Variational Harmonic Method for Parameterization of Computational Domain in 2D Isogeometric Analysis

Gang Xu (1, 2) , Bernard Mourrain (1) , Régis Duvigneau (3) , André Galligo (1, 4)

1 GALAAD - Geometry, algebra, algorithms
2 College of computer - Hangzhou Dianzi University
3 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
4 JAD - Laboratoire Jean Alexandre Dieudonné

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 map from the computational domain to parametric domain, a variational approach is proposed to construct the parameterization of computational domain for 2D isogeometric analysis. 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. A regular term is integrated into the optimization formulation to achieve more uniform grid near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method.

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Analyse numérique [math.NA]; Mécanique [physics.med-ph]

Gang Xu, Bernard Mourrain, Régis Duvigneau, André Galligo. Variational Harmonic Method for Parameterization of Computational Domain in 2D Isogeometric Analysis. 12th International CAD/Graphics 2011 conference, Sep 2011, Jinan, China. pp.223-228, ⟨10.1109/CAD/Graphics.2011.22⟩. ⟨inria-00585663v1⟩