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

Authors:
Gang Xu;Bernard Mourrain;Régis Duvigneau;André Galligo
Affiliations:
College of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, PR China and Galaad, INRIA Sophia-Antipolis, 2004 Route des Lucioles, 06902 Cedex, France;Galaad, INRIA Sophia-Antipolis, 2004 Route des Lucioles, 06902 Cedex, France;OPALE, INRIA Sophia-Antipolis, 2004 Route des Lucioles, 06902 Cedex, France;University of Nice Sophia-Antipolis, 06108 Nice Cedex 02, France
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

In isogeometric analysis, 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 focuses 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 iso-parametric 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.