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

Wave scattering from two-dimensional (2-D) random rough surfaces [three-dim ensional (3-D) scattering problem] has been previously analyzed using the s parse-matrix/canonical grid (SM/CG) method. The computational complexity an d 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 un knowns, Furthermore, the SM/CG method is FFT based, which facilitates the implementation on par allel processors. In this paper, we present a cost-effective solution by im plementing the SM/CG method on a Beowulf system consisting of PC's (process ors) connected by a 100 Base TX Ethernet switch. The workloads of computing the sparse-matrix-vector multiplication corresponding to the near interact ions and the fast Fourier transform (FFT) operations corresponding to the f ar interactions in the SM/CG method can be easily distributed among all the processors. Both perfectly conducting and lossy dielectric surfaces of Gau ssian spectrum and ocean spectrum are analyzed thereafter. When possible, s peedup factors against a single processor are given. It is shown that the S M/CG method for a single realization of rough surface scattering can be eff icently adapted for parallel implementation. The largest number of surface unknowns solved in this paper is over 1.5 million. On the other hand, a pro blem of 131 072 surface unknowns for a PEC random rough surface of 1024 squ are wavelengths only requires a CPU time of less than 20 min. We demonstrat e that analysis of a large-scale 2-D random rough surface feasible for a si ngle realization and for one incident angle is possible using the low-cost Beowulf system.