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Adaptive Pseudo-transient Continuation for Nonlinear Steady State Problems

Please always quote using this URN: urn:nbn:de:0297-zib-6814
  • Pseudo--transient continuation methods are quite popular for the numerical solution of steady state problems, typically in PDEs. They are based on an embedding into a time dependent initial value problem. In the presence of dynamical invariants the Jacobian matrix of the nonlinear equation system is bound to be singular. The paper presents a convergence analysis which takes this property into account -- in contrast to known approaches. On the basis of the new analysis adaptive algorithms are suggested in detail. These include a variant with Jacobian approximations as well as inexact pseudo--transient continuation, both of which play an important role in discretized PDEs. Numerical experiments are left to future work.

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Metadaten
Author:Peter Deuflhard
Document Type:ZIB-Report
Tag:Euler discretization; contractivity of ordinary differential equations; lar; linearly implicit; pseudo--transient continuation; stiff integration
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Hxx Nonlinear algebraic or transcendental equations / 65H10 Systems of equations
65-XX NUMERICAL ANALYSIS / 65Hxx Nonlinear algebraic or transcendental equations / 65H20 Global methods, including homotopy approaches [See also 58C30, 90C30]
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N06 Finite difference methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N22 Solution of discretized equations [See also 65Fxx, 65Hxx]
Date of first Publication:2002/03/21
Series (Serial Number):ZIB-Report (02-14)
ZIB-Reportnumber:02-14
Published in:Appeared in: P. Deuflhard: Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Springer 2004. Series Computational Mathematics, 35
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