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Marching on in time, time domain integral equation solvers represent an increasingly appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. Compared to their differential equation counterparts, these solvers automatically impose radiation conditions, do not require unknown fields to be discretized throughout homogeneous volumes, and are highly immune...
In this paper, we present new techniques for stabilizing marching on in time-based time domain integral equation (MOT-TDIE) solvers that distinguish themselves from the above ones in that they operate hand in glove with recently developed Calderon-based MOT-TDIE preconditioners. The proposed preconditioners provide simple mechanisms for eliminating "resonant" and "DC" eigenvalues...
A spatially hierarchical current expansion is used to construct a marching-on-in-time based time domain electric field integral equation solver. The formulation gives rise to well-conditioned linear systems and is immune to time domain low-frequency breakdown phenomena. Numerical results that demonstrate the effectiveness of the proposed hierarchical approach in comparison with existing technologies...
A novel algorithm that accelerates marching on in time-based time domain integral equation solvers by rapidly evaluating transient fields due to spatially finite and temporally bandlimited (historical and surface-bound) source constellations is described. The multi-level Cartesian non-uniform grid time domain (ML-CNGTD) algorithm accomplishes the rapid evaluation by restoring delay- and amplitude-compensated...
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