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

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