A 3-d capacitance extraction algorithm based on kernel independent hierarchical method and geometric moments

Abstract

A three dimensional (3-D) capacitance extraction algorithm based on a kernel independent hierarchical method and geometric moments is described. Several techniques are incorporated, which leads to a better overall performance for arbitrary interconnect systems. First, the new algorithm hierarchically partitions the bounding box of all interconnect panels to build the partition tree. Then it uses simple shapes to match the low order moments of the geometry of each box in the partition tree. Finally, with the help of a fast matrix-vector product, GMRES is used to solve the linear system. Experimental results show that our algorithm reduces the linear system's size greatly and at the same time maintains a satisfying accuracy. Compared with FastCap, the running time of the new algorithm can be reduced more than a magnitude and the memory usage can be reduced more than thirty times.