Numerical simulations of rough surface scattering with UV multi-level partitioning method

A UV multi-level partitioning method (UV-MLP) is developed to solve wave scattering by rough surfaces. The method consists of setting up a rank table of transmitting and receiving block sizes and their separation using fast coarse-coarse sampling. For a specific scattering problem with given geometry, the scattering structure is partitioned into multi-level blocks. By looking up the rank, the impedance matrix for a given transmitting and receiving block is expressed into a product of the U and matrix. We demonstrate the technique for three cases: a 2D scattering with a random rough surface; a 3D scattering problem of a random rough surface; a 2D urban building profile with large height variations where we combine the UV-MLP method with the multilevel steepest descent fast multipole method (ML-SD-FMM).