Multihomogeneous resultant formulae for systems with scaled support - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of Symbolic Computation Année : 2012

Multihomogeneous resultant formulae for systems with scaled support

Résumé

In this work, we develop a specialized quadrature rule for trimmed domains , where the trimming curve is given implicitly by a real-valued function on the whole domain. We follow an error correction approach: In a first step, we obtain an adaptive subdivision of the domain in such a way that each cell falls in a pre-defined base case. We then extend the classical approach of linear approximation of the trimming curve by adding an error correction term based on a Taylor expansion of the blending between the linearized implicit trimming curve and the original one. This approach leads to an accurate method which improves the convergence of the quadrature error by one order compared to piecewise linear approximation of the trimming curve. It is at the same time efficient, since essentially the computation of one extra one-dimensional integral on each trimmed cell is required. Finally, the method is easy to implement, since it only involves one additional line integral and refrains from any point inversion or optimization operations. The convergence is analyzed theoretically and numerical experiments confirm that the accuracy is improved without compromising the computational complexity.
Fichier principal
Vignette du fichier
mh-arx.pdf (288.66 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

inria-00355881 , version 1 (26-01-2009)
inria-00355881 , version 2 (03-02-2010)

Identifiants

Citer

Ioannis Emiris, Angelos Mantzaflaris. Multihomogeneous resultant formulae for systems with scaled support. Journal of Symbolic Computation, 2012, pp.820-842. ⟨10.1016/j.jsc.2011.12.010⟩. ⟨inria-00355881v2⟩
274 Consultations
297 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More