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PSCAN'96: New software for simulation and optimization of complex RSFQ circuits

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 1997年第2期7卷 2685-2689页

作者： Polonsky, S Shevchenko, P Kirichenko, A Zinoviev, D Rylyakov, A Dept. of Phys. State Univ. of New York Stony Brook NY USA

The first version of PSCAN program (Personal Superconductor Circuit ANalyzer) was introduced in 1991. The program is a general purpose superconductor circuit simulator with an emphasis on the design of Rapid Single-Flux-Quantum (RSFQ) circuits. In the intervening years a number of new features were gradually added to the program. In particular, verification of the correct circuit behavior was enhanced using a special hierarchical Single-Flux-Quantum Hardware Description Language (SFQHDL). Next, a fast heuristic algorithm for margin optimization was introduced, which increased the number of parameters that can be simultaneously optimized in reasonable CPU times. Finally, recently we improved the numerical algorithm used for the simulation by using sparse symmetric positive definite matrices (instead of general structure band matrices as before). As a result, simulation speed has increased almost tenfold. Now it takes about 30 seconds of a CPU time on HP715/100 workstation to run a 2,000-ps simulation of a 120-Josephson-junction circuit, and about a week to optimize all parameters of a two hundred Josephson junction circuit. We have merged all these improvements in a new version of our simulator, PSCAN'96, which will be released by the time of this conference.

关键词： Analytical models Central Processing Unit Circuit analysis circuit analysis computing circuit optimisation Circuit simulation Circuit synthesis Circuit testing complex RSFQ circuits digital integrated circuits fast heuristic algorithm Hardware hardware description languages hierarchical HDL Josephson junctions Josephson-junction circuit margin optimization numerical algorithm optimization software PSCAN'96 rapid single-flux-quantum circuits SFQHDL simulation software simulation speed improvement software packages sparse matrices sparse symmetric positive definite matrices superconducting integrated circuits superconductor circuit simulator Symmetric matrices transient analysis verification

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Homotopy approach to solving nonlinear rational expectation problems

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Computational Economics 1997年第1期10卷 47-65页

作者： Jensen, Mark J. Department of Economics Southern Illinois University Carbondale U.S.A. e-mail

Many numerical methods have been developed in an attempt to find solutions to nonlinear rational expectations models. Because these algorithms are numerical in nature, they rely heavily on computing power and take sizeable cycles to solve. In this paper we present a numerical tool known as homotopy theory that can be applied to these methods. Homotopy theory reduces the computing time associated with an iterative algorithm by using a rational expectation problem with known solutions and transforming it into the problem at hand. If this transformation is performed slowly, homotopy theory also helps the global convergence properties of the numerical algorithm. We apply homotopy theory to Den Haan and Marcet's Parameterized Expectation Approach to show how homotopies improve the computing speed and global convergence properties of this algorithm.

关键词： Homotopy theory Nonlinear rational expectations models numerical algorithm

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Computation of the filtration laws through porous media for a non-Newtonian fluid obeying the power law

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Computational Geosciences 1997年第2期1卷 127-153页

作者： Gipouloux, Olivier Equipe d'Analyse Numerique UMR 5585 Universite de Saint Etienne F-42023 Saint Etienne Cedex 23 Rue du Docteur Michelon France

We consider a stationary flow of an incompressible non-Newtonian flow through a porous medium, induced by an injection velocity when inertial effects are negligible. At the pore scale, the governing equations are based on a nonlinear relation between the stress and the rate of deformation. In such a situation, the limit problem obtained when the pore size tends to zero, is called the homogenized problem that leads to the filtration law. This filtration law is given by a non-linear system coupling a local problem on a typical cell of the porous medium to a global problem at the scale of the whole porous medium. We propose, in this work, a numerical method to solve this homogenized problem and apply this method when the velocity dependent viscosity is given by the power law. Finally, we propose some numerical experiments to illustrate our approach. © Baltzer Science Publishers BV.

