Abstract
This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational domain is available. The idea goes back to the Scaled Boundary Finite Element Method (SB-FEM), which has recently been extended to IGA. We take here a different viewpoint and study these parametrizations as bivariate or trivariate B-spline functions that are directly suitable for standard Galerkin-based IGA. Our main results are first a general framework for this class of parametrizations, including aspects such as smoothness and regularity as well as a generalization to domains that are not star-shaped. Second, using the Poisson equation as an example, we explain the relation between standard Galerkin-based IGA and the Scaled Boundary IGA by means of the Laplace–Beltrami operator and derive an equivalence theorem. Further results concern the separation of integrals in both approaches and an analysis of the singularity in the scaling center. Among the computational examples we present a rotor geometry that stems from a screw compressor machine and compare different parametrization strategies.
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