Comptes Rendus
no. 11
Numerical Analysis
Gradient-prolongation commutativity and graph theory

Presented by: Philippe G. Ciarlet

François Musy1; Laurent Nicolas2; Ronan Perrussel1, 2
1 Institut Camille Jordan, École Centrale de Lyon, 69134 Ecully cedex, France
2 Centre de génie électrique de Lyon, École Centrale de Lyon, 69134 Ecully cedex, France
Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 707-712.

This Note gives conditions that must be imposed to algebraic multilevel discretizations involving at the same time nodal and edge elements so that a gradient-prolongation commutativity condition will be satisfied; this condition is very important, since it characterizes the gradients of coarse nodal functions in the coarse edge function space. They will be expressed using graph theory and they provide techniques to compute approximation bases at each level.

Cette Note donne des conditions qui doivent être imposées aux discrétisations multiniveau algébriques en éléments finis nodaux et d'arête de façon à assurer la commutativité entre gradient et prolongement ; cette relation importante caractérise les gradients des fonctions nodales grossières dans l'espace des fonctions d'arête grossières. Ces conditions seront exprimées en terme de graphes et elles permettent d'introduire des méthodes de calcul des bases d'approximation aux différents niveaux.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.09.037

François Musy 1; Laurent Nicolas 2; Ronan Perrussel 1, 2

1 Institut Camille Jordan, École Centrale de Lyon, 69134 Ecully cedex, France
2 Centre de génie électrique de Lyon, École Centrale de Lyon, 69134 Ecully cedex, France 
@article{CRMATH_2005__341_11_707_0,
     author = {Fran\c{c}ois Musy and Laurent Nicolas and Ronan Perrussel},
     title = {Gradient-prolongation commutativity and graph theory},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {707--712},
     publisher = {Elsevier},
     volume = {341},
     number = {11},
     year = {2005},
     doi = {10.1016/j.crma.2005.09.037},
     language = {en},
}
TY  - JOUR
AU  - François Musy
AU  - Laurent Nicolas
AU  - Ronan Perrussel
TI  - Gradient-prolongation commutativity and graph theory
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 707
EP  - 712
VL  - 341
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crma.2005.09.037
LA  - en
ID  - CRMATH_2005__341_11_707_0
ER  - 
%0 Journal Article
%A François Musy
%A Laurent Nicolas
%A Ronan Perrussel
%T Gradient-prolongation commutativity and graph theory
%J Comptes Rendus. Mathématique
%D 2005
%P 707-712
%V 341
%N 11
%I Elsevier
%R 10.1016/j.crma.2005.09.037
%G en
%F CRMATH_2005__341_11_707_0
François Musy; Laurent Nicolas; Ronan Perrussel. Gradient-prolongation commutativity and graph theory. Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 707-712. doi : 10.1016/j.crma.2005.09.037. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.037/

[1] R. Hiptmair Finite elements in computational electromagnetism, Acta Numer., Volume 11 (2002), pp. 237-339

[2] R. Hiptmair Multigrid method for Maxwell's equations, SIAM J. Numer. Anal., Volume 36 (1999), pp. 204-225

[3] J. Mandel; M. Brezina; P. Vaněk Energy optimization of algebraic multigrid bases, Computing, Volume 62 (1999) no. 3, pp. 205-228

[4] F. Musy; L. Nicolas; R. Perrussel; M. Schatzman Compatible coarse nodal and edge elements through energy functionals, 2004 http://maply.univ-lyon1.fr/~perrussel/report.pdf (UMR MAPLY, internal report 394)

[5] S. Reitzinger; J. Schöberl An algebraic multigrid method for finite element discretizations with edge elements, Numer. Linear Algebra Appl., Volume 9 (2002), pp. 223-238

Cited by Sources:

Comments - Policy