A vectorization technique for the conjugate gradient method by using element matrices.

Abstract

With the wider use of vector-processing computers, much attention has come to be paid to the conjugate gradient method to solve a linear system of algebraic equations. However, in the case of finite element methods, it is rather difficult to tune up the computer program of the conjugate gradient method so as to make a big reduction in CPU time, because a coefficient matrix appearing in the finite element analysis is sparse and the nonzero components are irregularly located. In this paper, we present a vectorization technique for the conjugate gradient method by using element matrices only. The loop length attained by the present technique is as long as the number of elements and the rate of acceleration is very high.