Bridging Computer Aided Design and Simulation

Isogeometric analysis, NURBS and splines

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.

Simona, Abele ; Bonaventura, Luca ; de Falco, Carlo ; Schöps, Sebastian (2020):
IsoGeometric Approximations for Electromagnetic Problems in Axisymmetric Domains.
In: Computer Methods in Applied Mechanics and Engineering, 369, pp. 113211, ISSN: 0045-7825, DOI: 10.1016/j.cma.2020.113211, ARXIV: 1912.08570. [Article]

Egger, Herbert ; Harutyunyan, Mané ; Merkel, Melina ; Schöps, Sebastian (2020):
On the stability of harmonic mortar methods with application to electric machines.
In: Scientific Computing in Electrical Engineering SCEE 2020, Mathematics in Industry. Springer. ARXIV: 2005.12020, forthcoming. [In Proceedings]

Dölz, Jürgen ; Harbrecht, Helmut ; Kurz, Stefan ; Multerer, Michael ; Schöps, Sebastian ; Wolf, Felix (2020):
Bembel: The Fast Isogeometric Boundary Element C++ Library for Laplace, Helmholtz, and Electric Wave Equation.
In: Software X, 11, pp. 100476, DOI: 10.1016/j.softx.2020.100476, ARXIV: 1906.00785. [Article]

Dölz, Jürgen ; Kurz, Stefan ; Schöps, Sebastian ; Wolf, Felix. Chaillat-Loseille, Stéphanie ; Hiptmair, Ralf ; Steinbach, Olaf (editors) (2020):
Recent Advances of Isogeometric Boundary Element Methods for Electromagnetic Scattering Problems.
In: Boundary Element Methods, volume 5, 37–40. Mathematisches Forschungsinstitut Oberwolfach. DOI: 10.14760/OWR-2020-5. [In Proceedings]

Dölz, Jürgen ; Kurz, Stefan ; Schöps, Sebastian ; Wolf, Felix (2020):
A Numerical Comparison of an Isogeometric and a Parametric Higher-Order Raviart-Thomas Approach to the Electric Field Integral Equation.
In: IEEE Transactions on Antennas and Propagation, 68, (1), pp. 593–597, ISSN: 0018-926X, DOI: 10.1109/TAP.2019.2935778, ARXIV: 1807.03628. [Article]

Kurz, Stefan ; Schöps, Sebastian ; Wolf, Felix (2019):
Towards a Spectral Method of Moments using Computer Aided Design.
In: Advances in Radio Science, 17, pp. 59–63, ISSN: 1684-9973, DOI: 10.5194/ars-17-59-2019. [Article]

Dölz, Jürgen ; Kurz, Stefan ; Schöps, Sebastian ; Wolf, Felix (2019):
Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples.
In: SIAM Journal on Scientific Computing, 41, (5), pp. B983–B1010, ISSN: 1064-8275, DOI: 10.1137/18M1227251, ARXIV: 1807.03097. [Article]

Buffa, Annalisa ; Dölz, Jürgen ; Kurz, Stefan ; Schöps, Sebastian ; Vázquez, Rafael ; Wolf, Felix (2019):
Multipatch Approximation of the de Rham Sequence and its Traces in Isogeometric Analysis.
In: Numerische Mathematik, 144, (1), pp. 201–236, DOI: 10.1007/s00211-019-01079-x, ARXIV: 1806.01062. [Article]

Dölz, Jürgen ; Kurz, Stefan ; Schöps, Sebastian ; Wolf, Felix (2018):
An Overview of Isogeometric Boundary Element Methods for Acoustic and Electromagnetic Scattering Problems.
In: Proceedings in Applied Mathematics and Mechanics, volume 18. Wiley. DOI: 10.1002/pamm.201800100. [In Proceedings]

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, 330, pp. 83–101, ISSN: 0045-7825, DOI: 10.1016/j.cma.2017.10.020, ARXIV: 1708.09162. [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, 334, pp. 40–55, ISSN: 0045-7825, DOI: 10.1016/j.cma.2018.01.047, ARXIV: 1709.05301. [Article]

Bhat, Prithvi ; Bontinck, Zeger ; Corno, Jacopo ; Schöps, Sebastian ; De Gersem, Herbert (2018):
Modeling of a Permanent Magnet Synchronous Machine Using Isogeometric Analysis.
In: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 37, (5), pp. 1805–1814, DOI: 10.1108/COMPEL-01-2018-0014, ARXIV: 1708.02409. [Article]

Bontinck, Zeger ; Corno, Jacopo ; De Gersem, Herbert ; 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: International Compumag Society Newsletter, ISSN: 1026-0854, ARXIV: 1709.06004. [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, 201, pp. 1–7, ISSN: 0010-4655, DOI: 10.1016/j.cpc.2015.11.015, ARXIV: 1606.08209. [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, ISSN: 0018-9464, DOI: 10.1109/TMAG.2015.2462806. [Article]

Corno, Jacopo ; de Falco, Carlo ; De Gersem, Herbert ; Schöps, Sebastian (2015):
Isogeometric Analysis Simulation of TESLA Cavities Under Uncertainty.
In: Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA) 2015, 1508–1511. IEEE. ISBN: 978-1-4799-7805-2, DOI: 10.1109/ICEAA.2015.7297375, ARXIV: 1711.01828. [In Proceedings]