A block iteration scheme for the solution of systems of equations resulting from linear and nonlinear finite element models

Abstract

An algorithm combining direct and iterative solution procedures is proposed for the solution of the discrete equations resulting from static or dynamic finite element models. In this technique, the discrete model is broken into regular or irregular blocks of elements. The algorithm is composed of two analysis steps, which are repetitively carried out. In the first step, using the specified boundary data on the block boundaries, the solutions within the blocks are defined directly. In the second step the variables on the block boundaries are updated iteratively. The algorithm would be particularly useful in solving large nonlinear or dynamic problems.