Institute of Applied Geometry

The Principal Investigator

Bert Jüttler
JKU - Johannes Kepler University
Institute of Applied Geometry,
Altenberger Str. 69, 4040 Linz, Austria

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Starting date: March 1st, 2012
Prolongation: February 28, 2021

Project 7

Geometric Modeling for Numerical Simulation

This project will address the challenging geometric problems which arise in the connection with Isogeometric Analysis (IGA, see [1]). IGA is a very promising concept which will potentially lead to major improvements of the product design process in industry. However, it was soon realized that the models produced by the current CAD technology are not directly usable for IGA.

First, CAD models provide only a description of the domain boundary, while the numerical simulation often requires a parametrization of the volume. Consequently, computational techniques for creating NURBS volume parametrizations are needed. The existing techniques for NURBS volume parametrizations are mainly restricted to simple objects, where they were mainly used for shape editing via free-form volume deformations.

Second, the spline spaces used by CAD models do not provide the possibility of local re-finement, which is essential for an adaptive numerical simulation. While algorithms for h- and p-refinement are readily available (called knot insertion and degree elevation, respectively), the construction of locally refined spline spaces requires additional research and is currently being studied by several researchers.

Third, the technology is not directly applicable to situations where the geometry is not directly available in a CAD-type format, e.g., in medical applications.

The planned work in this subproject is organized in four activities.

[1] T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comp. Meth. in Appl. Mech. Engrg., 194:4135-4195, 2005. doi:10.1016/j.cma.2004.10.008.


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