一种高性能迭代预处理方法及其在岩土工程中的应用

岩土工程建设的发展极大地促进了三维数值模拟的应用。大规模三维有限元计算需要求解一系列大型线性方程组，这些线性方程组的求解直接影响着整个有限元计算的效率。复杂岩土工程问题通常涉及多相和多体耦合相互作用，各相之间或不同固体材料之间性质差别显著，可能导致Krylov子空间迭代法收敛缓慢，甚至求解失败。为了提高Krylov子空间迭代法的求解效率和可靠性，提出一种新的高效预处理技术，通过算例验证了所提出的分区块迭代预处理方法的有效性。

A high-performance preconditioner for iterative solutions of geotechnical applications

The rapid developments of geotechnical constructions have greatly expedited the applications of 3D numerical modeling. Large-scale 3D finite element computations may lead to a series of large linear systems of equations, and solving these linear equations may significantly influence the efficiency of entire finite element computation. Complex geotechnical problems usually involve multi-body and multiphase coupling interactions, and the remarkable contrast in material properties for different phases or materials may lead to slow convergence or even failure of a Krylov subspace iterative method. To improve the solution efficiency and reliability of a Krylov subspace iterative method, a robust preconditioner should be employed. Based on some typical geotechnical problems, a partitioned block preconditioner is developed. By using some numerical examples, performances of the preconditioners are examined and their applicability is evaluated.