Adaptive Nonuniform-Grid (NG) Algorithm for Fast Capacitance Extraction

A novel method for computing the capacitance matrices of arbitrary shaped three-dimensional geometries is presented. The proposed approach combines a novel nonuniform-grid (NG) algorithm for fast evaluation of potentials due to given source distributions with an iterative solution of the pertinent integral equations. The NG algorithm is based on the observation that locally the potential produced by a finite size source can be interpolated from its samples at a small number of points of a nonuniform spherical grid. This observation leads to a multilevel algorithm comprising interpolation and aggregation of potentials. The resulting hierarchical algorithm attains an O(N) asymptotic complexity and memory requirements. The computational efficiency is further improved for quasi-planar geometries by the use of adaptive grids