PDE-Based Parameterization Techniques for Isogeometric Analysis Applications

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.