Isogeometric Analysis

Geometry mappings in classical FEM and IGA
Geometry mappings in classical FEM and IGA

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 (see figure). 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.


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

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

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

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

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

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