# Equation Solving on a Parallel Computer

*by*D. Douglas Wilmarth, Floating Point Systems Inc, Dedham, MA, USA,

Carlton E. Jeffcoat, Floating Point Systems Inc, Dedham, MA, USA,

**Abstract:**The application of computers to the analysis of large structural systems is examined. The analysis procedure is presented as three distinct phases: (1) element formulation, (2) equation solution and (3) stress recovery. It is shown that in complex structural models the equation solution phase is the bottleneck in the analysis. The need is established for solution algorithms which efficiently use the particular computing system available to the engineer. The evolution of solution techniques is presented. The computer resource requirements of each algorithm is examined with emphasis on memory, access to mass storage devices, and computational requirements. Computational efficiency of vector inner products and vector combinations are evaluated and hardware requirements are extracted. The equation solution phase is evaluated for adaptation to parallel pipelined architectures. The Fast Matrix Solution Library from Floating Point systems is used as an example of an adaped equation solver. Its implemenation on the FPS-164, including the Matrix Algebra Accelerator is described.

**Subject Headings:**Computer analysis | Stress analysis | Computer programming | Algorithms | Structural systems | Vector analysis

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