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

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

5 Downloads (Pure)

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.
Original languageEnglish
Title of host publicationIsogeometric Analysis and Applications 2018
EditorsH. van Brummelen, C. Vuik, M. Möller, C. Verhoosel, B. Simeon
Place of PublicationCham
PublisherSpringer
Pages57-75
Number of pages19
ISBN (Electronic)978-3-030-49836-8
ISBN (Print)978-3-030-49835-1
DOIs
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
PublisherSpringer
Volume133
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

ConferenceIGAA: Conference on Isogeometric Analysis and Applications
CountryNetherlands
CityDelft
Period23/04/1826/04/18

Fingerprint Dive into the research topics of 'An IGA Framework for PDE-Based Planar Parameterization on Convex Multipatch Domains'. Together they form a unique fingerprint.

Cite this