Aztec在混凝土细观数值模拟中的应用研究

Study of application of Aztec in meso-scale simulation of concrete

细观数值模拟是混凝土性能研究的一种重要手段,但稀疏线性方程组求解在总体模拟时间中所占比重很大。由于属于三维问题,且规模很大,所以采用预条件Krylov子空间迭代是必由之路。Aztec是国际上专门设计用于求解稀疏线性方程组的软件包之一,由于目前混凝土细观数值模拟中的稀疏线性方程组对称正定,所以利用Aztec中提供的CG迭代法进行求解,并对多种能保持对称性的预条件选项进行了实验比较。结果表明,在基于区域分解的并行不完全Cholesky分解、无重叠对称化GS迭代、最小二乘等预条件技术中,第一种的效率最高,且在重叠度为0,填充层次为0时,效果最好;实验结果还表明,在本应用问题中,用RCM排序一般导致求解时间更长,从而没有必要采用。

Meso-scale simulation is an important way for performance study of concrete. But the solution of sparse linear systems occupies most of the total simulation time. Due to its three-dimensional origination and large scale, preconditioned Krylov subspace iterations are the best choices. Aztec is a software package developed in the community and designed specially to solve sparse linear systems. For the sparse linear systems in the meso-simulation of concrete are symmetric positive definite currently, the CG iteration provided in Aztec, is selected to solve the linear systems. Several preconditioning options which can preserve the symmetric characteristic are tested with experiments. The results show that among the par-allel incomplete Cholesky factorization based on domain decomposition, symmetrical Gauss-seidel iteration without over-lapping, least square preconditioners, the first is the most efficient and when the degree of overlapping and the level of fill are both selected as 0, the preconditioner is the best. At the same time, the results show that the time elapsed with RCM reordering is lager in general. Therefore, it should not be exploited in the simulation.