Parallel implementation of the sparse-matrix/canonical grid method for the analysis of two-dimensional random rough surfaces (three-dimensional scattering problem) on a Beowulf system

Abstract

Wave scattering from two-dimensional (2-D) random rough surfaces [three-dimensional (3-D) scattering problem] has been previously analyzed using the sparse-matrix/canonical grid (SM/CG) method. The computational complexity and memory requirement of the SM/CG method are O(N log N) per iteration and O(N), respectively, where N is the number of surface unknowns. Furthermore, the SM/CG method is FFT based, which facilitates the implementation on parallel processors. In this paper, we present a cost-effective solution by implementing the SM/CG method on a Beowulf system consisting of PCs (processors) connected by a 100 Base TX Ethernet switch. The workloads of computing the sparse-matrix-vector multiplication corresponding to the near interactions and the fast Fourier transform (FFT) operations corresponding to the far interactions in the SM/CG method can be easily distributed among all the processors. Both perfectly conducting and lossy dielectric surfaces of Gaussian spectrum and ocean spectrum are analyzed thereafter. When possible, speedup factors against a single processor are given. It is shown that the SM/CG method for a single realization of rough surface scattering can be efficiently adapted for parallel implementation. The largest number of surface unknowns solved in this paper is over 1.5 million. On the other hand, a problem of 131072 surface unknowns for a PEC random rough surface of 1024 square wavelengths only requires a CPU time of less than 20 min. We demonstrate that analysis of a large-scale 2-D random rough surface feasible for a single realization and for one incident angle is possible using the low-cost Beowulf system.