Large-scale capacitance calculation

Kapur, Sharad

doi:10.1145/337292.337767

Cited by 26 publications

(20 citation statements)

References 9 publications

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“…Substituting (11) and (12) into (10) generates a meshed system that can be solved by an iterative method coupled with an accelerated matrix-vector product technique [1], [2], [3], [4], [5]. The solution of I m subsequently allows one to determine branch currents in I b that contains the actual basis function weights.…”

Section: B Discretizationmentioning

confidence: 99%

“…To date, there exists numerous accelerated integral-equation based electromagnetic solvers [1], [2], [3], [4], [5], [6] that are capable of rapid and accurate resolution of large conductor system impedance, some of which can even account for the effects invoked by the presence of a semi-conductive substrate. However, the efficiency of these solvers is being continuously challenged by the ever increasing operating frequencies which generate skin and proximity effects that need to be carefully modeled in order to provide accurate impedance solutions.…”

Section: Introductionmentioning

confidence: 99%

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Optimization-based Wideband Basis Functions for Efficient Interconnect Extraction

Hu¹,

Moselhy²,

White³

et al. 2007

2007 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition

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Abstract-This paper introduces a technique for the numerical generation of basis functions that are capable of parameterizing the frequency-variant nature of cross-sectional conductor current distributions. Hence skin and proximity effects can be captured utilizing much fewer basis functions in comparison to the prevalently-used piecewise-constant basis functions. One important characteristic of these basis functions is that they only need to be pre-computed once for a frequency range of interest per unique conductor cross-sectional geometry, and they can be stored off-line with a minimal associated cost. In addition, the robustness of these frequency-independent basis functions are enforced using an optimization routine. It has been demonstrated that the cost of solving a complex interconnect system can be reduced by a factor of 170 when compared to the use of piecewise-constant basis functions over a wide range of operating frequencies. [6] that are capable of rapid and accurate resolution of large conductor system impedance, some of which can even account for the effects invoked by the presence of a semi-conductive substrate. However, the efficiency of these solvers is being continuously challenged by the ever increasing operating frequencies which generate skin and proximity effects that need to be carefully modeled in order to provide accurate impedance solutions. I. INTRODUCTIONSkin and proximity effects are troublesome for today's fast solvers due to the fact that most of the mixed potential integral equation (MPIE) solvers rely on piecewise-constant [7], [2], [6] or piecewise-linear basis functions to capture conductor current distributions. As frequency increases, the use of these basis functions has proven to be computationally expensive because a very fine discretization scheme must be applied in order to faithfully capture the exponential variation in crosssectional conductor current, thus generating densely-populated clusters of filaments with highly uneven aspect ratios. One might think this is not problematic if the discretized system were to be solved by a fast technique since, theoretically speaking, the computational cost only scales in a linear fashion with the total number of basis functions. However, in practice, direct computation must be used to account for the numerous near-distanced interactions generated by clusters of long and skinny filaments which takes a quadratic order of complexity to resolve.The explosive cost associated with high-frequency impedance simulations has spurred the development of methods that seek to either represent interior conductor current using surface field quantities [8]

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Section: B Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimization-based Wideband Basis Functions for Efficient Interconnect Extraction

Hu¹,

Moselhy²,

White³

et al. 2007

2007 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition

View full text Add to dashboard Cite

show abstract

“…Interaction matrices of the form (1.1), with the Green's function possibly replaced with its three dimensional analogue, may occur as system matrices in a variety of situations in materials science and electrical engineering, for example, particle coarsening and capacitance extraction [14,15,18,19]. The particular application which drives this work concerns Laplace's equation and the DirichletNeumann map in domains exterior to a number n of closed contours -a problem which, in turn, has relevance for microstructural evolution, see Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Reasons for this may include that the problems at large n could be most pronounced in two dimensions. Should the Greens' function in (1.1) be replaced with a more rapidly decaying one, established preconditioners are reported to work satisfactorily [15,18,20,23]. Furthermore, efficient linear solvers for large systems involve other key components besides preconditioners.…”

Section: Introductionmentioning

confidence: 99%

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

Helsing

2006

Bit Numer Math

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Abstract.A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green's function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse.AMS subject classification (2000): 65F10,65R20,65F35,78A30.

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“…The first generation of fast field solvers used dense matrix compression methods such as the Fast Multipole Method (FMM), the Precorrected-FFT (PFFT), and SVD compression [3,4,5,6,10]. All these methods decompose the matrix into an explicit direct part and a implicit far-field part.…”

Section: Introductionmentioning

confidence: 99%

Large-scale full-wave simulation

Kapur

2004

Proceedings of the 41st Annual Design Automation Conference

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We describe a new extraction tool, EMX (Electro-Magnetic eXtractor), for the analysis of RF, analog and high-speed digital circuits. EMX is a fast full-wave field solver. It incorporates two new techniques which make it significantly faster and more memory-efficient than previous solvers. First, it takes advantage of layout regularity in typical designs. Second, EMX uses a new method for computing the vectorpotential component in the mixed potential integral equation. These techniques give a speed-up of more than a factor of ten, together with a corresponding reduction in memory.

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Large-scale capacitance calculation

Cited by 26 publications

References 9 publications

Optimization-based Wideband Basis Functions for Efficient Interconnect Extraction

Optimization-based Wideband Basis Functions for Efficient Interconnect Extraction

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

Large-scale full-wave simulation

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