Solving complementarity problems : Application to a diphasic flow in porous media
type: Dataset
description: This manuscript deals with numerical methods for linear and nonlinear complementarity problems,and, more specifically, with solving gas phase appearance and disappearance modeled as a complementarity problem. In the first part of this manuscript, we focused on the plain Newton-min method to solve the linear complementarity problem (LCP for short) 0 6 x ⊥ (Mx+q) > 0 that can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x,Mx+q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm was known to converge in at most n iterations. We show that this resultno longer holds when M is a P-matrix of order > 3. On the one hand, we offer counter-examplesshowing that the algorithm may cycle in those cases. P-matrices are interesting since they are thoseensuring the existence and uniqueness of the solution to the LCP for an arbitrary q. Incidentally,convergence occurs for a P-matrix of order 1 or 2. On the other hand, we provide a new algorithmic characterization of P-matricity : we show that a nondegenerate square real matrix M is a P-matrixif and only if, whatever is the real vector q, the Newton-min algorithm does not cycle between twopoints. In order to force the convergence of the Newton-min algorithm with P-matrices, we havederived a new method, which is robust, easy to describe, and simple to implement. It is globallyconvergent and the numerical results reported in this manuscript show that it outperforms a methodof Harker and Pang. In the second part of this manuscript, we consider the modeling of migration of hydrogen produced by the corrosion of the nuclear waste packages in an underground storage including the dissolution of hydrogen. It results in a set of nonlinear partial differential equations with nonlinear complementarity constraints. We show how to apply a robust and efficient solution strategy, the Newton-min method considered for LCP in the first par…
landing page: https://theses.hal.science/tel-00776617
identifier: NNT: 2012PA090045
keyword: algorithme-de-newton-min
keyword: analyse-non-lisse
keyword: convergence-globale
keyword: convergence-quadratique
keyword: dissolution
keyword: global-convergence
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: milieu-poreux
keyword: newton-min-algorithm
keyword: nonsmooth-function
keyword: porous-media
keyword: quadratic-convergence
keyword: theses
issued: 2026-05-14T16:25:45.054698
modified: 2026-05-14T16:25:45.054704
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Solving complementarity problems : Application to a diphasic flow in porous media
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00776617
issued: 2026-05-14T16:25:45.060806
modified: 2026-05-14T16:25:44.997031