An optimal switching mechanism for a combined ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

An optimal switching mechanism for a combined Picard- Newton method for the solution of Richards´equation
Paper
Author:Javier Aparicio <japaricio@tlaloc.imta.mx> (Mexican Institute of Water Technology)
Álvaro Aldama <aaldama@tlaloc.imta.mx> (Mexican Institute of Water Technology)
Claudio Paniconi <putti@dmsa.unipd.it> (Center for advanced Studies, Research and Development in Sardinia)
Mario Putti <putti@dmsa.unipd.it> (Dept. Mathematical Methods and Models for Scientific Applications)
Presenter:Javier Aparicio <japaricio@tlaloc.imta.mx> (Mexican Institute of Water Technology)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000572
DOI:10.4122/1.1000000573

Richards’ equation, describing flow in partially saturated porous media, contains strong nonlinearities arising from pressure head dependencies in soil moisture and hydraulic conductivity. Additionally, the time- dependent nature of boundary conditions can alter the nonlinear characteristics of equation during a transient simulation. Various iterative methods are used for solving this nonlinear equation, most commonly the quadratically convergent Newton – Raphson technique and the simpler but only linearly convergent Picard method (successive approximation). The initial solution estimate can have a large influence on the behavior of these iterative schemes, and we have observed through many applications of our numerical subsurface flow models that the Newton scheme is more sensitive to the initial solution than the Picard scheme is used to calculate improved initial guess for the Newton iteration. This scheme should achieve quadratic convergence while improving the global behavior of the iteration at less cost and complexity than alternative globalization techniques such as line search and trust region methods. In this work the combined Picard – Newton method is investigated via a theoretical analysis, based on a Taylor – Frechét expansion of the nonlinear