A Large Matrix Reducgtion Method for Multiprocessors

Abstract

: This paper treats a basic study on a methodology of large reduction of the huge stiffness matrix equation with many unknowns for application on very high speed supercomputer or connection machines. Until recently the substructured method according to the Neumann-type single processing has been used for the above purpose, whereas the method described here differs from its predecessor as pertaining to non-Neumann-type plural processing by the system of multilinked computers. The characteristics of the method exist in an algebraic and mechanical idea for the very large structural matrix equation, to make it constitute a properly decided number of independently blocked-in submatrix equations so as to be able to utilize the supercomputer or connection machines in the most eficient way. For this purpose, the method presented in this paper shows how to relocate and add rows and columns in the original structural stiffness matrix equation, taking the effective stiffnesses of intersected boundary members into proper consideration. Next, this method is applied to a simple rectangular frame as the first step, this time to consider and verifv its adequacy. Finally, some remarks are made on the comparative state between analytical results by this parallel processing for substructured matrices on it, and by the usual direct processing for its original matrix. It is concluded that the method presented here may be thought suficiently appropriate and useful for the object.