The finite element solution of elliptical systems on a data parallel computer

A study is conducted of the finite element solution of elliptic partial differential equations on a data parallel computer. A nodal assembly technique is introduced which maps a single node to a single processor. The system of equations is first assembled and then solved in parallel using a conjugate gradient algorithm for unsymmetric, non-positive definite systems. Using this technique and a massively parallel machine, problems in excess of 100k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Helmholtz equation, are presented for both an infinite cylinder and an airfoil cross-section. Solutions are demonstrated for a wide range of object sizes. A summary of performance data is given for a set of test problems.