2019/04/05 by Jochen Hinz, Matthias Möller, Hinz, Jochen +3
Engineering · #Advanced Measurement and Metrology Techniques #Advanced Numerical Analysis Techniques #FOS: Mathematics #Manufacturing Process and Optimization #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1904.03009
openalex publication_date 2019/04/05 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
The first step towards applying isogeometric analysis techniques to solve PDE\nproblems on a given domain consists in generating an analysis-suitable mapping\noperator between parametric and physical domains with one or several patches\nfrom no more than a description of the boundary contours of the physical\ndomain. A subclass of the multitude of the available parameterization\nalgorithms are those based on the principles of Elliptic Grid Generation (EGG)\nwhich, in their most basic form, attempt to approximate a mapping operator\nwhose inverse is composed of harmonic functions. The main challenge lies in\nfinding a formulation of the problem that is suitable for a computational\napproach and a common strategy is to approximate the mapping operator by means\nof solving a PDE-problem. PDE-based EGG is well-established in classical\nmeshing and first generalization attempts to spline-based descriptions (as is\nmandatory in IgA) have been made. Unfortunately, all of the practically viable\nPDE-based approaches impose certain requirements on the employed spline-basis,\nin particular global C\≥ 1-continuity. This paper discusses a PDE-based\nEGG-algorithm for the generation of planar parameterizations with arbitrary\ncontinuity properties (where arbitrary stands for spline bases with global\nC\≥ 0-continuity). A major use case of the proposed algorithm is that of\nmulti-patch parameterization, made possible by the support of C\≥\n0-continuities. This paper proposes a specially-taylored solution algorithm\nthat exploits many characteristics of the PDE-problem and is suitable for\nlarge-scale applications. It is discussed for the single-patch case before\ngeneralizing its concepts to multipatch settings. This paper is concluded with\nthree numerical experiments and a discussion of the results.\n