An IGA Framework for PDE-Based Planar Parameterization on Convex Multipatch Domains

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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.
Original languageEnglish
Title of host publicationIsogeometric Analysis and Applications 2018
EditorsH. van Brummelen, C. Vuik, M. Möller, C. Verhoosel, B. Simeon
Place of PublicationCham
Number of pages19
ISBN (Electronic)978-3-030-49836-8
ISBN (Print)978-3-030-49835-1
Publication statusPublished - 2021
EventIGAA: Conference on Isogeometric Analysis and Applications: IGAA 2018 - TU Delft, Delft, Netherlands
Duration: 23 Apr 201826 Apr 2018
Conference number: 3rd

Publication series

NameLecture Notes in Computational Science and Engineering book series
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100


ConferenceIGAA: Conference on Isogeometric Analysis and Applications

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project

Otherwise 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.


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