Scott Alan Hutchinson

The Solution Of 3-D Biomedical Electrostatic Problems On A Data Parallel Computer

Many electromagnetic problems in the area of biomedical engineering can be approximated as electrostatic problems. These problems are governed by Laplace’s equation which is not ana lytically solvable for most real world problems. Often, numerical approximations are used which cast the problem in terms of a linear system of simultaneous equations. For three-dimensional problems, accurate results may require thousands of equations and may stretch the limits of available computing power. We present the finite element approximation to problems governed by Laplace’s equation on the Thinking Machines’ Connection Ma chine 2 (CM-2), a data parallel computer. Using this computer and our algorithm, problems with hundreds of thousands of equa tions can be solved in minutes. Biomedical research goals using this method are outlined including the investigation of problems in the area of defibrillation.

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

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.