In this paper a fast indirect boundaryelement method based on the multipole algorithm for capacitance extraction of three-dimensional (3-D) geometries, virtual cube multipole algorithm, is described. First,each 2-D boundary element is regarded as a set of particles with charge rather than a single particle, so the relations between the positions of elements themselves are considered instead of the relations between the center-points of the elements, and a new strategy for cube partitioning is introduced. This strategy overcomes the inadequacy of the methods that associating panels to particles, does not need to break up every panel contained in more than one cube, and has higher speed and precision. Next, a new method is proposed to accelerate the potential integration between the panels that are near to each other. Making good use of the similarity in the 2-D boundary integration,the fast potential integral approach decreases the burden of direct potential computing. Experiments confirm that the algorithm is accurate and has nearly linear computational growth as O(nm), where n is the number of panels and rn is the number of conductors. The new algorithm is implemented and the performance is compared with previous algorithms, such as Fastcap2 of MIT, for k×k bus examples.
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