This paper introduces a new integral formulation to calculate charge densities of conductor systems that may include multiple dielectric materials. We show that the conditioning of our formulation is much better than that of the standard equivalent charge formulation. When combined with a nonstandard discretization scheme, results can be obtained with higher accuracy at reduced numerical cost. We present a multipole accelerated implementation of our formulation. The results demonstrate that the new approach can cut the iteration count by a factor between two and four. Moreover, we will demonstrate that in the presence of sparsification errors and multiple dielectric materials second-kind formulations are much more accurate than the standard first-kind formulations.

The many levels of metal used in aggressive deep submicron pro-cess technologies has made fast and accurate capacitance extrac-tion of complicated 3-D geometries of conductors essential, and many novel approaches have been recently developed. In this paper we present an accelerated boundary-element method, like the well-known FASTCAP program, but instead of using an adaptive fast multipole algorithm we use a numerically generated multiscale ba-sis for constructing a sparse representation of the dense boundary-element matrix. Results are presented to demonstrate that the mul-tiscale method can be applied to complicated geometries, generates a sparser boundary-element matrix than the adaptive fast multipole method, and provides an inexpensive but effective preconditioner. Examples are used to show that the better sparsification and the ef-fective preconditioner yield a method that can be 25 times faster than FASTCAP while still maintain accuracy in the smallest cou-pling capacitances. 1

A new surface integral formulation and discretization approach for computing electromagnetoquasistatic impedance of general conductors is described. The key advantages of the formulation is that it avoids volume discretization of the conductors and the substrate, and a single discretization is accurate over the entire frequency range. Computational results from an on-chip inductor, a connector and a transmission line are used to show that the formulation is accurate and is "acceleration" ready. That is, the results demonstrate that an efficiently computed preconditioner insures rapid iterative method convergence and tests with projection show the required kernels can be approximated easily using a coarse grid.

Article Free Access Share on Multipole accelerated capacitance calculation for structures with multiple dielectrics with high permittivity ratios Authors: Johannes Tausch MIT Department of EECS, Cambridge, MA MIT Department of EECS, Cambridge, MAView Profile , Jacob White MIT Department of EECS, Cambridge, MA MIT Department of EECS, Cambridge, MAView Profile Authors Info & Claims DAC '96: Proceedings of the 33rd annual Design Automation ConferenceJune 1996 Pages 367–370https://doi.org/10.1145/240518.240588Published:01 June 1996Publication History 3citation230DownloadsMetricsTotal Citations3Total Downloads230Last 12 Months2Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF