Méthodes multiniveau algébriques pour les éléments d'arête. Application à l'électromagnétisme.

Abstract : The computation of the electric or magnetic field plays a key-role in the design of efficient communication tools, in the electromagnetic compatibility of electronic systems and also in the modelling of the interaction between the field and living tissues. This computation is frequently based on the discretisation of Maxwell's equations by the edge element method. Then, it leads to solve a linear system with a sparse but usually large matrix.

The aim of this work is to introduce an algebraic multilevel method for solving linear systems coming from the edge element method. Indeed, iterative multilevel methods generate algorithms which are the most efficient for some classes of partial differential equations. These methods are founded in their geometric version on a hierarchy of nested meshes; however, for realistic applications, this hierarchy cannot be constructed and the levels are then required to be algebraically defined.

Our algebraic strategy for defining the coarse levels is founded on the construction of nodal and edge coarse bases, which have to minimise an energy functional. This minimisation problem with constraint is solved by two techniques: for the first one Lagrange multipliers are used, for the second technique a sequence of flow problems in a graph is solved. Some numerical experiments illustrate the performances of the different versions of our method.
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https://tel.archives-ouvertes.fr/tel-00112227
Contributor : Ronan Perrussel <>
Submitted on : Monday, November 13, 2006 - 9:53:16 AM
Last modification on : Wednesday, December 12, 2018 - 3:30:07 PM
Long-term archiving on : Monday, September 20, 2010 - 4:31:26 PM

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  • HAL Id : tel-00112227, version 2

Citation

Ronan Perrussel. Méthodes multiniveau algébriques pour les éléments d'arête. Application à l'électromagnétisme.. Modélisation et simulation. Ecole Centrale de Lyon, 2005. Français. ⟨tel-00112227v2⟩

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