Solution of open region electromagnetic scattering problems on hypercube multiprocessors

The focus of this thesis is on the development of parallel algorithms which exploit hypercube multiprocessor computers for the solution of the scattering of electromagnetic fields by bodies situated in an unbounded space. Initially, algorithms based on the method of moments are investigated for coarse-grained MIMD hypercubes as well as fine-grained MIMD and SIMD hypercubes. It is shown that by exploiting the architecture of each hypercube, supercomputer performance can be obtained using the JPL Mark III hypercube and the Thinking Machine's CM2. Second, the use of the finite element method for the solution of the scattering by bodies constituted of composite materials is presented. For finite bodies situated in an unbounded space, the use of an absorbing boundary condition is investigated. A method known as the mixed-$\chi$ formulation is presented, which reduces the mesh density in the regions away from the scatterer enhancing the use of an absorbing boundary condition. The scattering by troughs or slots is also investigated using a combined FEM/MoM formulation. This method is extended to the problem of the diffraction of electromagnetic waves by thick conducting and/or dielectric gratings. Finally, the adaptation of the FEM method onto a coarse-grained hypercube is presented. The parallel algorithm is shown to be highly efficient by mapping the finite elements using a domain decomposition technique and solving the sparse matrix expression using the preconditioned biconjugate gradient method.U of I OnlyETDs are only available to UIUC Users without author permissio