No abstract

A numerically robust and computationally efficient approach for evaluating a planar layered substrate's static Green's function is developed based on the adaptive form of the Spectral Differential Equation Approximation Method. The method uses a pth order finite element method solution of the one-dimensional ordinary differential equation governing the spectrum of the layered media Green's function with spatial hadaptive meshing. The resulting pole-residue form of the Green's function spectrum enables analytic evaluation of the pertinent Sommerfeld integrals providing O(h p ) error control of the spatial layered medium Green's function in near, intermediate, and far zones. Detailed error analysis is presented enabling automation of the 1-Dimensional Finite Element Method mesh refinement, which guarantees a prescribed accuracy of the solution depending on the distance between the source and observation locations. The method is well-suited for computing Green's function databases used by method of moments capacitance and inductance extractors.