An incomplete factorization preconditioning method for solving vector finite element equations
一种用于计算矢量有限元方程组的不完全分解预处理方法

In this paper, an incomplete decomposition preconditioning method is presented combining with iterative method to solve vector finite element equations. In the preconditioning process, the coefficient matrix is decomposed and updated by the Multifrontal algorithm based on the Expanded Cholesky method. The basic linear algebra subprogram is used to calculate multiplication of dense matrices to ensure the computational efficiency of inner loop. Unlike the traditional preconditioning technique, the incomplete decomposition method borrows the concept of scaling matrix to improve the conditioning of the coefficient matrix. Moreover, a new version of dropping scheme is proposed to make the preconditioning method robust. The presented method and direct method are compared in terms of time and memory. Theory and numerical experiments show that the presented preconditioning method can greatly reduce the time and memory of decomposition, and ensure the accuracy and validity of the calculation.