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≥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.
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.
Original language | English |
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Title of host publication | Isogeometric Analysis and Applications 2018 |
Editors | H. van Brummelen, C. Vuik, M. Möller, C. Verhoosel, B. Simeon |
Place of Publication | Cham |
Publisher | Springer |
Pages | 57-75 |
Number of pages | 19 |
ISBN (Electronic) | 978-3-030-49836-8 |
ISBN (Print) | 978-3-030-49835-1 |
DOIs | |
Publication status | Published - 2021 |
Event | IGAA: Conference on Isogeometric Analysis and Applications: IGAA 2018 - TU Delft, Delft, Netherlands Duration: 23 Apr 2018 → 26 Apr 2018 Conference number: 3rd |
Publication series
Name | Lecture Notes in Computational Science and Engineering book series |
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Publisher | Springer |
Volume | 133 |
ISSN (Print) | 1439-7358 |
ISSN (Electronic) | 2197-7100 |
Conference
Conference | IGAA: Conference on Isogeometric Analysis and Applications |
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Country/Territory | Netherlands |
City | Delft |
Period | 23/04/18 → 26/04/18 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.