into multilevel blocks. By looking up the rank in the static problem, the impedance matrix for a given transmitting and receiving block is expressed into a product of U and V matrix. In this paper the method is illustrated by applying to a 3-D scattering problem of random nonpenetrable rough surface. The cases of Dirichelt and Neumann boundary conditions are treated. Numerical simulation results are illustrated. For 65,536 boundary unknowns on a rough surface, and using a single processor of 2.66 GHz, it takes about 34 CPU min and 1.8 Gb of memory to compute the solution using conjugate gradient iterations and multilevel UV to accelerate the matrix-column vector multiplication.