Browsing by Author "Melville, Robert C."

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    Globally Convergent Homotopy Methods for the DC Operating PointProblem
    Melville, Robert C.; Trajkovic, Ljiljana; Fang, San-Chin; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1990)
    Accurate and efficient computer simulation of a proposed design for an integrated circuit ("chip") is essential because of the difficulty and expense of building prototypes for such devices. The transistors and diodes in such circuits are modeled with nonlinear equations, hence simulation of circuits requires the solution of systems of nonlinear equations involving hundreds or even thousands of variables. This paper discusses the application of probability-one homotopy methods to various systems of nonlinear equations which arise in circuit simulation. The so-called "coercivity conditions" which are required for such methods are proved using concepts from circuit theory. The theoretical claims of global convergence for such methods are substantiated by experiments with a collection of examples which have proved difficult for commercial simulation packages which do not use homotopy methods. Moreover, by careful design of the homotopy equations, the performance of the homotopy methods can be made quite reasonable.
  • HOMPACK90: A Suite of FORTRAN 90 Codes for Globally Convergent Homotopy Algorithms
    Watson, Layne T.; Sosonkina, Masha; Melville, Robert C.; Morgan, Alexander P.; Walker, Homer F. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1996-07-01)
    HOMPACK90 is a FORTRAN 90 version of the FORTRAN 77 package HOMPACK (Algorithm 652), a collection of codes for finding zeros or fixed points of nonlinear systems using globally convergent probability-one homotopy algorithms. Three qualitatively different algorithms - ordinary differential equation based, normal flow, quasi-Newton augmented Jacobian matrix - are provided for tracking homotopy zero curves, as well as separate routines for dense and sparse Jacobian matrices. A high level driver for the special case of polynomial systems is also provided. Changes to HOMPACK include numerous minor improvements, simpler and more elegant interfaces, use of modules, new end games, support for several sparse matrix data structures, and new iterative algorithms for large sparse Jacobian matrices.
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    Preconditioned Iterative Methods for Sparse Linear Algebra Problems Arising in Circuit Simulation
    McQuain, William D.; Ribbens, Calvin J.; Watson, Layne T.; Melville, Robert C. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1992-05-01)
    The DC operating point of a circuit may be computed by tracking the zero curve of an associated artificial-parameter homotopy. Homotopy algorithms exist that are globally convergent with probability one for the DC operating point problem. These algorithms require computing the one-dimensional kernel of the Jacobian matrix of the homotopy mapping at each step along the zero curve, and hence the solution of a linear system of equations at each step. These linear systems are typically large, highly sparse, non-symmetric and indefinite. Several iterative methods which are applicable to such problems, including Craig's method, GMRES(k), BiCGSTAB, QMR, KACZ, and LSQR, are applied to a suite of test problems derived from simulations of actual bipolar circuits. Preconditioning techniques considered include incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method and preconditioner.
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    Sframe: An Efficient System for Detailed DC Simulation of Bipolar Analog Integrated Circuits Using Continuation Methods
    Melville, Robert C.; Moinian, Shahriar; Feldman, Peter; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1992)
    In this paper we describe an experimental system called sframe which is being incorporated into the design for manufacturability initiative at the Reading Works of AT&T Bell Laboratories. Our system is able to perform detailed and accurate DC analyses of integrated circuits containing several hundred transistors to be fabricated in a relatively complex junction isolated complementary technology.