Wave scattering with UV multilevel partitioning method for volume scattering by discrete scatterers

A UV multilevel partitioning method (UV‐MLP) is developed to solve the volume‐scattering problem. The method involves creating a rank table of transmitting and receiving block sizes and their separation. The table can be set up speedily using 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 predetermined table, the impedance matrix for a given transmitting and receiving block is expressed as a product of U and V matrices. We illustrate the method for 2D volume scattering by discrete scatterers. Multiple scattering is cast into the Foldy–Lax equations of partial waves. We show that UV decomposition can be applied directly to the impedance matrix of partial waves of higher order than the usual lowest‐order Green's function. Numerical results are illustrated for randomly distributed cylinders that are one wavelength in diameter. For scattering by 1024 cylinders on a single PC processor with a 2.6‐GHz CPU and 2‐GB memory, only 14 CPU min are required to obtain the numerical solution. If subsectional volumetric discretization with the method of moments (MoM) is applied to this problem, the equivalent number of volumetric unknowns is 80,425. Furthermore, for 4096 cylinders that have 321,700 equivalent numbers of volumetric unknowns, it takes only 7.34 sec for one matrix‐vector multiplication.