A Calderon Multiplicative Preconditioner for the PMCHWT Integral Equation
A Calderon Multiplicative Preconditioner for the PMCHWT Integral Equation
复制标题
DOI：
10.1109/tap.2011.2165465
复制
发表时间：
2011-12-01
影响因子：
5.7
通讯作者：
Michielssen, Eric
中科院分区：
文献类型：
--
作者：
Cools, Kristof;Andriulli, Francesco P.;Michielssen, Eric
可穿透物体的电磁散射通常通过 Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) 积分方程进行建模。不幸的是，该方程中涉及的算子的范围既不受上方限制，也不受下方限制。这意味着该方程会遭受密集离散化破坏；也就是说，对方程进行离散化后得到的矩阵的条件数随着网格密度的增加而增加。电场积分方程通常用于模拟完美导电体的散射，很容易出现类似的击穿现象。最近，利用卡尔德隆恒等式解决了这一问题。本文引入了Calderon预条件PMCHWT积分方程。通过构造 PMCHWT 算子的 Calderon 恒等式，表明新方程不会遭受密集离散化破坏。引入了涉及 Rao-Wilton-Glisson 和 Buffa-Christiansen 函数的一致离散化方案。该方案相当于将乘法矩阵预处理器应用于经典的PMCHWT系统，因此与现有的边界元代码和加速方案兼容。数值算例验证了该算法的效率和准确性。
Electromagnetic scattering by penetrable bodies often is modelled by the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) integral equation. Unfortunately the spectrum of the operator involved in this equation is bounded neither from above or below. This implies that the equation suffers from dense discretization breakdown; that is, the condition numbers of the matrix resulting upon discretizing the equation rise with the mesh density. The electric field integral equation, often used to model scattering by perfect electrically conducting bodies, is susceptible to a similar breakdown phenomenon. Recently, this breakdown was cured by leveraging the Calderon identities. In this paper, a Calderon preconditioned PMCHWT integral equation is introduced. By constructing a Calderon identity for the PMCHWT operator, it is shown that the new equation does not suffer from dense discretization breakdown. A consistent discretization scheme involving both Rao-Wilton-Glisson and Buffa-Christiansen functions is introduced. This scheme amounts to the application of a multiplicative matrix preconditioner to the classical PMCHWT system, and therefore is compatible with existing boundary element codes and acceleration schemes. The efficiency and accuracy of the algorithm are corroborated by numerical examples.