用于高对比度介质散射的三维时间步进对比度电流密度体积分方程的FFT加速与稳定化
FFT-acceleration and stabilization of the 3D Marching-on-in-Time Contrast Current Density Volume Integral Equation for scattering from high contrast dielectrics
AI总结：
本研究将FFT加速拓展至三维MOT-JVIE，并提出基于低群延迟线性相位高通FIR滤波器的正则化方法，在保证稳定性的同时降低精度损失，实现了百万体素级高介电常数介质体的电磁散射高效计算。
摘要：
将隐式因果时空Galerkin格式应用于对比度电流密度体积分方程，可得到一种被称为MOT-JVIE的时间步进格式，该格式通过完全嵌入的FIR（有限长单位冲激响应）滤波器实现加速与稳定，用于计算由超过百万体素离散化的高介电常数介质体的电磁散射。通过回顾此前针对二维时域面积分方程开发的两种基于快速傅里叶变换（FFT）的加速方法，我们明确了这些方案为何能获得相同阶数的加速效果，并将这种FFT加速方法拓展至三维MOT-JVIE。针对MOT-JVIE的正定稳定性分析（PDSA）表明，稳定的MOT-JVIE离散化所支持的体素数量受限于矩阵元素的有限精度。PDSA的应用带来了一项洞见：可通过正则化强制保证稳定性，但会以牺牲精度为代价。为最大程度降低对精度的影响，本文提出了FIR正则化方法，该方法基于低群延迟线性相位高通FIR滤波器。我们通过多个针对高介电常数介质散射体的数值实验，验证了经FFT加速、FIR正则化的MOT-JVIE的性能。
英文摘要：
An implicit causal space-time Galerkin scheme applied to the contrast current density volume integral equation gives rise to a marching-on-in-time scheme known as the MOT-JVIE, which is accelerated and stabilized via a fully embedded FIR filter to compute the electromagnetic scattering from high permittivity dielectric objects discretized with over a million voxels. A review of two different acceleration approaches previously developed for two-dimensional time-domain surface integral equations based on fast Fourier transforms (FFTs), leads to an understanding why these schemes obtain the same order of acceleration and the extension of this FFT-acceleration to the three-dimensional MOT-JVIE. The positive definite stability analysis (PDSA) for the MOT-JVIE shows that the number of voxels for a stable MOT-JVIE discretization is restricted by the finite precision of the matrix elements. The application of the PDSA provides the insight that stability can be enforced through regularization, at the cost of accuracy. To minimize the impact in accuracy, FIR-regularization is introduced, which is based on low group-delay linear-phase high-pass FIR-filters. We demonstrate the capabilities of the FFT-accelerated FIR-regularized MOT-JVIE for a number of numerical experiments with high permittivity dielectric scatterers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
