论文标题
关于无共振和高频稳定积分方程的光谱行为和归一化
On the Spectral Behavior and Normalization of a Resonance-Free and High-Frequency Stable Integral Equation
论文作者
论文摘要
尽管不含共振的配方，用于解决散射和辐射问题的CFIE遭受了不良条件的影响，在低频和高频方面，强烈取决于频率和离散密度，导致迭代求解器的收敛速度缓慢。这项工作为CFIE提供了一种新的预处理计划，可以治愈低频和高频以及密集的离散化崩溃。 CFIE的新预处理基于球形谐波分析和与Helmholtz型操作员的适当正则化。已经获得了数值结果，以证明在实际情况下这种新公式的有效性。
The CFIE used for solving scattering and radiation problems, although a resonance-free formulation, suffers from an ill-conditioning that strongly depends on the frequency and discretization density, both in the low- and high-frequency regime, resulting in slow convergence rates for iterative solvers. This work presents a new preconditioning scheme for the CFIE that cures the low- and the high-frequency as well as the dense discretization breakdown. The new preconditioner for the CFIE is based on a spherical harmonics analysis and the proper regularization with Helmholtz-type operators. Numerical results have been obtained to prove the effectiveness of this new formulation in real scenarios.
