Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications

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 : Parameterization of computational domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of multi-block computational domain in isogeometric version, i.e, how to generate analysis-suitable parameterization of the multi-block computational domain bounded by B-spline surfaces. Firstly, we show how to find good volume parameterization of single-block computational domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parametrization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of B-spline volume parameterization. By using this method, the resulted volume parameterization has no self-intersections, and the isoparametric structure has good uniformity and orthogonality. Then we extend this method to the multi-block case, in which the continuity condition between the neighbor B-spline volume should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on three-dimensional heat conduction problem.
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Computer-Aided Design, Elsevier, 2013, Special Issue on Solid and Physical Modeling 2012, 45 (2), pp.395-404. 〈10.1016/j.cad.2012.10.022〉
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Gang Xu, Bernard Mourrain, Régis Duvigneau, André Galligo. Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications. Computer-Aided Design, Elsevier, 2013, Special Issue on Solid and Physical Modeling 2012, 45 (2), pp.395-404. 〈10.1016/j.cad.2012.10.022〉. 〈hal-00685002v2〉

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