Multilevel Fast Multipole Acceleration in the Nyström Discretization of Surface Electromagnetic Integral Equations for Composite Objects
Multilevel Fast Multipole Acceleration in the Nyström Discretization of Surface Electromagnetic Integral Equations for Composite Objects
复制标题
复合物体表面电磁积分方程 Nyström 离散化的多级快速多极加速
DOI：
10.1109/tap.2010.2055809
复制
发表时间：
2010
影响因子：
5.7
通讯作者：
W. Chew
中科院分区：
文献类型：
--
作者：
M. Tong;W. Chew
基于表面积分方程 (SIE) Nyström 离散化的多级快速多极算法 (MLFMA) 是为了求解大型复合物体的电磁 (EM) 散射而开发的。传统上，MLFMA 基于 SIE 的矩量法 (MoM) 离散化，当鲁棒的 Rao-Wilton-Glisson (RWG) 基函数足以表示未知电流时，它通常效果很好。然而，在求解可穿透物体的电场积分方程（EFIE）和磁场积分方程（MFIE）时，RWG基函数可能无法同时表示电流和磁流，并且如何表示另一种电流可能是MoM中的一个问题。在这项工作中，我们使用 Nyström 方法作为离散 SIE 的工具，并结合 MLFMA 来加速大型电气问题的解决。 Nyström离散化的优点包括实现机制简单、对网格质量要求较低、不使用基础和测试函数。这些好处在 MLFMA 中是特别需要的，因为解决的问题通常非常大且复杂。数值例子证明了所提出方案的有效性。
The multilevel fast multipole algorithm (MLFMA) based on the Nyström discretization of surface integral equations (SIEs) is developed for solving electromagnetic (EM) scattering by large composite objects. Traditionally, the MLFMA is based on the method of moments (MoM) discretization for the SIEs and it usually works well when the robust Rao-Wilton-Glisson (RWG) basis function is enough to represent unknown currents. However, the RWG basis function may not represent both the electric and magnetic current in solving the electric field integral equation (EFIE) and magnetic field integral equation (MFIE) for penetrable objects, and how one represents another current could be a problem in the MoM. In this work, we use the Nyström method as a tool to discretize the SIEs and incorporate the MLFMA to accelerate the solutions for electrically large problems. The advantages of the Nyström discretization include the simple mechanism of implementation, lower requirements on mesh quality, and no use of basis and testing functions. These benefits are particularly desired in the MLFMA because the solved problems are very large and complex in general. Numerical examples are presented to demonstrate the effectiveness of the proposed scheme.