Joel R. Phillips

A precorrected-FFT method for electrostatic analysis of complicated 3-D structures

In this paper we present a new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations. Such integral equations arise, for example, in the extraction of coupling capacitances in three-dimensional (3-D) geometries. We present extensive experimental comparisons with the capacitance extraction code FASTCAP and demonstrate that, for a wide variety of geometries commonly encountered in integrated circuit packaging, on-chip interconnect and micro-electro-mechanical systems, the new precorrected-FFT algorithm is superior to the fast multipole algorithm used in FASTCAP in terms of execution time and memory use. At engineering accuracies, in terms of a speed-memory product, the new algorithm can be superior to the fast multipole based schemes by more than an order of magnitude.

A convex programming approach for generating guaranteed passive approximations to tabulated frequency-data

In this paper, we present a methodology for generating guaranteed passive time-domain models of subsystems described by tabulated frequency-domain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on- and off-chip interconnect effects, package parasitics, and passive devices common in high-frequency integrated circuit applications. The approach, which incorporates passivity constraints via convex optimization algorithms, is guaranteed to produce a passive-system model that is optimal in the sense of having minimum error in the frequency band of interest over all models with a prescribed set of system poles. We demonstrate that this algorithm is computationally practical for generating accurate high-order models of data sets representing realistic, complicated multiinput, multioutput systems.

Efficient full-wave electromagnetic analysis via model-order reduction of fast integral transforms

An efficient full-wave electromagnetic analysis tool would be useful in many aspects of engineering design. Development of integral-equation based tools has been hampered by the high computational complexity of dense matrix representations and difficulty in obtaining and utilizing the frequency-domain response. In this paper we demonstrate that an algorithm based on application of a novel model-order reduction scheme directly to the sparse model generated by a fast integral transform has significant advantages for frequency- and time-domain simulation.

Resampling Plans for Sample Point Selection in Multipoint Model-Order Reduction

Multipoint projection methods have gained much notoriety in model-order reduction of linear, nonlinear, and parameter-varying systems. A well-known difficulty with such methods lies in the need for clever point selection to attain model compactness and accuracy. In this paper, the authors present a method for sample point selection in multipoint projection-based model-order reduction. The proposed technique, which is borrowed from the statistical modeling area, is based on resampling schemes to estimate error and can be coupled with recently proposed order reduction schemes to efficiently produce accurate models. Two alternative implementations are presented: 1) a rigorous linear-matrix-inequality-based technique and 2) a simpler, more efficient, heuristic search. The goal of this paper is to answer two questions. First, can this alternative metric be effective in selecting sample points in the sense of placing points in regions of high error without recourse to evaluation of the larger system? Second, if the metric is effective in this sense, under what conditions are substantial improvements in the model reduction efficiency achieved? Results are shown that indicate that the metric is indeed effective in a variety of settings, therefore opening the possibility for performing adaptive error control

An FFT-based approach to including non-ideal ground planes in a fast 3-D inductance extraction program

It is noted that including non-ideal ground planes in 3-D inductance extraction programs is computationally expensive, as the ground plane must be finely discretized to ensure that the current distribution throughout the plane is accurately computed. This makes standard volume-element algorithms unsuitable because they require n/sup 2/ computation time and storage, where n is the number of filaments into which the ground plane is discretized. In the present work it is noted that, by using a preconditioned iterative method combined with an FFT (fast Fourier transform)-based algorithm to compute the iterates, one can reduce the computation time to effectively n log n, and substantially reduce required storage. Experimental results are presented which show that using the FFT-based approach is more than an order of magnitude faster than computing the iterates explicitly, even on problems with as few as a thousand volume-filaments. The FFT-based algorithm is compared with a GMRES (generalized minimal residual)-style algorithm.

Self-field effects in two-dimensional Nb Josephson-junction arrays

We have measured two-dimensional niobium Josephson junction arrays in which self induced fields are important. We find an increase of the depinning current when /spl lambda//sub /spl perp//, the penetration depth in the array, is of the order of one. There is evidence for a destruction of commensurate vortex states in the arrays as the depinning current becomes almost independent of the applied magnetic field. Our data also show that self-field effects change the array flux-flow dynamics and decrease the effective array viscosity.<<ETX>>

Generating High-Accuracy Simulation Models Using Problem-Tailored Orthogonal Polynomials Basis

The problem of computing high-accuracy simulation models for systems described by tabulated frequency data is of paramount importance in the modeling arena. Standard algorithms for this task involve generating rational function approximations to the data. However, for complicated data sets, high-order approximations are required. Unfortunately, numerical conditioning problems arise when attempting to fit high-order rational approximations to the data, effectively limiting the accuracy of the models that can be generated. While robust fitting schemes based on orthogonal polynomial exist, they usually pose strict constraints on the data points, which are either hard or even impossible to guarantee. Furthermore, the approximation must still be translated such that it can directly be used inside a simulator. In this paper, we present an algorithm for robustly generating such a model using only the data given. The model is supported on a problem-tailored orthogonal polynomial basis. We also present a method for directly generating a state-space model associated with a rational function described in terms of such polynomials, effectively making the model amenable for simulation. An extension to the MIMO case is described and it is shown that the method is easily included with existing passivity enforcing procedures. Finally, we demonstrate the proposed technique by constructing approximations to several real-world data sets

Some Empirical Results on Using Multipole-Accelerated Iterative Methods to Solve 3-D Potential Integral Equations

We briefly describe the now well-known multipole-accelerated algorithm for solving potential integral equations, and present computational results from solving several three-dimensional problems. The results indicate that the accuracy of the algorithm is dependent on the integral formulation used, and that the efficiency of the method is somewhat dependent on geometric density.

Applications of the Multi-Interval Chebyshev Collocation Method in RF Circuit Simulation

In this paper, we discuss the multi-interval Chebyshev (MIC) method for analog and radio-frequency (RF) circuit simulations. The method has been applied in a wide variety of circuit analyses including periodic steady-state, time-varying small signal, and cyclostationary noise analyses for both driven and autonomous circuits. In contrast to traditional analog/RF circuit simulations using either low-order time-domain integration methods or harmonic balance methods, we show that the MIC method can efficiently achieve high accuracy on strongly nonlinear circuits possessing waveforms with rapid transitions. In addition, it has the same flexibility in simulating frequency-dependent components as the harmonic balance methods but can use similar preconditioning strategies and matrix-implicit Krylov-subspace solvers as time-domain techniques, leading to good convergence on nonlinear problems.

3-D extraction techniques for signal integrity analysis

In this survey paper we describe recently developed techniques for 3-D extraction of complicated interconnect structures which are both fast and sufficiently accurate to perform signal integrity analysis.