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 wellapproximated 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 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 mildy planar.