The NURBS book
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
A mixed finite volume scheme for anisotropic diffusion problems on any grid
Numerische Mathematik
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
SIAM Journal on Numerical Analysis
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
ISOGAT: A 2D tutorial MATLAB code for Isogeometric Analysis
Computer Aided Geometric Design
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A finite volume method for geometries parameterized by Non-Uniform Rational B-Splines (NURBS) is proposed. Since the computational grid is inherently defined by the knot vectors of the NURBS parameterization, the mesh generation step simplifies here greatly and furthermore curved boundaries are resolved exactly. Based on the incompressible Navier-Stokes equations, the main steps of the discretization are presented, with emphasis on the preservation of geometrical and physical properties. Moreover, the method is combined with a structural solver based on isogeometric finite elements in a partitioned fluid-structure interaction coupling algorithm that features a gap-free and non-overlapping interface even in the case of non-matching grids.