Etude des méthodes multigrilles dans le cadre de la résolution de systèmes linéaires

Abstract

This work presents multigrid methods for solving linear systems. The aim of developing multigrid methods is to remedy the drawbacks of the relaxation iterative methods. When a linear system is obtained by the discretization of a continuous problem, the application of a relaxation scheme on coarses grids than the initial discretization grid is proved to be efficient because either it gives a good starting point for the scheme or it can approximate the error comitted after the application of relaxation on the finer grid. Multigrid methods use these properties to approximate the solution of linear systems. We will first study the relaxation methods then the multigrid methods and we will end this work by introducing the algebraic multigrid methods, which are an adaptation of the classical multigrid methods for linear systems that are not the result of a discretization.

Date of Award	2005
Original language	French
Supervisor	Annick Sartenaer (Supervisor), Benoît Colson (Jury) & Philippe TOINT (Jury)