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

This paper identifies imbalanced columns (or rows) as a significant source of ill-conditioning in the preconditioned coefficient matrix using the stan dard Jacobi preconditioner, for finite element solution of Biot's consolida tion 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-o f-freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quas i-minimal residual method. To alleviate storage requirements, element-by-el ement iterative strategies are implemented. Numerical experiment results sh ow that the proposed preconditioner reduces both the number of iteration an d CPU execution time significantly as compared with the standard Jacobi pre conditioner. Copyright (C) 2001 John Wiley & Sons, Ltd.