J. Tausch and J. White. A multiscale method for fast capacitance extraction. In Design Automation Conference, pages 537--42, June 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Effect, Parasitic extraction, Interconnect analysis. 1. INTRODUCTION The new generation of fast electromagnetic analysis programs, based on accelerated integral equation methods, has reduced from days to minutes the time required to analyze thousands of simultaneously interacting conductors [1, 2, 3, 4, 5]. As good as these fast solvers are, they are either inappropriate for, or are very inefficient at, analyzing interconnect exhibiting high frequency effects. With processor clock speeds now exceeding two gigahertz and harmonics exceeding twenty gigahertz, it is no longer possible to ignore these ....

....(12) Equation (9) can be combined with the remaining equations (3) and (4) in several ways [6, 17, 18] to generate a dense system of equations for the basis function weights. Iterative methods combined with fast matrix vector product techniques are then commonly used to solve such system [1, 2, 3, 4, 5]. 2.3 The classical piece wise constant basis functions approach A classical choice for the basis functions is to use piece wise constant functions. For instance small panels with a uniform charge distribution can be used for the surface charge [1] Short thin filaments with a uniform current ....

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J. Tausch and J. White. A multiscale method for fast capacitance extraction. In Design Automation Conference, pages 537--42, June 1999.

....for the underlying black box substrate solver. Most of this is not new research, but is included for completeness and as a resource for workers starting out in this area. Chapter 3 gives a description of the wavelet based sparsification algorithm. This is essentially an adaptation of the work of [22] to our problem, although there are some differences. In particular, the use of the combine solves technique is new. The low rank method of Chapter 4 is new, although one of the major underlying ideas, the use of the SVD to sparsify matrix sections corresponding to well separated sets of ....

....then get a sparse approximation G8 of G simply by dropping small entries in G. We give results later which show that this leads to much more accurate results than simply dropping small entries in the original G for realistic problems. The algorithms for computing Q are based on those developed in [22] for 1 r potential from charge matrices. Here is a quick summary of the main differences. 45 First, since G is a current from potential matrix, for us the analogous quantity to charge in [22] is potential, and the analogous quantity to potential in [22] is current. We use polynomial moments ....

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J. Tausch and J. White, "A multiscale method for fast capacitance extraction," in Proceedings of the 36th Design Automation Conference, New Orleans, LA, 1999, pp. 537 542.

....pressing task: the verification problem. The past decade s intense development of accelerated integral equation solvers has made it possible to perform static and quasistatic electromagnetic analysis of packages or circuit boards with hundreds of conductors in just a few minutes on a workstation [1, 2, 3, 4]. The computational performance provided by these fast algorithms makes it now feasible to consider developing tools which can readily perform full board analysis, for use in applications such as SI and EMI diagnosis and resolution. This work was supported by the MARCO Interconnect Focus Center, ....

J. Tausch and J. White. A Multiscale Method for Fast Capacitance Extraction. In Design Automation Conference, June 1999.

....the potential of our method. I. Introduction The past decade s intense development of accelerated integral equation solvers has made it possible to perform electromagnetic analysis of packages or circuit boards with hundreds of conductors in just a few minutes on a workstation [1] 2] 3] [4]. The computational performance provided by these fast algorithms makes it now feasible to consider developing tools which can readily perform full board analysis, for use in applications such as electromagnetic compatibility diagnosis and resolution. If the application requires many full wave ....

J. Tausch and J. White. A multiscale method for fast capacitance extraction. In Design Automation Conference, June 1999.

....is that a large vector must be applied to a large matrix a large number of times. The main thrust of research in the past decade has been to develop techniques to accelerate the matrix vector product. These methods are based on the fast multipole method [3, 10] the FFT [13] SVD [6] multiscale [21] and dimension reduction ideas [5] All the above papers describe algorithms for the single layer equation, which is an integral equation of the rst kind and therefore ill conditioned. The conditioning e ects the performance of the algorithms in two negative ways. First, iterative methods ....

....the rst kind and therefore ill conditioned. The conditioning e ects the performance of the algorithms in two negative ways. First, iterative methods converge slowly, and second, small errors introduced by accelerated matrix vector products can be magni ed. While the preconditioners described in [22, 10, 21] can accelerate the speed of iterative solvers, the sensitivity of the error is inherent to the integral formulation. The presence of multiple dielectric materials complicates matters further. In this case the rst kind equation on the conductor surfaces must 1 be supplemented with a second kind ....

Johannes Tausch and Jacob White. A multiscale method for fast capacitance extraction. In 36th Design Automation Conference, pages 537-542, New Orleans, LA, 1999.

....in the new basis for arbitrary surfaces in a black box fashion. The basis functions have vanishing moments and thus integral operators from potential theory are sparse with respect to the basis, even for complex, multiply connected domains. Some of the material presented here was reported in [14]. The outline of this paper is as follows. Before we describe in detail the construction of the multilevel basis in Section 3, we will review in Section 2 the expansion of Coulombic Multiscale Bases for Integral Equations 3 potentials by spherical harmonics. We will describe in Section 4 how ....

Johannes Tausch and Jacob White. A multiscale method for fast capacitance extraction. In 36th Design Automation Conference, pages 537-542, New Orleans, LA, 1999.

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J. Tausch and J. White, "A multiscale Method for Fast Capacitance Extraction", Proc. of the 36th Design Automation Conference, New Orleans, LA, June 1999, pp. 537-542.

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