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An Introduction to Isogeometric Analysis with Application to Thermal Conduction

Régis Duvigneau 1 
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : 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. High-order, h- and 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.
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Submitted on : Wednesday, June 10, 2009 - 4:18:41 PM
Last modification on : Saturday, June 25, 2022 - 11:01:31 PM
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  • HAL Id : inria-00394151, version 1


Régis Duvigneau. An Introduction to Isogeometric Analysis with Application to Thermal Conduction. [Research Report] RR-6957, INRIA. 2009, pp.28. ⟨inria-00394151⟩



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