关键词： Filtration law Homogenization Non-Newtonian fluid numerical algorithm Porous medium Power law

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Computation of numerical Pade-Hermite and simultaneous Pade systems .2. A weakly stable algorithm

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 1996年第2期17卷 268-297页

作者： Cabay, S Jones, AR Labahn, G BELL NO RES LTD OTTAWAON K1Y 4H7CANADA UNIV WATERLOO DEPT COMP SCIWATERLOOON N2L 3G1CANADA

For k + 1 power series a(0)(z),...,a(k)(z), we present a new iterative, look-ahead algorithm for numerically computing Pade-Hermite systems and simultaneous Pade systems along a diagonal of the associated Pade tables. The algorithm computes the systems at all those points along the diagonal at which the associated striped Sylvester and mosaic Sylvester matrices are well conditioned. The operation and the stability of the algorithm is controlled by a single parameter tau which serves as a threshold in deciding if the Sylvester matrices at a point are sufficiently well conditioned. We show that the algorithm is weakly stable and provide bounds for the error in the computed solutions as a function of tau. Experimental results are given which show that the bounds reflect the actual behavior of the error. The algorithm requires O(\\n\\(2) + s(3)\\n\\) Operations to compute Pade-Hermite and simultaneous Fade systems of type n = [n(0),...,n(k)], where \\n\\ = n(0)+...+n(k) and s is the largest step-size taken along the diagonal. An additional application of the algorithm is the stable inversion of striped and mosaic Sylvester matrices.

关键词： Pade-Hermite approximants simultaneous Pade approximants striped Sylvester inverses mosaic Sylvester inverses numerical algorithm numerical stability

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Matrix partitioning on a virtual shared memory parallel machine

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1996年第4期7卷 343-355页

作者： Charny, B Audre Inc. San Diego CA USA

The general problem considered in the paper is partitioning of a matrix operation between processors of a parallel system in an optimum load-balanced way without potential memory contention. The considered parallel system is defined by several features the main of which is availability of a virtual shared memory divided into segments. if partitioning of a matrix operation causes parallel access to the same memory segment with writing data to the segment by al least one processor, then contention between processors arises which implies performance degradation. To eliminate such situation, a restriction is imposed on a class of possible partitionings, so that no two processors would write data to the same segment. On the resulting class of contention-free partitionings, a load-balanced optimum partitioning is defined as satisfying independent minimax criteria. The main result of the paper is an algorithm for finding the optimum partitioning by means of analytical solution of respective minimax problems. The paper also discusses implementation and performance issues related to the algorithm, on the basis of experience at Kendall Square Research Corporation, where the partitioning algorithm was used for creating high-performance parallel matrix libraries.

关键词： basic matrix operations matrix partitioning minimax criteria numerical algorithm optimum load balance parallel multiprocessor performance virtual shared memory

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numerical technique of non stationary electromagnetic theory

Numerical technique of non stationary electromagnetic theory

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VIth International Conference on Mathematical Methods in Electromagnetic Theory (MMET 96)

作者： Sirenko, Y Yashina, N Inst of Radiophysics and Electronics of the Natl Acad of Sciences of Ukraine Kharkov Ukraine

ISBN: (纸本)9660200269

The main subject of present communication is the review of modern methods and algorithms for numerical analyses of transient processes in open compact, waveguide and periodic resonators. The number of considered problems is rather big one and that is the reason to reformulate several authentic results orienting them towards less complicated scalar problems: 2d scattering bodies;all ″metal″ boundaries are supposed to be perfectly conducting;filling and wave propagation medium are supposed to be non magnetic, non absorbing, non dispersive;field is supposed to be E-polarized. Computation of scattering characteristics of elementary discontinuities is of special importance in this approach. We have developed specialized algorithms, using formally correct numerical subroutines in key steps of solution constructing, including analytical regularization of operator equations of the first kind.

关键词： boundary value problem transient process numerical algorithm

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An iterative aggregation/disaggregation procedure for modelling the long-term behaviour of continuous-time evanescent random processes

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 1996年第1期56卷 77-95页

作者： Stewart, DE Bebbington, MS MASSEY UNIV DEPT STATPALMERSTON NORTHNEW ZEALAND

We describe a multilevel aggregation/disaggregation method for finding the quasistationary distribution and decay parameters for continuous-time Markov chains. This complements existing techniques dealing with the discrete-time case, or for finding the stationary distribution. Finding the quasistationary distribution is equivalent to calculating the eigenvector corresponding to the smallest eigenvalue of the q-matrix restricted to the non-absorbing class. The method presented here is similar to an algebraic multigrid, with restriction operators that depend on the current approximation to the solution. The smoothers are short Arnoldi iterations or Gauss-Seidel iterations. numerical results are presented for a variety of models of differing character, including simple epidemic, bivariate SIS, predator-prey, and the cubic auto-catalator. These indicate that the number of cycles required grows only very slowly with the size of the problem.

