We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs) We provide software for accessing and managing the Collection, from MATLAB™, Mathematica™, Fortran, and C, as well as an online search capability Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task

The university of Florida sparse matrix collection

Numerical Initial Value Problems in Ordinary Differential Equations

This paper describes an algorithm for generating provably passive reduced-order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. The approach proposed here, PRIMA, is a general method for obtaining passive reduced-order macromodels for linear RLC systems. In this paper, PRIMA is demonstrated in terms of a simple implementation which extends the block Arnoldi technique to include guaranteed passivity while providing superior accuracy. While the same passivity extension is not possible for MPVL, comparable accuracy in the frequency domain for all examples is observed.

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PRIMA: passive reduced-order interconnect macromodeling algorithm

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

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The Quadratic Eigenvalue Problem

In this paper, we introduce PVL, an algorithm for computing the Pade approximation of Laplace-domain transfer functions of large linear networks via a Lanczos process. The PVL algorithm has significantly superior numerical stability, while retaining the same efficiency as algorithms that compute the Pade approximation directly through moment matching, such as AWE and its derivatives. As a consequence, it produces more accurate and higher-order approximations, and it renders unnecessary many of the heuristics that AWE and its derivatives had to employ. The algorithm also computes an error bound that permits to identify the true poles and zeros of the original network. We present results of numerical experiments with the PVL algorithm for several large examples. >

Efficient linear circuit analysis by Pade approximation via the Lanczos process

A method for the efficient computation of accurate reduced-order models of large linear circuits is described. The method, called MPVL, employs a novel block Lanczos algorithm to compute matrix Pade approximations of matrix-valued network transfer functions. The reduced-order models, computed to the required level of accuracy, are used to speed up the analysis of circuits containing large linear blocks. The linear blocks are replaced by their reduced-order models, and the resulting smaller circuit can be analyzed with general-purpose simulators, with significant savings in simulation time and, practically, no loss of accuracy.

Reduced-Order Modeling of Large Linear Subcircuits via a Block Lanczos Algorithm

This paper introduces a new, efficient technique for analyzing noise in large RF circuits subjected to true multitone excitations. Noise statistics in such circuits are time-varying, hence cyclostationary stochastic processes, characterized by harmonic power spectral densities (HPSDs), are used to describe noise. HPSDs are used to devise a harmonic-balance-based noise algorithm with the property that required computational resources grow almost linearly with circuit size and nonlinearity. Device noises with arbitrary spectra (including thermal, shot, and flicker noises) are handled, and input and output correlations, as well as individual device contributions, can be calculated. HPSD-based analysis is also used to establish the nonintuitive result that bandpass filtering of cyclostationary noise can result in stationary noise. Results from the new method are validated against Monte Carlo simulations. A large RF integrated circuit (>300 nodes) driven by a local oscillator (LO) tone and a strong RF signal is analyzed in less than two hours. The analysis predicts correctly that the presence of the RF tone leads to noise folding, affecting the circuit's noise performance significantly.

Cyclostationary noise analysis of large RF circuits with multitone excitations

Lucent TechnologiesThis paper discusses the analysis of large linear electrical networks consisting of passive components, such as resistors, capacitors, inductors, and transformers. Such networks admit a symmetric formulation of their circuit equations. We introduce SyPVL, an efficient and numerically stable algorithm for the computation of reduced-order models of large, linear, passive networks. SyPVL represents the specialization of the more general PVL algorithm, to symmetric problems. Besides the gain in efficiency over PVL, SyPVL also preserves the symmetry of the problem, and, as a consequence, can often guarantee the stability of the resulting reduced-order models. Moreover, these reduced-order models can be synthesized as actual physical circuits, thus facilitating compatibility with existing analysis tools. The application of SyPVL is illustrated with two interconnect-analysis examples.

Reduced-order modeling of large passive linear circuits by means of the SYPVL algorithm

In this paper, we present a new implementation of the harmonic balance method which extends its applicability to circuits 2-3 orders of magnitude larger than was previously practical. The results reported here extend our previous work which only considered large circuits operating in a mildly nonlinear regime. The new implementation is based on quadratically convergent Newton methods and is able to simulate general nonlinear circuits. The significant efficiency improvement is achieved by use of Krylov subspace methods and a problem-specific preconditioner for inverting the harmonic balance Jacobian matrix. The analysis of radio-frequency mixers, implemented in integrated circuit technology, is an important application of our new method. We describe the theory behind the method, then report performance results on a complete receiver design using detailed transistor models.

Peter Feldmann

Papers

Efficient linear circuit analysis by Pade approximation via the Lanczos process

Reduced-Order Modeling of Large Linear Subcircuits via a Block Lanczos Algorithm

Cyclostationary noise analysis of large RF circuits with multitone excitations

Reduced-order modeling of large passive linear circuits by means of the SYPVL algorithm

Efficient frequency domain analysis of large nonlinear analog circuits