Nonlinear Krylov-Secant Solvers

Abstract

This report describes a new family of Newton-Krylov methods for solving nonlinear systems of equations arising from the solution of Richards' equation and in fully implicit formulations in air-water systems. The approach is to perform secant (Broyden) updates restricted to the Krylov subspace generated by the GMRES iterative solver. This approach is introduced as Krylov-secant methods. One of the most attractive features of these methods is their performance of sequence of rank-one updates without explicitly recalling the computation or action of the Jacobian matrix. Implications of these updates in line-search globalization strategies, computation dynamic tolerances (forcing terms) and the use of preconditioning strategies are presented. Numerical results show improvements over traditional implementations.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2006
Accession Number
ADA446287

Entities

People

  • Hector Klie
  • Mary F. Wheeler

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Convergence
  • Differential Equations
  • Engineering
  • Equations
  • Flow
  • Globalization
  • Groundwater
  • Iterations
  • Linear Systems
  • Nonlinear Systems
  • Partial Differential Equations
  • Saturation
  • Simulations
  • Standards
  • Wetting

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research