Accession Number:

ADA446287

Title:

Nonlinear Krylov-Secant Solvers

Descriptive Note:

Corporate Author:

TEXAS UNIV AT AUSTIN DEPT OF MTHEMATICS AND INST OF COMPUTATIONAL ENGINEERING AND SCIENCES

Personal Author(s):

Report Date:

2006-01-01

Pagination or Media Count:

25.0

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.

Subject Categories:

  • Theoretical Mathematics
  • Numerical Mathematics
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE