Nonlinear Krylov-Secant Solvers∗
نویسندگان
چکیده
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 basic 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 of dynamic ∗
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