Isogeometric Analysis

Isogeometric Analysis

Isogeometric Analysis (IGA) was born, less than a decade ago, with the goal of bridging the gap between Computer Aided Design (CAD) and Finite Element Method (FEM). The main distinctive feature of IGA is that CAD geometries, commonly defined in terms of Non-Uniform Rational B-splines (NURBS), are represented exactly throughout the analysis, regardless of the level of mesh refinement, while in standard FEM the computational domain needs to be remeshed when performing h-refinement and its geometry approaches the exact one only in the limit of vanishing mesh size h.

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Moreover, in addition to h-refinement and p-refinement, k-refinement was introduced as a combination of degree elevation and mesh refinement, yielding approximation spaces with higher regularity properties. k-refinement has the advantage of not increasing the number of degrees of freedom of the problem, but produces matrices with larger bandwidth.

The research at the chair deals, for example, with applications in electrical engineering, domain decomposition methods, uncertainty quantification and isogeometric boundary elements.

References

Georg, Niklas ; Ackermann, Wolfgang ; Corno, Jacopo ; Schöps, Sebastian (2019):
Uncertainty Quantification for Maxwell's Eigenproblem based on Isogeometric Analysis and Mode Tracking.
In: Computer Methods in Applied Mechanics and Engineering, Elsevier, S. 228-244, 350, ISSN 0045-7825,
DOI: 10.1016/j.cma.2019.03.002,
[Online-Edition: https://doi.org/10.1016/j.cma.2019.03.002],
[Article]

Dölz, Jürgen ; Harbrecht, Helmut ; Kurz, Stefan ; Schöps, Sebastian ; Wolf, Felix (2018):
A Fast Isogeometric BEM for the Three Dimensional Laplace- and Helmholtz Problems.
In: Computer Methods in Applied Mechanics and Engineering, Elsevier, S. 83-101, 330, ISSN 0045-7825,
DOI: 10.1016/j.cma.2017.10.020,
[Online-Edition: https://doi.org/10.1016/j.cma.2017.10.020],
[Article]

Bontinck, Zeger ; Corno, Jacopo ; Schöps, Sebastian ; De Gersem, Herbert (2018):
Isogeometric Analysis and Harmonic Stator-Rotor Coupling for Simulating Electric Machines.
In: Computer Methods in Applied Mechanics and Engineering, S. 40-55, 334, ISSN 0045-7825,
DOI: 10.1016/j.cma.2018.01.047,
[Online-Edition: https://doi.org/10.1016/j.cma.2018.01.047],
[Article]

Bontinck, Zeger ; Corno, Jacopo ; Gersem, Herbert De ; Kurz, Stefan ; Pels, Andreas ; Schöps, Sebastian ; Wolf, Felix ; de Falco, Carlo ; Dölz, Jürgen ; Vázquez, Rafael ; Römer, Ulrich (2017):
Recent Advances of Isogeometric Analysis in Computational Electromagnetics.
In: ICS Newsletter (International Compumag Society), 3, [Online-Edition: http://www.compumag.org/jsite/images/stories/newsletter],
[Article]

Corno, Jacopo ; de Falco, Carlo ; De Gersem, Herbert ; Schöps, Sebastian (2016):
Isogeometric Simulation of Lorentz Detuning in Superconducting Accelerator Cavities.
In: Computer Physics Communications, Elsevier, S. 1-7, 201, ISSN 0010-4655,
[Online-Edition: http://doi.org/10.1016/j.cpc.2015.11.015],
[Article]

Pels, Andreas ; Bontinck, Zeger ; Corno, Jacopo ; De Gersem, Herbert ; Schöps, Sebastian (2015):
Optimization of a Stern-Gerlach Magnet by Magnetic Field-Circuit Coupling and Isogeometric Analysis.
In: IEEE Transactions on Magnetics, 51, (12), [Online-Edition: http://dx.doi.org/10.1109/TMAG.2015.2462806],
[Article]

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