论文标题
积分方程的Laplacian过滤器：进一步的发展和快速算法
Laplacian Filters for Integral Equations: Further Developments and Fast Algorithms
论文作者
论文摘要
本文将Laplacian过滤的准螺旋分解概念扩展到了我们最近引入的，即基于无基础投影仪的设置。该扩展允许对电磁积分运算符光谱进行离散分析，而无需像以前那样通过显式循环星形分解。我们还提出了一个快速的方案，用于评估未知数总数中准线性复杂性中的过滤器。与以下事实是，仅需要一个对数的这些过滤器来解决电场积分方程的H再填充分解，这会导致有效的预处理，使Calderón策略在不依赖Barycentric改进的情况下与Calderón策略相媲美。数值结果证实了理论上预测的行为和方法的有效性。
This paper extends the concept of Laplacian filtered quasi-Helmholtz decompositions we have recently introduced, to the basis-free projector-based setting. This extension allows the discrete analyses of electromagnetic integral operators spectra without passing via an explicit Loop-Star decomposition as previously done. We also present a fast scheme for the evaluation of the filters in quasi linear complexity in the total number of unknowns. Together with the fact that only a logarithmic number of these filters are required for solving the h-refinement breakdown of electric field integral equation, this results in an effective preconditioner that rivals Calderón strategies in performance without relying on barycentric refinements. Numerical results confirm the theoretically predicted behavior and the effectiveness of the approach.
