Solution of Sparse Linear Systems with the Software Package LIS for Meso-scale Finite Element Simulation of Concrete Fractures

摘要

Meso-scale simulation of concrete with finite elements is very time consuming, in which solution of the related linear systems occupies most of the time. In this paper, the software package LIS, which is designed to solve sparse linear systems and sparse linear eigenvalue problems in parallel, is adopted to accelerate the simulation. The flexural fracture of wet-sieved and three-graded concrete beams is simulated. For the linear systems considered are all symmetric positive definite, the preconditioned conjugate gradient is used all the time. And five symmetric preconditioners including ILU(0), ILU(1), SSOR, SAINV, and SAAMG are tested. The results show that, though the number of iterations with the smoothed aggregation based algebraic multigrid preconditioner SAAMG is less than that with the others, the average solution time is longer than that with the simple preconditioners ILU(O) and SSOR, and its efficiency is closely related to the selection of parameters.