Abstract
Non-associated flow rule is essential when the popular Mohr-Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes non-symmetric when this non-associated flow rule is applied. Efficient solution of this large-scale non-symmetric linear system is of practical importance. The standard Krylov solver for a non-symmetric solver is Bi-CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s=6) is more efficient than Bi-CGSTAB when the preconditioner is the incomplete factorization with zero fill-in of global stiffness matrix K-ep (ILU(0)-K-ep). Iteration time is reduced by 40% by using IDR(s=6) with ILU(0)-K-ep. To further reduce computational cost, the global stiffness matrix K-ep is divided into two parts. The first part is the linear elastic stiffness matrix K-e, which is formed only once at the beginning of solution step. The second part is a low-rank matrix , which is re-formed at each Newton-Raphson iteration. Numerical studies show that IDR(s=6) with this ILU(0)-K-e preconditioner is more time effective than IDR(s=6) with ILU(0)-K-ep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright (c) 2013 John Wiley & Sons, Ltd.