Newton-Krylov Solvers for Time-Steppers

Abstract

We study how the Newton-GMRES iteration can enable dynamic simulators (time-steppers) to perform fixed-point and path-following computations. For a class of dissipative problems, whose dynamics are characterized by a slow manifold, the Jacobian matrices in such computations are compact perturbations of the identity. We examine the number of GMRES iterations required for each nonlinear iteration as a function of the dimension of the slow subspace and the time-stepper reporting horizon. In a path-following computation, only a small number (one or two) of additional GMRES iterations is required.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2004
Accession Number
ADA446724

Entities

People

  • Carl Timothy Kelley
  • I. G. Kevrekidis
  • Li Qiao

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Chemical Engineering
  • Computational Science
  • Computations
  • Convergence
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Equations
  • Equations Of State
  • Formulas (Mathematics)
  • Integral Equations
  • Nonlinear Algebraic Equations
  • Partial Differential Equations
  • Simulators
  • Standards
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Linear Algebra
  • Robotics and Automation.