PARADISE - Parameterization of computational domains for isogeometric analysis
Sprache der Bezeichnung:
Englisch
Original Kurzfassung:
Isogeometric analysis (IA), which was introduced in 2005 by Tom Hughes et al., is a novel technique for numerical simulation
which uses the same spaces of functions for the representation of the geometry and for the numerical simulation. It has
the potential of closing the gap between numerical simulation and computer aided design, which is caused by the different
representations of geometry (piecewise linear vs. rational splines = NURBS). This gap is currently a bottleneck in the design
process, since the design and the numerical simulation phase cannot be connected in a seamless fashion, but only through
time-consuming conversion processes.
The application of IA leads to new challenging problems for geometric design, which are related to the representation of
computational domains by NURBS parameterizations. The project will address some of them.
More precisely, it will discuss computational methods for generating NURBS parameterizations for several classes of
computational domains, such as CSG models, general CAD models, and domains obtained from medical data. It will also
analyze the quality of these parameterizations with respect to the distribution of singularities and with respect to the distortion
which is introduced by the parameterization. Additional points of interest are the construction of locally refinable spaces of
test functions for IA, which are compatible with NURBS parameterizations and support both h-refinement (knot insertion) and
p-refinement (degree elevation), domain decomposition techniques and design optimization.
These three topics will be analyzed in close connection to related applications to numerical optimization and to shape
optimization. The execution of the project requires the combination of knowledge available at the host institution with the
expertise of some of its European partners, as well as the profound education of the fellow in Computer Science and Applied
Mathematics.
Sprache der Kurzfassung:
Englisch
Englische Bezeichnung:
PARADISE - Parameterization of computational domains for isogeometric analysis
Forschungs-