Date: Thu, 21 Nov 1996 20:55:28 GMT Server: Apache/1.1b3 Content-type: text/html Linda Petzold

Linda Petzold

Professor
Numerical analysis, differential-algebraic equations, scientific computing, mathematical software
petzold@cs.umn.edu
(612)625-2013

Positions Held:

Education:

Ph.D. 1978, Computer Science, University of Illinois at Urbana-Champaign
B.A. 1974, Mathematics, University of Illinois at Urbana-Champaign

Research in the group of Professor Petzold is centered on the analysis and development of numerical methods for differential equations and differential-algebraic equation (DAE) systems, scientific computing, parallel computing and mathematical software.

Differential equations and differential-algebraic systems arise in a wide variety of scientific and engineering applications. Differential-algebraic equations often occur as differential equations which are subject to constraints. The constraints may be linear or nonlinear, equality or inequality. DAE systems arise frequently as initial value problems in the computer-aided design and modeling of mechanical systems subject to constraints (multibody systems), circuit simulation, flowsheeting for chemical processes, modeling of the flow of incompressible fluids, and in many other applications. Boundary value problems in DAEs arise in parameter estimation and control for multibody systems and for chemical processes and determination of periodic solutions for circuits. The presence of the constraints in a DAE system leads to an interesting mathematical structure and presents challenges for numerical algorithms. Current research focuses on numerical methods for real-time simulation of mechanical systems, parameter estimation and optimal control of differential-algebraic systems, and parallel methods and software for very-large-scale systems of DAEs in geophysics and other applications.

Research Monograph:

K. E. Brenan, S. L. Campbell and L. R. Petzold, The Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, Elsevier Science Publishing Co., (1989).

Research Articles:

R. S. Maier, L. R. Petzold and W. Rath, Using DASPK on the TMC CM5: Experiences with Two Programming Models, Proc. 1993 Scalable Parallel Libraries Conf., 1993 (with R. S. Maier and W. Rath).

R. S. Maier, L. R. Petzold and W. Rath, Solving Large-Scale Differential-Algebraic Equations via DASPK on the CM5, submitted to Concurrency: Practice and Experience, 1994.

P. N Brown, A. C. Hindmarsh and L. R. Petzold, Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems, to appear, SIAM J. Scientific Computing.

U. Ascher and L. R. Petzold, The Numerical Solution of Delay-Differential-Algebraic Equations of Retarded and Neutral Type, to appear, SIAM J. Numerical Analysis.

U. Ascher, H. Chin, L. R. Petzold and S. Reich, Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds, submitted to Mechanics of Structures and Machines, 1993.

U. Ascher and L. R. Petzold, Stability of Computational Methods for Constrained Dynamics Systems, SIAM J. on Scientific and Statistical Computing 14, 1993.

L. R. Petzold, Numerical Solution of Differential-Algebraic Equations in Mechanical Systems Simulation, Physica D 60 (1992), 269-279.

U. Ascher and L. R. Petzold, Projected Implicit Runge-Kutta Methods for Differential-Algebraic Equations, SIAM J. on Numerical Analysis 28 (1991), 1097-1120.

C. W. Gear, B. J. Leimkuhler and L. R. Petzold, Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations, SIAM J. on Numerical Analysis 28 (1991).


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