An Introduction to Isogeometric Analysis with Application to Thermal Conduction
نویسنده
چکیده
In this report, we present a new method, namely isogeometric analysis, proposed by T. Hughes and his collaborators, whose objective is to combine Computer Aided Design (CAD) tools and Finite-Element (FE) solvers into a single software entity. This consists in replacing grids by parametric surfaces and volumes to define the integration elements used in a variational formulation. This approach allows to define a computational domain that matches exactly the geometry of the problem, whatever the number of degrees of freedom. Highorder, hand p-adaptive schemes, as well as hierarchical solving strategies can be constructed. After presenting the method and comparing with classical finite-element approach, some numerical experiments are carried out using a thermal conduction test-case. Key-words: Isogeometric analysis, finite-elements, thermal conduction ∗ Opale Project-Team in ria -0 03 94 15 1, v er si on 1 10 J un 2 00 9 Une introduction à l’analyse isogéométrique avec application à la conduction thermique Résumé : On présente dans ce rapport une nouvelle méthode, appelée analyse isogéométrique, proposée par T. Hughes et ses collaborateurs pour fusionner les outils de Conception Assistée par Ordinateur (CAO) et les solveurs éléments-finis (EF) en une seule entité logicielle. Cela consiste à remplacer les maillages par des surfaces et volumes paramétrés pour définir les éléments d’intégration utilisés dans une formulation variationnelle. Cette approche permet de définir un domaine de calcul qui correspond exactement à la géométrie du problème, quel que soit le nombre de degrés de liberté. On peut construire des schémas d’ordre élevé het p-adaptatifs, ainsi que des stratégies hiérarchiques de résolution. Après une présentation de la méthode et une comparaison avec une méthode éléments-finis classique, quelques expériences numériques sont menées, dans le cadre d’un problème de conduction thermique. Mots-clés : Analyse isogéométrique, élément-finis, conduction thermique in ria -0 03 94 15 1, v er si on 1 10 J un 2 00 9 An introduction to isogeometric analysis 3
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