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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。
The development of geotechnical engineering has greatly promoted the application of three-dimensional numerical simulation. Large-scale three-dimensional finite element calculations need to solve a series of large linear equations, the solution of these linear equations directly affect the efficiency of the entire finite element calculation. Complicated geotechnical engineering problems usually involve multi-phase and multi-body coupling interactions, with significant differences in properties between phases or between different solid materials, which may lead to slow convergence and even failure of the Krylov subspace iteration method. In order to improve the efficiency and reliability of the Krylov subspace iterative method, a new efficient preprocessing technique is proposed. The effectiveness of the proposed iterative preprocessing method is verified by an example.