The Influence of Contrast and Temporal Expansion on the Marching-on-in-Time Contrast Current Density Volume Integral Equation

Q3 Engineering

Progress In Electromagnetics Research B Pub Date : 2023-09-12 DOI:10.2528/PIERB23091305

Petrus W.N. van Diepen, M. C. Beurden, R. Dilz

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引用次数: 0

Abstract

The contrast current density volume integral equation, discretized with piecewise constant spatial basis and test functions and Dirac-delta temporal test functions and the piecewise polynomial temporal basis functions, results in a causal implicit marching-on-in-time scheme that we refer to as the marching-on-in-time contrast current density volume integral equation (MOT-JVIE). The companion matrix stability analysis of the MOT-JVIE solver shows that for a fixed spatial and temporal step size, the stability is independent of the scatterer's dielectric contrast for quadratic spline temporal basis functions. Whereas, Lagrange and cubic spline exhibit instabilities at higher contrast. We relate this stability performance to the expansion and testing procedure in time. We further illustrate the capabilities of the MOT-JVIE based on quadratic spline temporal basis functions by: comparing the MOT-JVIE solution to time-domain results from literature and frequency-domain results from a commercial combined field integral equation solver. Finally, we present a long time sequence for a high-constrast scatterer discretized with 24,000 spatial unknowns.

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对比度和时间扩展对按时间行进的对比度电流密度体积积分方程的影响

对比度电流密度体积积分方程采用片断常数空间基函数和检验函数、狄拉克-德尔塔时间检验函数以及片断多项式时间基函数进行离散化，从而得到一种因果隐式按时间行进方案，我们称之为按时间行进对比度电流密度体积积分方程（MOT-JVIE）。MOT-JVIE 求解器的伴生矩阵稳定性分析表明，在固定的空间和时间步长下，二次样条时基函数的稳定性与散射体的介电对比度无关。而拉格朗日和三次样条曲线在对比度较高时表现出不稳定性。我们将这种稳定性能与时间扩展和测试程序联系起来。我们通过比较 MOT-JVIE 解决方案与文献中的时域结果以及商用组合场积分方程求解器的频域结果，进一步说明了基于二次样条时基函数的 MOT-JVIE 的能力。最后，我们展示了用 24,000 个空间未知数离散化的高对比度散射体的长时间序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Progress In Electromagnetics Research B Engineering-Electrical and Electronic Engineering

CiteScore

2.70

自引率

0.00%

发文量

期刊介绍： Progress In Electromagnetics Research (PIER) B publishes peer-reviewed original, comprehensive and tutorial review articles on all aspects of electromagnetic theory and applications. It is a new journal in 2008, and freely available to all readers via the Internet. Manuscripts submitted to PIER B must not have been submitted simultaneously to other journals. Authors are solely responsible for the factual accuracy of their articles, and all articles are understood to have received clearance(s) for publication.