A generalised Jacobi preconditioner for finite element solution of large-scale consolidation problems

Publisher Summary Finite element simulations of very large-scale soil–structure interaction problems typically involve the solution of a very large, ill-conditioned, and indefinite Biot system of equations. The traditional preconditioned conjugate gradient solver coupled with the standard Jacobi (SJ) preconditioner is inefficient for this class of problems. This chapter presents a robust generalized Jacobi (GJ) preconditioner that is extremely effective for solving very large-scale Biot's finite element equations using the symmetric quasi-minimal residual method. It was derived as a diagonal approximation to a theoretical form, which can be proven mathematically to possess an attractive eigenvalue clustering property. The GJ preconditioner is formed, inverted, and implemented within an element-by-element framework as readily as the SJ preconditioner. Significantly better result can be achieved by applying a small negative scalar to the block of the generalized Jacobi preconditioner.