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- W2934536830 abstract "The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from no more than a description of the boundary contours of the physical domain. A subclass of the multitude of the available parameterization algorithms are those based on the principles of Elliptic Grid Generation (EGG) which, in their most basic form, attempt to approximate a mapping operator whose inverse is composed of harmonic functions. The main challenge lies in finding a formulation of the problem that is suitable for a computational approach and a common strategy is to approximate the mapping operator by means of solving a PDE-problem. PDE-based EGG is well-established in classical meshing and first generalization attempts to spline-based descriptions (as is mandatory in IgA) have been made. Unfortunately, all of the practically viable PDE-based approaches impose certain requirements on the employed spline-basis, in particular global $C^{geq 1}$-continuity. This paper discusses a PDE-based EGG-algorithm for the generation of planar parameterizations with arbitrary continuity properties (where arbitrary stands for spline bases with global $C^{geq 0}$-continuity). A major use case of the proposed algorithm is that of multi-patch parameterization, made possible by the support of $C^{geq 0}$-continuities. This paper proposes a specially-taylored solution algorithm that exploits many characteristics of the PDE-problem and is suitable for large-scale applications. It is discussed for the single-patch case before generalizing its concepts to multipatch settings. This paper is concluded with three numerical experiments and a discussion of the results." @default.
- W2934536830 created "2019-04-11" @default.
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- W2934536830 date "2019-04-05" @default.
- W2934536830 modified "2023-09-27" @default.
- W2934536830 title "An IGA Framework for PDE-Based Planar Parameterization with Arbitrary Interface Continuity" @default.
- W2934536830 hasPublicationYear "2019" @default.
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