Finite Element Analysis with Conjugate Gradient Method Preconditioned by a Norm Scaling

Abstract

In this paper, a norm scaling preconditioning algorithm for the conjugate gradient method is proposed in the finite element analysis. Although the present scaling algorithm requires the same memory size and computational time in each iteration step as the usual diagonal scaling preconditioning algorithm, the number of iterations to convergence of the former is smaller than that of the latter. The implementation of the method on parallel environment and some numerical examples are also described to verify the effectiveness of this preconditioning algorithm.