Stability Analysis of the Time Domain Integral Equation Method for Radar Scattering Analysis

Authors: Elwin van ‘t Wout, Duncan van der Heul, Harmen van der Ven and Kees Vuik

Source: FERMAT, Volume 17, Communication 8, Sep-Oct, 2016

Abstract: The Time Domain Integral Equation (TDIE) method is an appealing method for timedependent scattering analysis of electromagnetic waves. As a surface integral equation method, it is computationally efficient for scattering models at arbitrarily shaped objects and automatically satisfies radiation conditions for exterior problems. The time-domain formulation allows for the simulation of broadband signals at materials with nonlinear constitutive relations. However, its applicability has long been restricted by computational difficulties to obtain stable simulations for large-scale objects. Here, a stability analysis will be presented that is based on an established functional framework and stability theorem for a variational formulation of the electric field integral equation (EFIE). The functional framework will be extended to the differentiated version of the EFIE, which is more efficient to discretize and more conventional in engineering literature. Then, a discrete equivalence between Petrov-Galerkin and collocation schemes will be presented. This allows for a stability study of popular temporal basis functions. The impact of the stability theorem on the choice of discretization scheme is given by the recommendation to use quadratic spline basis function in the standard Marching-on-in-Time scheme. Computational experiments of time-dependent scattering at a generic aircraft confirm the stability analysis of the TDIE method.

Keywords: electromagnetic scattering, integral equation method, time domain analysis, stability.

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Stability Analysis of the Time Domain Integral Equation Method for Radar Scattering Analysis