论文标题
时间谐波麦克斯韦方程的层次结构lu预处理
Hierarchical LU preconditioning for the time-harmonic Maxwell equations
论文作者
论文摘要
时间谐波麦克斯韦方程用于研究电场和磁场对彼此的影响。尽管使用FEM解决该系统所产生的线性系统稀疏，但直接求解器无法达到线性复杂性。实际上，由于不确定的系统矩阵，迭代求解器的收敛缓慢。在这项工作中，我们研究了使用由Nédélec的边缘FEM离散化引起的Galerkin矩阵的$ \ CH $ -MATRIX近似的效果，以直接求解线性系统。我们还研究了应用$ \ Mathcal {h} -lu $分解作为预处理的影响，我们研究了使用迭代求解器求解线性系统的迭代次数。
The time-harmonic Maxwell equations are used to study the effect of electric and magnetic fields on each other. Although the linear systems resulting from solving this system using FEMs are sparse, direct solvers cannot reach the linear complexity. In fact, due to the indefinite system matrix, iterative solvers suffer from slow convergence. In this work, we study the effect of using the inverse of $\CH$-matrix approximations of the Galerkin matrices arising from Nédélec's edge FEM discretization to solve the linear system directly. We also investigate the impact of applying an $\mathcal{H}-LU$ factorization as a preconditioner and we study the number of iterations to solve the linear system using iterative solvers.
