J. R. Philips and J. K. White, "A Precorrected-FFT Method for Capacitance Extraction of Complicated 3-D Structures," Proc. of the IEEE/ACM International Conference on Computer-Aided Design, pp. 268-271, November 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....study the capacitance extraction problem of three dimensional (3 D) electrical conductors of complex structures. Fast and accurate capacitance extraction is important in the design and verification of deep submicron very large scale integration (VLSI) circuits and packaging [9] 10] 13] 15] [17] and MEMS [19] Although there are a number of algorithms and commercial software for capacitance extraction, they are far from adequate. The 2 D 2.5 D algorithms are based on pattern matching. These algorithms are fast and capable of full chip extraction, but are inaccurate. The 3 D algorithms ....

.... [7] In this paper we propose a different time algorithm, which is based on a different hierarchical algorithm for the body problem by Appel [1] Efficient algorithms that are not based on the body problem include the precorrected fast Fourier transform (FFT) algorithm of Phillips and White [17], the singular value decomposition (SVD) algorithm of Kapur and Long [9] 10] etc. The running times of the precorrected FFT algorithm and SVD algorithm are both . Le Coz and Iverson [11] proposed a Monte Carlo algorithm and successfully turned it into the popular commercial software QuickCap. ....

[Article contains additional citation context not shown here]

J. R. Phillips and J. White, "A precorrected FFT method for capacitance extraction of complicated 3-D structures," in Proc. 1994 ICCAD, pp. 268--271.

....of Kapur et al. 63] is efficient and independent of kernel type, but in general case it still requires O(N operations for constructing the matrix and O(NlogN) operations per iteration for solving it. These methods use Galerkin discretisation in pulse functions basis. Precorrected FFT algorithm [64] is similar to SVD algorithm in terms of efficiency and is based on collocation technique. 1 xxF ( log The other main reason for the high computational cost of capacitance extraction with traditional approaches is the need to solve for the field distribution or superficial charge density ....

J.R. Phillips and J. White, "A Precorrected-FFT Method for Capacitance Extraction of Complicated 3-D Structures", 1994.

....of the physical design. 5.2. Parasitics Modeling Techniques The modeling of process related effects is a fairly mature field, with a wide range of tools, models, and techniques in use. Models range from empirical, easy to evaluate equations [20] to computationally intensive field solvers [19]. Awide range ofparasitics modeling tools are available both commercially and from universities. Commercially available tools provide reasonable accuracy (within 10 of field solvers) on large designs, and field solver accuracy is possible on a per net basis [21 ] Most commercial tools handle ....

J. R. Phillips and J. White, "A PrecorrectedFFT Method for Capacitance Extraction of Complicated 3-D Structures," Proc. ICCAD-94, pp. 268- 271.

....a current injected at a great distance is seen to have a very similar effect at two or more close by pick up points. Similarly, injecting a current in any of the closeby points has nearly the same effect on another distant pick up point. The DCT can be modified to account for this fact as in [17], thus resulting in an overall smaller coefficient of potential matrix, and hence in higher computational efficiency. Recently, a sensitivity analysis feature has been added to some substrate extractors. Computing sensitivities of substrate coupling is useful to project the effect of small ECOs ....

J. R. Phillips and J. White, "Precorrected-FFT Method for Capacitance Extraction of Complicated 3-D Structures", in Proc. IEEE International Conference on Computer Aided Design, pp. 268--271, November 1994.

....dramatically compressed using multipole expansions. While the algorithm is fast, because this implementation of the FMM is tailored to the free space 1=jjr Gamma r 0 jj kernel, dealing with common situations such as layered dielectrics is difficult. Another approach called the Precorrected FFT [13] combines the use of the Fast Fourier Transform with an interpolation based approach for the rapid computation of the matrix vector products. This algorithm has a much smaller memory requirement than the FMM. More recently, IES 3 ( ice cube ) an Integral Equation Solver for three dimensional ....

J. R. Philips and J. White. A precorrected-FFT method for capacitance extraction of complicated 3-D structures. In Proceedings of the International Conference on ComputerAided Design, Nov. 1994.

....another far away panel p j , can be considered the same for small variations in the distance between panels. Similar ideas have been used extensively in multipole accelerated algorithms [17, 14, 11] The approach developed here is reminiscent of other precorrected algorithms previously published [18] and relies on a simple coarser grid projection method, which can be used in combination with the DCT to accelerate the computation of the matrix vector product while taking into account all of the substrate boundary effects. Consider a group of panels at some location (call it cell g i ) and ....

....nearest neighbor cells. Since the approximation is of poor accuracy for nearby panel interactions, it is necessary to compute the nearest neighbor interactions directly for each panel, and to make appropriate corrections to Phi p . This is done in a manner similar to the precorrected FFT scheme [18]. First, we remove from every cell potential the influence of the self and nearest neighbor cell s currents. The contribution of the current on a specific cell i to the average potential of another cell k, i k can be written as i k = q i h i k , where q i is the sum of all the injected ....

