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.

翻译：本文着重论述通过利用受拉普拉西亚过滤器规范化的第一种或第二种先决条件操作者获得的低到中频-频率制度中的一体化方程式快速直接解决器,通过过滤处理边界元素离散产生的光谱错误是恰当的,此外,过滤还允许使用低级别代表器对所有相关操作者进行紧凑的扰动。数字结果显示这些方法的有效性及其在直接解决整体方程式方面的有效性。