论文标题
Laplacian滤波循环星形分解和准螺丝llaplacian滤波器：定义，分析和有效算法
Laplacian Filtered Loop-Star Decompositions and Quasi-Helmholtz Laplacian Filters: Definitions, Analysis, and Efficient Algorithms
论文作者
论文摘要
准螺旋分解是电磁问题积分方程建模的基本工具，因为它们具有溶液，操作员矩阵和辐射磁场的螺线管和非甲状腺液组件的重新磁管和非甲固醇组件的能力。但是，这些工具本身是无法修改不同操作员的改进频谱行为的能力，并且通常需要与其他预处理策略结合使用。本文介绍了过滤的准螺旋分解的新概念，分别在两个化身中提出了它们：滤波的循环函数和Quasi-Helmholtz laplacian滤波器。由于他们能够操纵操作员的光谱中的大部分，因此可以从这些新工具中得出新的预处理和快速求解器的家族。介绍了电场积分方程的频率和H-再填充预处理的情况，并显示了数值结果，显示了新提出的分解的实际有效性。
Quasi-Helmholtz decompositions are fundamental tools in integral equation modeling of electromagnetic problems because of their ability of rescaling solenoidal and non-solenoidal components of solutions, operator matrices, and radiated fields. These tools are however incapable, per se, of modifying the refinement-dependent spectral behavior of the different operators and often need to be combined with other preconditioning strategies. This paper introduces the new concept of filtered quasi-Helmholtz decompositions proposing them in two incarnations: the filtered Loop-Star functions and the quasi-Helmholtz Laplacian filters. Because they are capable of manipulating large parts of the operators' spectra, new families of preconditioners and fast solvers can be derived from these new tools. A first application to the case of the frequency and h-refinement preconditioning of the electric field integral equation is presented together with numerical results showing the practical effectiveness of the newly proposed decompositions.
