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Construction dʼun champ continu de métriques

Patrick Laug 1, * Houman Borouchaki 2, 1 
* Corresponding author
1 Gamma3 - Automatic mesh generation and advanced methods
Inria Paris-Rocquencourt, ICD - Institut Charles Delaunay
Abstract : Adaptive computation using adaptive meshes is now recognized as essential for solving complex PDE problems. This computation requires, at each step, the definition of a continuous metric field to govern the generation of the adapted meshes. In practice, via an appropriate a posteriori error estimation, metrics are calculated at the vertices of the computational domain mesh. In order to obtain a continuous metric field, the discrete field is interpolated in the whole domain mesh. In this Note, a new method for interpolating discrete metric fields, based on a so-called "natural decomposition" of metrics, is introduced. The proposed method is based on known matrix decompositions and is computationally robust and efficient. Some qualitative comparisons with classical methods are made to show the relevance of this methodology.
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Patrick Laug, Houman Borouchaki. Construction dʼun champ continu de métriques. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2013, 351 (15-16), pp.639-644. ⟨10.1016/j.crma.2013.07.009⟩. ⟨hal-00936779⟩



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