论文标题
基于运算符过滤的低频的积分方程的快速直接求解器
Fast Direct Solvers for Integral Equations at Low-Frequency Based on Operator Filtering
论文作者
论文摘要
本文着重于通过利用预处理的第一类或第二种操作员使用Laplacian滤波器正规化的低到中等频率方程的积分方程的快速直接求解器。通过过滤，可以正确处理由边界元素离散化引起的光谱误差，这些误差还允许使用低级别表示来用于所有相关操作员的紧凑扰动。数值结果显示了方法的有效性及其在积分方程的直接解决方案中的有效性。
This paper focuses on fast direct solvers for integral equations in the low-to-moderate-frequency regime obtained by leveraging preconditioned first kind or second kind operators regularized with Laplacian filters. The spectral errors arising from boundary element discretizations are properly handled by filtering that, in addition, allows for the use of low-rank representations for the compact perturbations of all operators involved. Numerical results show the effectiveness of the approaches and their effectiveness in the direct solution of integral equations.
