Recent Advances of Isogeometric Analysis in Computational Electromagnetics

Bontinck, Zeger; Corno, Jacopo; Gersem, Herbert De; Kurz, Stefan; Pels, Andreas; Schöps, Sebastian; Wolf, Felix; Falco, Carlo de; Dölz, Jürgen; Vázquez, Rafael

doi:10.48550/arxiv.1709.06004

Cited by 4 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many methods of geometry parameterization exist, such as free-form deformation [21], the polynomial and spline method (NURBS) [22], iso-geometric analysis [23], and computeraided design (CAD). From these categories, CAD seems to have certain capabilities that make it incredibly attractive to design engineers, such as efficiency, compactness, and adaptation to complex configurations.…”

Section: Parameterizationmentioning

confidence: 99%

The Adjoint Variable Method for Computational Electromagnetics

2022

View full text Add to dashboard Cite

Optimization using finite element analysis and the adjoint variable method to solve engineering problems appears in various application areas. However, to the best of the authors’ knowledge, there is a lack of detailed explanation on the implementation of the adjoint variable method in the context of electromagnetic modeling. This paper aimed to provide a detailed explanation of the method in the simplest possible general framework. Then, an extended explanation is offered in the context of electromagnetism. A discrete design methodology based on adjoint variables for magnetostatics was formulated, implemented, and verified. This comprehensive methodology supports both linear and nonlinear problems. The framework provides a general approach for performing a very efficient and discretely consistent sensitivity analysis for problems involving geometric and physical variables or any combination of the two. The accuracy of the implementation is demonstrated by independent verification based on an analytical test case and using the finite-difference method. The methodology was used to optimize the parameters of a superconducting energy storage device and a magnet press and the optimization of the topology of an electromagnet. The objective function of each problem was successfully decreased, and all constraints stipulated were met.

show abstract

Section: Parameterizationmentioning

confidence: 99%

The Adjoint Variable Method for Computational Electromagnetics

2022

View full text Add to dashboard Cite

show abstract

“…The use of IGA in cavity simulation has been shown to be beneficial both in terms of accuracy and of overall reduction of the computational cost [6,22]. For an overview of the applicability of IGA to other electromagnetic problems, we refer to [23].…”

Section: Isogeometric Analysismentioning

confidence: 99%

Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking

Georg

Ackermann

Corno

et al. 2019

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities used in particle accelerators for example are sensitive to small geometry deformations. The occurring variations are motivated by measurements of an available set of resonators from which we propose to extract a small number of relevant and independent deformations by using a truncated Karhunen-Loève expansion. The random deformations are used in an expressive uncertainty quantification workflow to determine the sensitivity of the eigenmodes. For the propagation of uncertainty, a stochastic collocation method based on sparse grids is employed. It requires the repeated solution of Maxwell's eigenvalue problem at predefined collocation points, i.e., for cavities with perturbed geometry. The main contribution of the paper is ensuring the consistency of the solution, i.e., matching the eigenpairs, among the various eigenvalue problems at the stochastic collocation points. To this end, a classical eigenvalue tracking technique is proposed that is based on homotopies between collocation points and a Newton-based eigenvalue solver. The approach can be efficiently parallelized while tracking the eigenpairs. In this paper, we propose the application of isogeometric analysis since it allows for the exact description of the geometrical domains with respect to common computer-aided design kernels, for a straightforward and convenient way of handling geometrical variations and smooth solutions.

show abstract

“…geometry representation. Isogeometric methods are well understood for the case of electromagnetism [8,9] and a corresponding finite element approach has already been applied to Maxwell's eigenvalue problem [10].…”

Section: Introductionmentioning

confidence: 99%

Solving Maxwell's Eigenvalue Problem via Isogeometric Boundary Elements and a Contour Integral Method

Kurz,

Schöps,

Unger

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Recent Advances of Isogeometric Analysis in Computational Electromagnetics

Cited by 4 publications

References 0 publications

The Adjoint Variable Method for Computational Electromagnetics

The Adjoint Variable Method for Computational Electromagnetics

Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking

Solving Maxwell's Eigenvalue Problem via Isogeometric Boundary Elements and a Contour Integral Method

Contact Info

Product

Resources

About