The Finite Element Solution of Two-Dimensional Transverse Magnetic Scattering Problems on the Connection Machine

Abstract

A study is conducted of the finite element solution of the partial differential equations governing twodimensional electromagnetic field scattering problems on a SIMD computer. A nodal assembly technique is introduced which maps a single node to a single processor. The physical domain is first discretized in parallel to yield the node locations of an 0-grid mesh. Next, the system of equations is assembled and then solved in parallel using a conjugate gradient algorithm for complexvalued, non-symmetric, non-positive definite systems. Using this technique and Thinking Machines Corporation’s Connection Machine-2 (CM-2) , problems with more than 250k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Helmholtz wave equations are presented for a variety of infinite cylinders and airfoil crosssections. Solutions are demonstrated for a wide range of objects. A summary of performance data is given for the set of test problems.