Rapid developments of computer technology expedite applications of three-dimensional finite element modeling and simulations

of practical geotechnical problems. In three-dimensional finite element modeling, the size of linear equations arising from finite

element discretization of geotechnical problems is usually very large, and their solutions often dominate the entire finite element

computations. To remarkably accelerate the computational speed, the advanced fundamental iterative algorithm and the high-performance

computer architecture are needed. In this study, a GPU computer device with high price/performance ratio is adopted to accelerate the

preconditioned Krylov subspace iterative method, and attentions are particularly paid to the acceleration effects of GPU on the matrix-

vector multiplications. Based on the numerical examples, several popular preconditioned iterative methods are assessed on different

computing architectures and some suggestions on how to select the preconditioned iterative methods on different computing platforms are

also given.