Mattan Kamon

FASTHENRY: a multipole-accelerated 3-D inductance extraction program

A mesh analysis equation formulation technique combined with a multipole-accelerated Generalized Minimal Residual (GMRES) matrix solution algorithm is used to compute the 3-D frequency dependent inductances and resistances in nearly order n time and memory where n is the number of volume-filaments. The mathematical formulation and numerical solution are discussed, including two types of preconditioners for the GMRES algorithm. Results from examples are given to demonstrate that the multipole acceleration can reduce required computation time and memory by more than an order of magnitude for realistic integrated circuit packaging problems. >

A coordinate-transformed Arnoldi algorithm for generating guaranteed stable reduced-order models of RLC circuits

Abstract Since the first papers on asymptotic waveform evaluation (AWE), Pade-based reduced order models have become standard for improving coupled circuit-interconnect simulation efficiency. Such models can be accurately computed using bi-orthogonalization algorithms like Pade via Lanczos (PVL), but the resulting Pade approximates can still be unstable even when generated from stable RLC circuits. For certain classes of RC circuits it has been shown that congruence transforms, like the Arnoldi algorithm, can generate guaranteed stable and passive reduced-order models. In this paper we present a computationally efficient model-order reduction technique, the coordinate-transformed Arnoldi algorithm, and show that this method generates arbitrarily accurate and guaranteed stable reduced-order models for RLC circuits. Examples are presented which demonstrates the enhanced stability and efficiency of the new method.

Efficient Reduced-Order Modeling of Frequency-Dependent Coupling Inductances associated with 3-D Interconnect Structures

Since the first papers on asymptotic waveform evaluation (AWE), reduced order models have become standard for improving interconnect simulation efficiency, and very recent work has demonstrated that bi-orthogonalization algorithms can be used to robustly generate AWE-style macromodels. In this paper we describe using block Arnoldi-based orthogonalization methods to generate reduced order models from FastHenry, a multipole-accelerated three dimensional inductance extraction program. Examples are analyzed to demonstrate the efficiency and accuracy of the block Arnoldi algorithm.

FastHenry: A Multipole-Accelerated 3-D Inductance Extraction Program

In [1], it was shown that an equation formulation based on mesh analysis can be combined with a GMRES-style iterative matrix solution technique to make a reasonably fast 3-D frequency dependent inductance and resistance extraction algorithm. Unfortunately, both the computation time and memory required for that approach grow faster than n/sup 2/, where n is the number of volume-filaments. In this paper, we show that it is possible to use multipole-acceleration to reduce both required memory and computation time to nearly order n. Results from examples are given to demonstrate that the multipole acceleration can reduce required computation time and memory by more than an order of magnitude for realistic packaging problems.

Efficient reduced-order modeling of frequency-dependent coupling inductances associated with 3-D interconnect structures

Reduced-order modeling techniques are now commonly used to efficiently simulate circuits combined with interconnect, but generating reduced-order models from realistic 3-D structures has received less attention. In this paper we describe a Krylov-subspace based method for deriving reduced-order models directly from the 3-D magnetoquasistatic analysis program FASTHENRY. This new approach is no more expensive than computing an impedance matrix at a single frequency.<<ETX>>

Automatic generation of accurate circuit models of 3-D interconnect

In order to optimize high-speed systems, designers need tools that automatically generate reduced order SPICE compatible models from geometric descriptions of interconnect and packaging. In this paper, we consider structures small compared to a wavelength, and use a discretized integral formulation combined with an Arnoldi-based model-order reduction strategy to compute efficiently accurate reduced-order models from three-dimensional (3-D) structures. Several issues are addressed including: (1) formulation to insure passivity in the reduced-order models; (2) efficient reduction using preconditioned inner-loop iterative methods; (3) expansion about multiple s-domain points. Results are presented on several industrial examples to demonstrate the capabilities and speed of these new methods.

FastPep: a fast parasitic extraction program for complex three-dimensional geometries

In this paper we describe a computationally efficient approach to generating reduced-order models from PEEC-based three-dimensional electromagnetic analysis programs. It is shown that a recycled multipole-accelerated approach applied to recent model order reduction techniques requires nearly two orders of magnitude fewer floating point operations than direct techniques thus allowing the analysis of larger, more complex three-dimensional geometries.

Efficient techniques for inductance extraction of complex 3-D geometries

The combination of a mesh analysis equation formulation technique with a preconditioned GMRES matrix solution algorithm to accelerate the determination of inductances of complex three-dimensional structures is described. Addition of the preconditioner to GMRES can reduce the cost of solution to m/sup 2/ operations compared to m/sup 2/ for direct inversion. Results from FASTHENRY, a 3-D inductance extraction program, demonstrate that the iterative approach can accelerate solution times by more than an order of magnitude.<<ETX>>

A mixed nodal-mesh formulation for efficient extraction and passive reduced-order modeling of 3D interconnects

As VLSI circuit speeds have increased, reliable chip and system design can no longer be performed without accurate three-dimensional interconnect models. In this paper, we describe an integral equation approach to modeling the impedance of interconnect structures accounting for both the charge accumulation on the surface of conductors and the current traveling in their interior. Our formulation, based on a combination of nodal and mesh analysis, has the required properties to be combined with Model Order Reduction techniques to generate accurate and guaranteed passive low order interconnect models for efficient inclusion in standard circuit simulators. Furthermore, the formulation is shown to be more flexible and efficient than previously reported methods.

Generating compact, guaranteed passive reduced-order models of 3-D RLC interconnects

As very large scale integration (VLSI) circuit speeds and density continue to increase, the need to accurately model the effects of three-dimensional (3-D) interconnects has become essential for reliable chip and system design and verification. Since such models are commonly used inside standard circuit simulators for time or frequency domain computations, it is imperative that they be kept compact without compromising accuracy, and also retain relevant physical properties of the original system, such as passivity. In this paper, we describe an approach to generate accurate, compact, and guaranteed passive models of RLC interconnects and packaging structures. The procedure is based on a partial element equivalent circuit (PEEC)-like approach to modeling the impedance of interconnect structures accounting for both the charge accumulation on the surface of conductors and the current traveling in their interior. The resulting formulation, based on nodal or mixed nodal and mesh analysis, enables the application of existing model order reduction techniques. Compactness and passivity of the model are then ensured with a two-step reduction procedure where Krylov-subspace moment-matching methods are followed by a recently proposed, nearly optimal, passive truncated balanced realization-like algorithm. The proposed approach was used for extracting passive models for several industrial examples, whose accuracy was validated both in the frequency domain as well as against measured time-domain data.