- journal article metadata
European Mathematical Society Publishing House
2016-10-14 23:45:00
Oberwolfach Reports
Oberwolfach Rep.
OWR
1660-8933
1660-8941
General
10.4171/OWR
http://www.ems-ph.org/doi/10.4171/OWR
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Mathematisches Forschungsinstitut Oberwolfach
13
2016
1
Mini-Workshop: Mathematical Foundations of Isogeometric Analysis
Thomas
Hughes
The University of Texas at Austin, AUSTIN, UNITED STATES
Bert
Jüttler
Johannes Kepler Universität Linz, LINZ, AUSTRIA
Angela
Kunoth
Universität zu Köln, KÖLN, GERMANY
Bernd
Simeon
Technische Universität Kaiserslautern, KAISERSLAUTERN, GERMANY
Isogeometric Analysis (IgA) is a new paradigm which is designed to merge two so far disjoint disciplines, namely, numerical simulations for partial differential equations (PDEs) and applied geometry. Initiated by the pioneering 2005 paper of one of us organizers (Hughes), this new concept bridges the gap between classical finite element methods and computer aided design concepts. Traditional approaches are based on modeling complex geometries by computer aided design tools which then need to be converted to a computational mesh to allow for simulations of PDEs. This process has for decades presented a severe bottleneck in performing efficient simulations. For example, for complex fluid dynamics applications, the modeling of the surface and the mesh generation may take several weeks while the PDE simulations require only a few hours. On the other hand, simulation methods which exactly represent geometric shapes in terms of the basis functions employed for the numerical simulations bridge the gap and allow from the beginning to eliminate geometry errors. This is accomplished by leaving traditional finite element approaches behind and employing instead more general basis functions such as B-Splines and Non-Uniform Rational B-Splines (NURBS) for the PDE simulations as well. The combined concept of Isogeometric Analysis (IgA) allows for improved convergence and smoothness properties of the PDE solutions and dramatically faster overall simulations. In the last few years, this new paradigm has revolutionized the engineering communities and triggered an enormous amount of simulations and publications mainly in this field. However, there are several profound theoretical issues which have not been well understood and which are currently investigated by researchers in Numerical Analysis, Approximation Theory and Applied Geometry.
Numerical analysis
Approximations and expansions
Geometry
341
385
10.4171/OWR/2016/8
http://www.ems-ph.org/doi/10.4171/OWR/2016/8