Nonlinear Krylov-Secant Solvers
TEXAS UNIV AT AUSTIN DEPT OF MTHEMATICS AND INST OF COMPUTATIONAL ENGINEERING AND SCIENCES
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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.
- Theoretical Mathematics
- Numerical Mathematics
- Fluid Mechanics