Electromagnetic field computations on massively parallel computers

Abstract

A general overview is given of the use of massively parallel computers in the determination of electromagnetic fields. The emphasis is on parallel machines with a single-instruction multiple-data (SIMD) architecture. Various measures of program performance are critically discussed as is the issue of scalability of the computations. An analysis of the parallelism inherent in the method of moments (MoM), the finite-difference time-domain (FDTD) method, and the finite element method (FEM) is presented. Since communication is an important component in a parallel algorithm, the interconnection network between processors becomes an essential consideration in program analysis. Most of the discussion centers around two-dimensional meshes and hypercubes, complemented by a brief overview of embedding theory, which allows other networks to be emulated. These theoretical concepts are illustrated on a specific example involving the modeling, by the FDTD method, of the scattering of a plane wave off a dielectric sphere. Calculations were performed on the MasPar MP-1 family of SIMD computers. Specific models used contain between 1024 and 8192 processors arranged in a two-dimensional mesh with nearest and next-nearest neighbor connections between PEs. Code development, starting from a sequential program, is discussed, as are the details of the data mapping. Timing results are presented for a range of problem sizes and show considerable speed-up compared to sequential programming. These results are compared and contrasted with those obtained by other authors.