Floating Random Walk Capacitance Solver Tackling Conformal Dielectric With On-the-Fly Sampling on Eight-Octant Transition Cubes

A novel technique is proposed to deal with conformal dielectrics for extracting capacitances with floating random walk (FRW) method. It is based on the observation that the transition probabilities for the eight-octant cube exhibit a kind of symmetry and are closely related to those of a single-dielectric transition cube. We first theoretically proved this observation, and then proposed an approach generating the transition probabilities without any precalculation and memory cost. This enables on-the-fly sampling on eight-octant transition cubes and derives an improved FRW algorithm for capacitance extraction with conformal dielectrics. Compared with the existing approach, the proposed improved algorithm saves substantial memory cost and is more accurate. The numerical results have validated the theoretic analysis and demonstrated the benefits of the proposed capacitance solver for handling conformal dielectrics.