An IGA Framework for PDE-Based Planar Parameterization on Convex Multipatch Domains
| Autor: | Hinz, J.P., Möller, M., Vuik, Cornelis, van Brummelen, H., Vuik, C., Verhoosel, C., Simeon, B. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Lecture Notes in Computational Science and Engineering ISBN: 9783030498351 Isogeometric Analysis and Applications 2018 |
| Popis: | 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≥1-continuity.This paper discusses an EGG-algorithm for the generation of planar parameterizations with locally reduced smoothness (i.e., with support for locally only C0-continuous bases). A major use case of the proposed algorithm is that of multipatch parameterizations, made possible by the support of C0-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. |
| Databáze: | OpenAIRE |
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