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2023-11-29
The Influence of Contrast and Temporal Expansion on the Marching-on-in-Time Contrast Current Density Volume Integral Equation
By
Progress In Electromagnetics Research B, Vol. 104, 21-33, 2024
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-contrast scatterer discretized with 24,000 spatial unknowns.
Citation
Petrus Wilhelmus Nicolaas (Pieter) Van Diepen, Martijn Constant van Beurden, and Roeland Johannes Dilz, "The Influence of Contrast and Temporal Expansion on the Marching-on-in-Time Contrast Current Density Volume Integral Equation," Progress In Electromagnetics Research B, Vol. 104, 21-33, 2024.
doi:10.2528/PIERB23091305
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