Resumen
Richards’ equation is essential in hydrogeological modeling. It serves as a generalization of the famous Darcy’s law, allowing for the description of water movement in soils under both saturated and unsaturated conditions. However, despite its importance for practical applications, this equation has gained a poor reputation due to the difficulties encountered in its numerical resolution. In fact, solving the algebraic systems that arise from its discretization can become problematic due to the stiffness of the nonlinear closure laws. After a brief introduction to Richards’ equation, from both hydrogeological and mathematical perspectives, I will present some nonlinear preconditioning methods aimed at improving the performance of the associated Newton’s method. Specifically, I will discuss traditional techniques based on the careful selection of primary variables, as well as more recent approaches involving domain decomposition methods. The latter are particularly interesting, both numerically and theoretically, as they allow for global convergence analysis.
Ponente
Dr. Konstantin Brenner
Laboratoire de Mathématiques J.A. Dieudonné, Côte d’Azur University
Inscripción
https://shorturl.at/jq1Ak
Informes
luis.lopez@aries.iimas.unam.mx
calleja@mym.iimas.unam.mx