J. Phillips and J. White. A precorrected-FFT method for capacitance extraction of complicated 3-D structures. In Proceedings of the Int. Conf. on Computer-Aided Design, November 1994.

....by IES 3 more than makes up for the FMM s smaller startup cost. In contrast, in a particle simulation environment where the geometry (and hence the matrix) changes after each multiply, the FMM has a definite advantage [3] We did not have access to the Precorrected FFT version of FastCap [9], but based on the relative performance of both approaches to the FMM version of FastCap, we believe that our approach still has performance advantages. Also note that there have been recent advances in the FMM algorithms [2] but they have not yet been incorporated into extraction programs such ....

J. R. Philips and J. White. A precorrected-FFT method for capacitance extraction of complicated 3-d structures. In International Conference on Computer-Aided Design, November 1994.

....2.7 from that computed by FastCap. 1 Introduction In this paper, we study the capacitance extraction problem of three dimensional perfect electrical conductors of complex structures. Fast and accurate capacitance estimation is important in the design of high performance integrated circuits [8, 9, 10, 11, 12, 13, 15]. Two examples of three dimensional complex structures for which capacitance strongly affects performance are DRAM cells and chip carriers used in high density packaging [10] 1.1 Integral Equation Approach We assume the conductors are embedded in a homogeneous dielectric medium, though our ....

.... for the n body problem [6] In this paper we propose a different O(n) time algorithm, which is based on a different O(n) time hierarchical algorithm for the n body problem by Appel [1] Efficient algorithms that are not based on the n body problem include an FFT algorithm of Phillips and White [13], and the singular value decomposition (SVD) algorithm of Kapur and Zhao [9, 8] The FFT algorithm and the SVD algorithm are about twice as fast as FastCap for test examples [13, 8] though the running time of both algorithms are O(n log n) 1.2 The n Body Problem In the n body problem, each of ....

[Article contains additional citation context not shown here]

J. R. Phillips and J. White, "A precorrected FFT method for capacitance extraction of complicated 3-D structures," Proc. 1994 ICCAD, 268--271.

....the PcDCT algorithm is to realize that the effect of an injected current in a panel on the potential of another far away panel can be considered the same for small variations in the distance between panels. Thus the PcDCT algorithm is similar to other precorrected algorithms previously published [9]. Consider a group of panels at some location (call it group g i ) and another group, g j , far away from g i . If a current is injected in some panel in g i , this current will have a similar effect on every panel of g j , as long as the distance between groups is large, where large depends of ....

J. Phillips and J. White. A precorrected-FFT method for capacitance extraction of complicated 3-D structures. In Proceedings of the Int. Conf. on Computer-Aided Design, November 1994.

....ply. However, in all three cases, multiplying by the associated matrix is equivalent to evaluring a potential at n points due to n sources. This computation can be performed in order n operations using the fast multipole algorithm [6] or in n log n operations using a precorrected FFT method [7]. As a brief explanation of how the fast multipole achieves its efficiency, consider the configuration, depicted in 2 D for simplicity, given in Figure 1. In the figure, the obvious approach to determining the electrostatic potential at the n evaluation points from the n2 point charges ....

....of the kernal, and so the approach can be combineds with modified Green s funcFigure 2: Representation of the four steps of the precorrected FFT algorit.hm. Figure 3: Half of a pin connect structure. Thirty five pins shown. tion methods for problems with ground planes or layered dielectrics [7]. 4 Results The 35 pin package shown in Figure 3 can have sufficient inductive coupling to cause signal integrity problems. To demonstrate the efficiency of multipole acceleration, the CPU time versus number of filaments for direct versus multipole methods is plotted in Figure 4 (from FASTHENleY ....

J. Phillips and J. White, "A Precorrected-FFT method for Capacitance Extraction of Complicated 3-D Structures," Proc. Int. Con on CAD, Santa Clara, California, November 1994.

....extraction can be substantially reduced using a clusterof workstations based parallel computer. In the next section we present background on 3 D capacitance extraction, and describe one of the recently developed fast methods for computing capacitances, the precorrected FFT accelerated method [1]. In Section 3 we describe the algorithms used to parallelize the precorrected FFT based capacitance extraction program and in Section 4 computational results are presented. Conclusions are given in Section 5. This research was supported by ARPA under ONR contract DABT63 94 C0053 and FBI contract ....

....the major cost of the algorithm is the order n operations required to form the dense matrix P and the order n operations to compute the dense matrix vector products for each GMRES iteration. Sparsification techniques, such as fast multipole algorithms [4] 5] or precorrected FFT methods [1], avoid forming P and can be used to compute densematrix vector products in order n or nlogn operations. Empirical studies on typical 3 D capacitance extraction problems indicate that precorrected FFT methods generally use the least memory and CPU time. In the precorrected FFT method, once ....

J. R. Phillips and J. White, "A Precorrected-FFT method for capacitance extraction of complicated 3-D structures," Proc. of the Int. Conf. on CAD, Santa Clara, CA, Nov., 1994.

