Toeplitz-Plus-Hankel Matrix Recovery for Green's Function Computations on General Substrates

Rapidly diversifying technology and declining computational costs are popularizing technologically flexible simulation and verification techniques, even at some cost in performance. This paper investigates a data-driven, sampling-based approach for computing substrate Green's functions, which is more technology flexible than specialized layered media methods, at the cost of speed and accuracy. Our method is based on assuming that grid-sampled Green's functions can be well approximated by Toeplitz-plus-Hankel (TPH) matrices, and uses a least squares procedure to recover a TPH matrix from a small number of samples. We show that sample location is crucial, and that good sample locations are the ones that minimize an associated graph-diameter-based condition number estimate. The method's expected effectiveness is demonstrated on noise-polluted samples of layered media Green's functions. More surprisingly, we show that the method is effective even when applied to a substrate geometry that is only mildly planar.