Abstract
Finite element simulations of very large-scale soil-structure interaction problems (e.g. excavations, tunnelling, pile-rafts, etc.) typically involve the solution of a very large, ill-conditioned, and indefinite Biot system of equations. The traditional preconditioned conjugate gradient (PCG) solver coupled with the standard Jacobi (SJ) preconditioner can be very inefficient for this class of problems. This paper presents a robust generalised Jacobi (GJ) preconditioner that is extremely effective for solving very large-scale Biot's finite element equations using the symmetric quasi-minimal residual (QMR) method. It was derived as a diagonal approximation to a theoretical form, which can be proven mathematically to possess an attractive eigenvalue clustering property.