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An IGA framework for PDE-based planar parameterization on convex multipatch domains. (English) Zbl 1495.65214

van Brummelen, Harald (ed.) et al., Isogeometric analysis and applications 2018. Selected papers based on the presentations at the third conference, IGAA 2018, Delft, The Netherlands, April 23–26, 2018. Cham: Springer. Lect. Notes Comput. Sci. Eng. 133, 57-75 (2021).
This article discusses an elliptic grid generation algorithm for the generation of planar parameterizations with locally reduced smoothness (in the class \(C^0\)-continuous bases). The approach relies on an iterative Newton-Krylov method operating on the Schur-complement of the linear part of the resulting nonlinear system of equations, which operates efficiently and reduces memory requirements. As application, the authors discuss single and multipatch parameterizations in some specific settings.
For the entire collection see [Zbl 1467.65001].

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
65D17 Computer-aided design (modeling of curves and surfaces)
65H10 Numerical computation of solutions to systems of equations
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References:

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