Improving Newton's method performance by parametrization: the case of Richards equation

Brenner, Konstantin; Cancès, Clément

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Improving Newton's method performance by parametrization: the case of Richards equation

Author(s) :

Brenner, Konstantin [Auteur]
COmplex Flows For Energy and Environment [COFFEE]
Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]

Journal title :

SIAM Journal on Numerical Analysis

Pages :

1760--1785

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2017

ISSN :

0036-1429

English keyword(s) :

Finite Volumes
parametrization
Newton's method
Richards equation

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Planète et Univers [physics]/Sciences de la Terre/Hydrologie

English abstract : [en]

The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new ...
Show more >The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new primary unknown for the continuous equation in order to stabilize Newton's method by parametrizing the graph linking the pressure and the saturation. The resulting form of Richards equation is then discretized thanks to a monotone Finite Volume scheme. We prove the well-posedness of the numerical scheme. Then we show under appropriate non-degeneracy conditions on the parametrization that Newton’s method converges locally and quadratically. Finally, we provide numerical evidences of the efficiency of our approach.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Approche géométrique pour les écoulements en milieux poreux: théorie et numérique
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :