LARGE SPARSE MATRIX METHOD FOR EQUILIBRIUM EQUATION

Ho-Jong Jang

Department of Mathematics
Hanyang University, Seoul 133-791, Korea

Robert E. White

Center for Research in Scientific Computation
Department of Mathematics
North Carolina State University, Raleigh, NC 27695


Abstract

We consider some numerical solution method for the equilibrium equations Af+E'g=r, Ef=s. Algebraic problems of this form evolve from many applications such as structural optimization, fluid flow, and circuits. An important approach, called the force method, to the solution to such problems involves dimension reduction nullspace computation for E. With emphasis on parallel computation, Plemmons and White suggested the substructuring method for nullspace computation. The purpose of this paper is to investigate the substructuring method for the solution step of the force method in the context of the structural analysis and fluid flow. In structural analysis we adopt linearly constrained sum-of-squares schemes to the solution step of the force method and examine this scheme based on substructuring method. The equilibrium matrix E reflects some type of conservation law such as an incompressible fluid case. A number of interesting characterizations of this problem are discussed, and some parallel iterative schemes are suggested. These schemes are based upon transformed iterative methods and substructuring concepts.