....(15) and transform techniques, avoids forming most of P and reduces the cost of forming Pq to order n log n operations. A. The Precorrected FFT Approach The precorrected FFT approach generates an implicit approximation to P which can be used to compute the matrix vector products Pq rapidly [14]. In this approach, the interaction between nearby panels is computed explicitly. These entries in the potentiaj coefficient matrix, are computed by employing Equation (18) In a subsequent step, the portion of the matrix vector product Pq associated with distant interactions is computed by ....

....section III. In earlier approaches to electromechanical simulations [5] 6] 19] a multipole algorithm [8] is employed to efficiently compute the matrix vector product. The precorrected FFT algorithm, as compared to the multipole algorithm, has been shown to be faster and more memory efficient [14]. The computation of the matrix vector product with the precorrected FFF technique is summarized in Figure 2(b) ftrra of Elasttstafid : i i)irei Calchttibn i : Discrtie:Doin fiin. 1 i i Projd. cChe i i i onto (fia : Linear:BaSis:FunctiOns: I : Co trucrMaiefial, Oetmctri ....

J.R. Phillips and J. White, "A Precorrected-FFT method for capacitance extraction of complicated 3-D structures," Proc. ICCAD 1994.

....within each Newton iteration, requires only a matrix vector roduct involvin the matrix z. and p g , o the charge increment vector, Aq. In earlier approachesto electromechanical simulations [1] 2] 3] a multipole algorithm is employed to efficiently compute the matrix vector product. In [10], a precorrected Fast Fourier Transform (FFr) algorithm for computing the matrix vector product was presented, and as compared to multipole algorithm, has been shown to be faster and utilizes less memory. The precorrected FFI algorithm is employed in our direct Newton technique and the ....

J.R. Phillips and J. White, "A Precorrected-FFT method for capacitance extraction of complicated 3-D structures," Proc. ICCAD 1994.

....hi is just a single panel. The precorrected FFT technique If Gaussian elimination is used to solve (6) O(n a) operations and O(n 2) storage is required. Typical engineering problems may have thousands or tens of thousands of panels, so that Gaussian elimination is not a feasible approach. In [19, 18] it was shown that the precorrected FFT method described below is an efficient approach to solving (6) reducing the number of operations and memory required to nearly O(n log n) As can be seen from Fig. 2, for solution of Laplace s in typical engineering geometries, the precorrected FFT method ....

J. Phillips and J. White, "A Precorrected-FFT method for Capacitance Extrac- tion of Complicated 3-D Structures," Proceedings of the Int. Conf. on ComputerAided Design, Santa Clara, California, November 1994.

....is a commonly used approach to solving the coupled electromechanical problem. However, for very complicated three dimensional geometries, the electrostatic pressures can be computed much more efficiently using multipole or precorrected FFT accelerated iterative methods applied directly to (5) 7] [8]. The difficulty addressed in this paper is finding approaches which lets one use the most efficient algorithm for each of the domains but still allows one to solve the coupled problem. III. COUPLED METHODS Boundary element discretization of (5) leads to a system of equations of the form P #u # ....

J. R. Phillips and J. White, "A Precorrected-FFT method for capacitance extraction of complicated 3-D structures," Proc. ICCAD 1994.

....i is just a single panel. The precorrected FFT technique If Gaussian elimination is used to solve (6) O(n 3 ) operations and O(n 2 ) storage is required. Typical engineering problems may have thousands or tens of thousands of panels, so that Gaussian elimination is not a feasible approach. In [19, 18] it was shown that the precorrected FFT method described below is an efficient approach to solving (6) reducing the number of operations and memory required to nearly O(n log n) As can be seen from Fig. 2, for solution of Laplace s in typical engineering geometries, the precorrected FFT method ....

J. Phillips and J. White, "A Precorrected-FFT method for Capacitance Extraction of Complicated 3-D Structures," Proceedings of the Int. Conf. on ComputerAided Design, Santa Clara, California, November 1994.

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J. R. Philips and J. K. White, "A Precorrected-FFT Method for Capacitance Extraction of Complicated 3-D Structures," Proc. of the IEEE/ACM International Conference on Computer-Aided Design, pp. 268-271, November 1994.

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J. R. Phillips and J. White, "A precorrected-FFT method for capacitance extraction of complicated 3-D structures," in IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers. New York: IEEE Computer Society Press, 1994, pp. 268--271.

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J. R. Philips and J. K. White, "A Precorrected-FFT Method for Capacitance Extraction of Complicated 3-D Structures," Proc. of the IEEE/ACM International Conference on ComputerAided Design, pp. 268-271, 1994.

No context found.

J. Phillips and J. White, "A precorrected FFT method for capacitance extraction of complicated 3-D structures," in Proceedings of the Int. Conf. on Computer-Aided Design, pp. November 1994, Santa Clara, California.

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J. R. Phillips and J. White: "A Precorrected-FFT Method for Capacitance Extraction of Complicated 3-D Structures", International Conference on Computer Aided Design, San Jose, CA, USA, Nov 1994

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J. Phillips and J. White, "A precorrected FFT method for capacitance extraction of complicated 3-D structures," in Proceedings of the Int. Conf. on Computer-Aided Design, pp. November 1994, Santa Clara, California.

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