关键词： quasistationary distribution numerical algorithm V-cycle

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Alternative split-operator approach for solving chemical reaction groundwater transport models

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ADVANCES IN WATER RESOURCES 1996年第5期19卷 261-275页

作者： Barry, DA Bajracharya, K Miller, CT Department of Environmental Engineering University of Western Australia Nedlands Western Australia 6907 Department of Environmental Sciences and Engineering University of North Carolina Chapel Hill North Carolina 27599-7400 USA

Various schemes are available to solve coupled transport/reaction mathematical models, one of the most efficient and easy to apply being the two-step split-operator method in which the transport and reaction steps are performed separately. Operator splitting, however, does not solve exactly the fully coupled numerical model derived from the governing partial differential and algebraic equations describing the transport and reaction processes. An error, proportional to Delta t (the time step used in the numerical solution) is introduced. Thus, small time steps must be used to ensure that accurate solutions result. An alternative scheme is presented, which iterates to the exact solution of the fully coupled numerical model. The new scheme enables accurate solutions to be calculated more efficiently than the two-step method, while maintaining separation of the transport and reaction steps in the calculations. As in the two-step method, the reaction calculations are performed node-wise throughout the computation grid. However, because the scheme relies on LU factorisation of the coefficient matrix in the transport equation solution, the reaction calculations must be performed in sequence, the sequence order being determined by the ordering of the nodes in the grid. Also, because LU factorisation is used, the scheme is limited to solute transport problems for which LU factorisation is a practical solution method. Copyright (C) 1996 Elsevier Science Limited

关键词： numerical algorithm LU factorisation iterative solution Crank-Nicolson scheme nonequilibrium reactions equilibrium reactions multispecies transport fixed-point iteration

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Spectral and Diffraction Characteristics of Open Cavities with Gyrotropic (Plasma) Inclusions

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Radiophysics and Quantum Electronics 1996年第9期39卷 777-777页

作者： Brovenko, A. V. Melezhik, P. N. Poedinchuk, A. E. Shestopalov, V. P. Institute of Radiophysics and Electronics National Academy of Sciences Khar'kov Ukraine

We develop a mathematically rigorous electrodynamic model which describes the spectral characteristics of 2-D open cavities with circular gyrotropic plasma cylinders. As a result, we construct and substantiate a numerical algorithm for calculating the spectrum of natural frequencies of this type of the structure. Oscillatory processes in a 2-D two-mirror cavity with circular plasma cylinders are analyzed in the bands in which hybrid intertype oscillations occur.

关键词： Nonlinear optic numerical algorithm Open cavity Quantum electronics Spectral characteristic

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An improved technique to determine the controlling unstable equilibrium point in a power system

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS 1996年第4期43卷 313-323页

作者： Treinen, RT Vittal, V Kliemann, W IOWA STATE UNIV SCI & TECHNOL DEPT MATHAMESIA 50011

The accuracy of stability assessment provided by the transient energy function (TEF) method depends on the determination of the controlling unstable equilibrium point (UEP), The technique that currently determines the controlling UEP in the TEF method is based on the so-called exit point method and has also been recently labeled the BCU method, The exit point method consists of two basic steps, First, the exit point is approximated by the point theta(egsa), where the first maximum of the potential energy along the fault-on trajectory is encountered, Second, the minimum gradient point theta(mgp) along the trajectory from theta(egsa) is computed, The controlling UEP is then obtained by solving a system of nonlinear algebraic equations with theta(mgp) as an initial guess, It has been observed that this method lacks robustness in the sense that the following two problems may occur, 1) There may be no detection of the minimum gradient point theta(mgp) and hence, no determination of the controlling UEP, 2) if theta(mgp) is found, then based on the definition of the controlling UEP, it may not be in the domain of convergence of the controlling UEP for the particular solving algorithm used, Hence, another equilibrium point, possibly a stable equilibrium paint, not the controlling UEP will be located, This results in a flawed transient stability assessment, The result of this research has been the development of a new numerical technique for determining the controlling UEP, With an initial starting point that is close to the exit point this technique efficiently produces a sequence of points, An analytical foundation for this method is given which shows that under certain assumptions this sequence will converge to the controlling UEP, Hence this new technique exhibits a substantial improvement over the exit point method because of the following reasons: (1) the technique does not attempt to detect the point theta(mgp), (2) the technique can produce a point that is close to t

关键词： power system analysis computing power system stability power system transients BCU method IEEE 50-generator controlling unstable equilibrium point convergence exit point minimum gradient point nonlinear algebraic equations numerical algorithm power syste differential algebraic equations Power system analysis computing Power system stability Riccati equations exit point power systems power system transients Converge

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