Improving the robustness of a surface integral formulation for wideband impedance extraction of 3D structures

In order for parasitic extraction of high-speed integrated circuit interconnect to be sufficiently efficient, and fit with model-order reduction techniques, a robust wideband surface integral formulation is essential. One recently developed surface integral formulation has shown promise, but was plagued with numerical difficulties of poorly understood origin. We show that one of that formulation´s difficulties was related to the inaccuracy in the approach to evaluate integrals over discretization panels, and we present an accurate approach based on an adapted piecewise quadrature scheme. We also show that the condition number of the original system of integral equations can be reduced by differentiating one of the integral equations. Computational results on a ring and a spiral inductor are used to show that the new quadrature scheme and the differentiated integral formulation improve accuracy and accelerate the convergence of iterative solution methods.