适用于PEC散射的宽带稳定Calderón预处理仅含矢量势的积分方程
Broadband Stable Calderón-Preconditioned Vector-Potential-Only Integral Equations for PEC Scattering
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中文总结 AI 辅助
针对PEC散射问题，本文提出稳定化的第一类Calderón预处理仅含矢量势的积分方程，经数值验证其在任意低频下均能精确计算近场、远场及势函数，结果与机器和求积精度无关。
中文摘要 AI 辅助
针对理想电导体（PEC）的散射问题，本文提出了一种稳定化的第一类Calderón预处理仅含矢量势的积分方程。该方法可在矢量势和标量势上均产生精确的低频结果，其中标量势通过后处理步骤采用Lorenz规范计算，近场和远场均可在任意低频下精确计算，且该后处理步骤的结果与机器精度和求积精度无关。首先，研究了自由度、近场和远场的低频缩放特性；接着，基于该低频缩放特性推导了稳定化方法：利用拟亥姆霍兹投影器稳定化矢量势旋度的切向迹，基于静态标量势的投影器稳定化矢量势的法向迹。数值实验表明，该稳定化方法在极低频率下仍能给出精确结果。
英文摘要
We propose a stabilized first-kind, Calderón preconditioned, vector-potential-only integral equation, for scattering at perfect electrical conductors. The method yields accurate low-frequency results for both the vector and the scalar potential, where the scalar potential is computed using the Lorenz gauge in the post-processing. Both the near and far fields can be accurately computed at arbitrarily low frequencies. This is achieved in a post-processing step and is independent of machine and quadrature precision. First, the low-frequency scaling of the degrees of freedom, and the near and far fields, are studied. Next, stabilized methods are derived based on the low-frequency scaling. The tangential trace of the curl of the vector-potential is stabilized leveraging quasi-Helmholtz projectors, while the normal trace of the vector-potential is stabilized with a projector based on the static scalar potential. Numerical experiments are presented showing that the stabilized method shows accurate results even for very low frequencies.
