PDE-Based Parameterization Techniques for Isogeometric Analysis Applications

Jochen Hinz

Research output: ThesisDissertation (TU Delft)

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The aim of this dissertation is to introduce the concept of PDE-based parameterization using Isogeometric Analysis (IGA) techniques and to present first results. IGA is a numerical technique that employs the spline- and NURBS-based geometric modeling tools of Computer Aided Geometric Design (CAGD) as a basis for numerical simulation using the principles of Finite Element Analysis (FEA). Thiswork proposes techniques that employ a parametric domain comprised of one (singlepatch) or several (multipatch) unit quadrilaterals and find an analysis-suitable mapping operator that parameterizes the physical domain. Here, the only input is a NURBS-based correspondence between the boundaries of the parametric and physical domain. To achieve this, this work adopts the principles of Elliptic Grid Generation (EGG), a PDE-based technique from classical meshing, and proposes discretizations that are suitable for an IGA-based computational workflow. The PDE-based problem formulation is motivated by the prospect of employing the same numerical technique for the geometrical as well as the computational aspects of the numerical simulation pipeline.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
  • Vuik, C., Supervisor
  • Möller, M., Advisor
Award date17 Jul 2020
Print ISBNs978-94-6384-146-7
Publication statusPublished - 2020

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