Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Harmonic volumetric mapping for solid modeling applications
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Application of B-spline techniques to the modeling of airplane wings and numerical grid generation
Computer Aided Geometric Design
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Swept Volume Parameterization for Isogeometric Analysis
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Direct-Product Volumetric Parameterization of Handlebodies via Harmonic Fields
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Adaptive isogeometric analysis using rational PHT-splines
Computer-Aided Design
Variational Harmonic Method for Parameterization of Computational Domain in 2D Isogeometric Analysis
CADGRAPHICS '11 Proceedings of the 2011 12th International Conference on Computer-Aided Design and Computer Graphics
Parameterization of star-shaped volumes using green's functions
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Computer Aided Geometric Design
Journal of Computational Physics
Isogeometric analysis on triangulations
Computer-Aided Design
An optimization approach for constructing trivariate B-spline solids
Computer-Aided Design
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Parameterization of the 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 the multi-block computational domain in an 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 the single-block computational domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parameterization, 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 resulting 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 volumes should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on the three-dimensional heat conduction problem.