Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method

Gang Xu 1, 2 Bernard Mourrain 1 Régis Duvigneau 3 André Galligo 1, 4
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
3 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 isogeometric anlaysis, parameterization of computational domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the computational domain to parametric domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of computational domain from CAD boundary for 2D and 3D isogeometric applications. Different from the previous elliptic mesh generation method in finite element analysis, the proposed method focus on isogeometric version, and converts the elliptic PDE into a nonlinear optimization problem, in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal isoparametric structure near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method in 2D and 3D isogeometric analysis.
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Gang Xu, Bernard Mourrain, Régis Duvigneau, André Galligo. Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method. [Research Report] 2011. ⟨inria-00585663v2⟩

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