The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same...

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

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...

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...

Spline-based meshing techniques for industrial applications

Isogeometric Analysis (IgA) has become an accepted framework for the mod-elling, simulation and optimization (MSO) of engineering processes. However, the fully automatized generation of analysis-suitable parameterizations of geometries as they arise in practical workflows is still a challenging task, which often requires application-specific...

Elliptic grid generation techniques in the framework of isogeometric analysis applications

The generation of an analysis-suitable computational grid from a description of no more than its boundaries is a common problem in numerical analysis. Most classical meshing techniques for finite-volume, finite-difference or finite-element applications such as the Advancing Front Method (Schöberl, 1997), Delaunay Triangulation (Triangle, 1996...

Spline-Based Parameterization Techniques for Twin-Screw Machine Geometries

The fully automated generation of computational meshes for twin-screw machine geometries constitutes a mandatory aspect for the numerical simulation (and shape-optimization) of these devices but proves to be a challenging task in practice. Therefore, the successful generation of computational meshes requires sophisticated mathematical tools....

Isogeometric Analysis of a Reaction-Diffusion Model for Human Brain Development

In my thesis I present a numerical scheme to tackle the Gray-Scott Reaction-Diffusion Model for Human Brain Development. The numerical scheme is based on the principles of Isogeometric Analysis and a number of simulations are given in the report.