Efficient numerical methods for capacitance extraction based on boundary element method

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Title: Efficient numerical methods for capacitance extraction based on boundary element method
Author: Yan, Shu
Abstract: Fast and accurate solvers for capacitance extraction are needed by the VLSI industry in order to achieve good design quality in feasible time . With the development of technology , this demand is increasing dramatically . Three -dimensional capacitance extraction algorithms are desired due to their high accuracy . However , the present 3D algorithms are slow and thus their application is limited . In this dissertation , we present several novel techniques to significantly speed up capacitance extraction algorithms based on boundary element methods (BEM ) and to compute the capacitance extraction in the presence of floating dummy conductors . We propose the PHiCap algorithm , which is based on a hierarchical refinement algorithm and the wavelet transform . Unlike traditional algorithms which result in dense linear systems , PHiCap converts the coefficient matrix in capacitance extraction problems to a sparse linear system . PHiCap solves the sparse linear system iteratively , with much faster convergence , using an efficient preconditioning technique . We also propose a variant of PHiCap in which the capacitances are solved for directly from a very small linear system . This small system is derived from the original large linear system by reordering the wavelet basis functions and computing an approximate LU factorization . We named the algorithm RedCap . To our knowledge , RedCap is the first capacitance extraction algorithm based on BEM that uses a direct method to solve a reduced linear system . In the presence of floating dummy conductors , the equivalent capacitances among regular conductors are required . For floating dummy conductors , the potential is unknown and the total charge is zero . We embed these requirements into the extraction linear system . Thus , the equivalent capacitance matrix is solved directly . The number of system solves needed is equal to the number of regular conductors . Based on a sensitivity analysis , we propose the selective coefficient enhancement method for increasing the accuracy of selected coupling or self -capacitances with only a small increase in the overall computation time . This method is desirable for applications , such as crosstalk and signal integrity analysis , where the coupling capacitances between some conductors needs high accuracy . We also propose the variable order multipole method which enhances the overall accuracy without raising the overall multipole expansion order . Finally , we apply the multigrid method to capacitance extraction to solve the linear system faster . We present experimental results to show that the techniques are significantly more efficient in comparison to existing techniques .
URI: http : / /hdl .handle .net /1969 .1 /3230
Date: 2006-04-12


Efficient numerical methods for capacitance extraction based on boundary element method. Available electronically from http : / /hdl .handle .net /1969 .1 /3230 .

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