On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Bivariate spline spaces and minimal determining sets
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
ACM SIGGRAPH 2003 Papers
A First Course in Finite Elements
A First Course in Finite Elements
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
A normalized basis for quintic Powell--Sabin splines
Computer Aided Geometric Design
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
A normalized basis for reduced Clough-Tocher splines
Computer Aided Geometric Design
Isogeometric analysis and shape optimization via boundary integral
Computer-Aided Design
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We present a method for isogeometric analysis on the triangulation of a domain bounded by NURBS curves. In this method, both the geometry and the physical field are represented by bivariate splines in Bernstein-Bezier form over the triangulation. We describe a set of procedures to construct a parametric domain and its triangulation from a given physical domain, construct C^r-smooth basis functions over the domain, and establish a rational Triangular Bezier Spline (rTBS) based geometric mapping that C^r-smoothly maps the parametric domain to the physical domain and exactly recovers the NURBS boundaries at the domain boundary. As a result, this approach can achieve automated meshing of objects with complex topologies and allow highly localized refinement. Isogeometric analysis of problems from linear elasticity and advection-diffusion analysis is demonstrated.