A modified Jacobi preconditioner for solving ill-conditioned biot's consolidation equations using symmetric quasi-minimal residual method

Abstract

This paper identifies imbalanced columns (or rows) as a significant source of ill-conditioning in the preconditioned coefficient matrix using the standard Jacobi preconditioner, for finite element solution of Biot's consolidation equations. A simple and heuristic preconditioner is proposed to reduce this source of ill-conditioning. The proposed preconditioner modifies the standard Jacobi preconditioner by scaling the excess pore pressure degree-of-freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quasi-minimal residual method. To alleviate storage requirements, element-by-element iterative strategies are implemented. Numerical experiment results show that the proposed preconditioner reduces both the number of iteration and CPU execution time significantly as compared with the standard Jacobi preconditioner. Copyright © 2001 John Wiley & Sons, Ltd.