J.R.Phillips and J. White, "Efficient Capacitance Extraction of 3D Structures Using Generalized Precorrected FFT methods," Proceedings of the IEEE 3rd Topical Meeting on Electrical Performance of Electronic Packaging, Monterey, CA, November 1994. 3  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of electrostatic and magnetoquasistatic analysis, the major cost of the algorithm is computing the dense matrix vector products. A variety of sparsification techniques have been applied to rapidly compute the matrix vector products, such as fast multipole algorithms [3] or precorrected PFT methods [8]. The precorrected FFT approach to computing distant interactions is to exploit the fact that evaluation points distant from a cube can be accurately computed by representing the given cube s charge distribution This work was supported by ARPA contrwcts N00174 93 C 0035 and DABT63 94 C 0053, NSF ....

....than even the optimized fast multipole algorithms used in programs like FASTCAP [2] However, to achieve the best. speed from precorrected FFT methods, the three dimensional convolution associated with computing grid charges from grid potentials must be optimized. For the results presented in [8], the three dimensional convolution was computed using zeropadding combined with the general three dimensional FFT routines from [7] The convoIution ca be made nearly five times faster by combining three tricks specific to our problem. The first trick for optimizing the use of the FFT to compute ....

J.R.Phillips and J. Wt, ite, "Efficient Capacitance Extraction of 3D Structures Using Generalized Pre- corrected FFT methods," Proceedings of the IEEE 3rd TopicaI Meeting on Electrical Perormance Electronic Packaging, Monterey, CA, November 1994.

....more reliant on accurate computer simulation tools. Signal integrity problems, like ground plane noise, are particular hard to simulate because so much of the problem geometry must be included to achieve accurate results. Multipole and precorrected FFT accelerated Method of Moments techniques [1, 3, 2, 4, 8] are one of the few techniques that are fast enough to analyze signal integrity problems, so optimizing these techniques seem worthwhile even if the resulting optimizations are somewhat incremental. In this paper we describe two optimizations to accelerated method of moments simulation, the first ....

....optimizations are somewhat incremental. In this paper we describe two optimizations to accelerated method of moments simulation, the first is an even better preconditioner than presented in [4] and the second is several optimizations of the FFT based convolution used in precorrected FFT methods [8]. 2 A New Preconditioner for Efficient Inductance Extraction Iterative algorithms used to solve the dense systems of equations resulting from the integral equations of magnetoquasistatic analysis rely on preconditioning to insure fast convergence. The preconditioning matrix must be a good ....

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J.R.Phillips and J. White, "Efficient Capacitance Extraction of 3D Structures Using Generalized Precorrected FFT methods," Proceedings of the IEEE 3rd Topical Meeting on Electrical Performance of Electronic Packaging, Monterey, CA, November 1994. 3

....method while still preserving the high order of accuracy of multipole based representations. For example, the approach can be combined with modified Green function techniques for handling ground planes, symmetry planes, or flat dielectric interfaces, with only minimal modification to the algorithm [36]. The algorithm is also capable of handling the Helmholtz kernel associated with full wave electromagnetic analysis [30] The major drawback of our algorithm is its poor performance on very inhomogeneous problems. The use of the FFT to evaluate the grid potentials is very inefficient in this case, ....

J. R. Phillips and J. K. White, "Efficient capacitance extraction of 3D structures using generalized pre-corrected FFT methods," in Proc. IEEE 3rd Topical Meeting on Electrical Performance of Electronic Packaging, Nov. 1994.

....efficiency for high accuracy [15, 16, 17] In addition, much recent work has focussed on allowing for more general Greens functions like those associated with layered me dia. There is the panel clustering idea [11] a multigrid style method [18] projection to a uniform grid combined with the FFT [9, 19] a technique based on the singularvalue decomposition [4] and approaches based on using wavelet like methods [20, 21, 22] 4 Model Order reduction The now standard approach to efficient circuitinterconnect simulation is to represent the interconnect with moment matching based reduced order ....

J. R. Phillips and J. K. White, "Efficient capac- itance extraction of 3D structures using generalized pre-corrected FFT methods," in Proceedings IEEE 3rd topical meeting on electrical performance of electronic packaging, November 1994. 913

....Fig. 22. Three level interconnect (m =1 mesh) operation. Since the fast multipole algorithm is used, the net cost is twice that of the problem without the groundplane. It would also be possible to use precorrected FFT methods with a modified Green s function to include the groundplane [21]. IX. MODEL ORDER REDUCTION RESULTS In this section, we present numerical results of our multipole accelerated, preconditioned model order reduction algorithm and demonstrate its accuracy and efficiency. Throughout, polysilicon conductivity and oxide permittivity will be assumed unless otherwise ....

J. R. Phillips and J. K. White, "Efficient capacitance extraction of 3-D structures using generalized precorrected FFT methods," in Proc. IEEE 3rd Topical Meeting on Electrical Performance Electron. Packaging, Nov. 1994.

.... is well known to have numerical accuracy difficulties when permittivity ratios are high [9] If the dielectric materials form flat layers, then the problem with ECF can be avoided by using layered media Green s functions [10] 11] and appropriately modified sparsification techniques [12] [13]. For problems with arbitrarily shaped dielectric interfaces with moderate permittivity ratios, it is possible to use ECF, though for such problems, the Galerkin boundary element method is far more accurate than centroid collocation [14] For sufficiently high permittivity ratios, the ECF ....

J. R. Phillips and J. White, "Efficient capacitance extraction of 3D structures using generalized pre-corrected FFT methods," in Proc. IEEE 3rd Topical Meeting Electrical Performance Electron. Packag., Monterey, CA, Nov. 1994.

....an iterative method is used to solve the system of equations, then only matrix vector products are required. A variety of sparsification techniques have been applied to rapidly compute the matrix vector products, such as the fast multipole algorithms [3, 4, 1, 5] and the precorrected FFT methods [8]. As the example in figure (1) and the performance data given in Table (1) demonstrate, these methods are extremely effective. Sparsification techniques like fast multipole or precorrected FFT algorithms start by dividing the problem domain containing the discretized structure into cubes, where ....

J. R. Phillips and J. K. White, "Efficient capacitance extraction of 3D structures using generalized pre-corrected FFT methods," in Proceedings IEEE 3rd topical meeting on electrical performance of electronic packaging, November 1994.

.... dense systems of equations which are extremely expensive to solve [2] In the last several years, very fast MOM solvers have been developed by combining iterative matrix solution methods with matrix sparsification based on fast multipole algorithms [3, 4, 1, 5] or the precorrected FFT method [7]. These fast methods have made it possible to quickly and accurately analyze very complicated structures, and in addition the existence of these fast methods has renewed interest in improved integral formulations. In this paper we describe a modified integral formulation, a second kind formulation ....

J. R. Phillips and J. K. White, "Efficient capacitance extraction of 3D structures using generalized pre-corrected FFT methods," in Proceedings IEEE 3rd topical meeting on electrical performance of electronic packaging, November 1994.

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J.R. Phillips and J.K. White, "Efficient Capacitance Extraction of 3D Structures using Generalized Pre-Corrected FFT Methods, " in Proc. IEEE 3rd Topical Meeting on Electrical Performance of Electronic Packaging, IEEE, New York, 1994, pp. 253--256.

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