Integer matrix factorization for mesh defect detection
Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 717-720.

The topological features of a given domain Ω in 3 are here analyzed by means of the homology groups of first and second order. Algebraic topology together with a particular 𝒬ℛ type factorization in can be used to know whether Ω is connected and simply connected, as well as to check if a given discretization of Ω by means of simplices has been correctly realized.

Les caractéristiques topologiques d'un domaine Ω de 3 sont analysées ici à l'aide des groupes d'homologie du premier et second ordre. La topologie algébrique et une factorization particulière de type 𝒬ℛ dans peuvent être utilisées afin de savoir si Ω est connexe et simplement connexe, de même que pour vérifier si une discrétisation de Ω par éléments simpliciaux a été bien réalisée.

Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02318-X
Rapetti, Francesca 1; Dubois, François 2; Bossavit, Alain 3

1 Laboratoire de mathématiques J.A. Dieudonné, CNRS & Université de Nice et Sophia-Antipolis, Parc Valrose, 06108 Nice cedex 02, France
2 Laboratoire des applications scientifiques du calcul intensif, CNRS, bat. 506, Université Paris Sud, 91403 Orsay, France
3 EdF, Division recherche et développement, 1, avenue du Général de Gaulle, 92141 Clamart cedex, France
@article{CRMATH_2002__334_8_717_0,
     author = {Rapetti, Francesca and Dubois, Fran\c{c}ois and Bossavit, Alain},
     title = {Integer matrix factorization for mesh defect detection},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {717--720},
     publisher = {Elsevier},
     volume = {334},
     number = {8},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02318-X},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02318-X/}
}
TY  - JOUR
AU  - Rapetti, Francesca
AU  - Dubois, François
AU  - Bossavit, Alain
TI  - Integer matrix factorization for mesh defect detection
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 717
EP  - 720
VL  - 334
IS  - 8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(02)02318-X/
DO  - 10.1016/S1631-073X(02)02318-X
LA  - en
ID  - CRMATH_2002__334_8_717_0
ER  - 
%0 Journal Article
%A Rapetti, Francesca
%A Dubois, François
%A Bossavit, Alain
%T Integer matrix factorization for mesh defect detection
%J Comptes Rendus. Mathématique
%D 2002
%P 717-720
%V 334
%N 8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02318-X/
%R 10.1016/S1631-073X(02)02318-X
%G en
%F CRMATH_2002__334_8_717_0
Rapetti, Francesca; Dubois, François; Bossavit, Alain. Integer matrix factorization for mesh defect detection. Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 717-720. doi : 10.1016/S1631-073X(02)02318-X. http://www.numdam.org/articles/10.1016/S1631-073X(02)02318-X/

[1] Bossavit, A. Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements, Academic Press, New York, 1998

[2] Chan, T.F. Rank revealing QR factorizations, Linear Algebra Appl., Volume 88/89 (1987), pp. 67-82

[3] Dubois, F.; Rapetti, F. Du tourbillon au champ de vitesse, Workshop at the Conservatoire des Arts et Métiers de Paris, on the subject “Modèles fluides et représentation en toubillons”, 1, 2000, pp. 127-153 see also in MATAPLI 65 (2001) 87–88

[4] Giblin, P.J. Graphs, Surfaces and Homology. An Introduction to Algebraic Topology, Chapman and Hall Math. Ser., 1977

[5] R. Hiptmair, J. Ostrowski, Generators of H1(Γh,Z) for triangulated surfaces: Construction and classification, Sonderforschungsbereich 382, Universität Tübingen, Report 160, 2001

[6] Kettunen, L.; Forsman, K.; Bossavit, A. Discrete spaces for divergence- and curl-free fields, IEEE Trans. Magn., Volume 34 (1998) no. 5, pp. 2851-2854

[7] Stillwell, J. Classical Topology and Combinatorial Group Theory, Graduate Texts in Math., 72, Springer-Verlag, 1993

Cited by Sources: