Hierarchical block boundary-element method (HBBEM): a fast field solver for 3-D capacitance extraction

As feature size decrease, fast and accurate parasitic capacitance extraction has become increasingly critical for verification and analysis in very large scale integration design. In this paper, a fast hierarchical-block boundary-element method based on the boundary-element method (BEM) is presented for three-dimensional (3-D) capacitance extraction, which can give out the global capacitance matrix directly. It assigns the global computation of 3-D domain into local computation in BEM blocks by hierarchical partition 3-D structure. The boundary capacitance matrix (BCM) is computed in the BEM block using all the known conditions. Reuse technology can decrease the running time. After merging the BCMs of all BEM blocks, the global capacitance matrix for a given set of conductors can be computed. Numerical results show that this global hierarchical approach can get very high speed in 3-D computation with equal accuracy as the 3-D field solver.