Planar Parametrization in Isogeometric Analysis

Jens Gravesen, Anton Evgrafov, Dang-Manh Nguyen, Peter Nørtoft

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Abstract

Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric analysis to shape optimization, where the geometry varies from one optimization iteration to another. We propose a general framework for handling the geometry parametrization in isogeometric analysis and shape optimization. It utilizes an expensive non-linear method for constructing/updating a high quality reference parametrization, and an inexpensive linear method for maintaining the parametrization in the vicinity of the reference one. We describe several linear and non-linear parametrization methods, which are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysis-oriented methods. Their performance is illustrated through a few numerical examples.
Original languageEnglish
Title of host publicationMathematical Methods for Curves and Surfaces : 8th International Conference, MMCS 2012, Oslo, Norway, June 28 – July 3, 2012, Revised Selected Papers
Number of pages189
PublisherSpringer
Publication date2014
ISBN (Print)978-3-642-54381-4
ISBN (Electronic)978-3-642-54382-1
DOIs
Publication statusPublished - 2014
Event8th International Conference on Mathematical Methods for Curves and Surfaces (MMCS 2012) - Oslo, Norway
Duration: 28 Jun 20123 Jul 2012
http://heim.ifi.uio.no/~cagd/2012/

Conference

Conference8th International Conference on Mathematical Methods for Curves and Surfaces (MMCS 2012)
Country/TerritoryNorway
CityOslo
Period28/06/201203/07/2012
Internet address
SeriesLecture Notes in Computer Science
Volume8177
ISSN0302-9743

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