IsoGeometric approximations for electromagnetic problems in axisymmetric domains

Simona, Abele; Bonaventura, Luca; Falco, Carlo de; Schöps, Sebastian

doi:10.1016/j.cma.2020.113211

Cited by 12 publications

(9 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let S P : Ω2D → Ω 2D denote the bivariate geometry mapping from the reference domain Ω2D := (0, 1) 2 to the physical domain, from which eventually a 3D description is obtained by revolution [41]. Assuming that S P is piecewise smoothly invertible we may define the approximation space V h as…”

Section: B Isogeometric Analysismentioning

confidence: 99%

Freeform shape optimization of a compact DC photo-electron gun using isogeometric analysis

Förster,

Schöps,

Enders

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

Compact DC high-voltage photo-electron guns are able to meet the challenging demands of highcurrent applications such as energy-recovery linacs. A main design parameter for such sources is the electric field strength, which depends on the electrode geometry and is limited by the field-emission threshold of the electrode material. In order to minimize the maximum field strength for optimal gun operation, isogeometric analysis (IGA) can be used to exploit the axisymmetric geometry and describe its cross section by non-uniform rational B-splines, the control points of which are the parameters to be optimized. This computationally efficient method is capable of describing CADgenerated geometries using open source software (GeoPDEs, NLopt, Octave) and it can simplify the step from design to simulation. We will present the mathematical formulation, the software workflow and the results of an IGA-based shape optimization for a planned high-voltage upgrade of the DC photogun teststand Photo-CATCH at TU Darmstadt. Simulations assuming a bias voltage of −300 kV yielded maximum field gradients of 9.06 MV m −1 on the surface of an inverted-insulator electrode and below 3 MV m −1 on the surface of the photocathode.

show abstract

Section: B Isogeometric Analysismentioning

confidence: 99%

Freeform shape optimization of a compact DC photo-electron gun using isogeometric analysis

Förster,

Schöps,

Enders

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another important benefit to using IGA instead of the standard finite element method (FEM) is the comparatively reduced number of degrees of freedom (dofs) in relation to the accuracy of the approximate PDE solution [15]. Owning to these advantages, IGA has been employed to resolve problems governed by PDEs in numerous domains of application, exemplarily, structural analysis [14,44,54,56], fluid mechanics [1,5,23,31,38,61], and electromagnetics [8,9,19,20,58].…”

Section: Introductionmentioning

confidence: 99%

Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries

Ion¹,

Loukrezis²,

Gersem³

2022

Preprint

View full text Add to dashboard Cite

This work develops a numerical solver based on the combination of isogeometric analysis (IGA) and the tensor train (TT) decomposition for the approximation of partial differential equations (PDEs) on parameter-dependent geometries. First, the discrete Galerkin operator as well as the solution for a fixed geometry configuration are represented as tensors and the TT format is employed to reduce their computational complexity. Parametric dependencies are included by considering the parameters that control the geometry configuration as additional dimensions next to the physical space coordinates. The parameters are easily incorporated within the TT-IGA solution framework by introducing a tensor product basis expansion in the parameter space. The discrete Galerkin operators are accordingly extended to accommodate the parameter dependence, thus obtaining a single system that includes the parameter dependency. The system is solved directly in the TT format and a low-rank representation of the parameter-dependent solution is obtained. The proposed TT-IGA solver is applied to several test cases which showcase its high computational efficiency and tremendous compression ratios achieved for representing the parameter-dependent IGA operators and solutions.

show abstract

“…Isogeometric analysis (IGA), introduced by Hughes et al (2005), is a widely used Galerkin method for solving partial differential equations. IGA has been successfully employed in various electromagnetic (Buffa et al, 2010(Buffa et al, , 2014Nguyen et al, 2012;Simpson et al, 2018;Simona et al, 2020) and geotechnical (Shahrokhabadi et al, 2019;Hageman et al, 2019) applications. IGA uses spline basis functions introduced in computer-aided design (CAD) as shape functions of finite element analysis (FEA).…”

Section: Introductionmentioning

confidence: 99%

Massive database generation for 2.5D borehole electromagnetic measurements using refined isogeometric analysis

Hashemian

García

Rivera

et al. 2021

Computers & Geosciences

View full text Add to dashboard Cite

Borehole resistivity measurements are routinely inverted in real-time during geosteering operations. The inversion process can be efficiently performed with the help of advanced artificial intelligence algorithms such as deep learning.These methods require a massive dataset that relates multiple Earth models with the corresponding borehole resistivity measurements. In here, we propose to use an advanced numerical method -refined isogeometric analysis (rIGA)to perform rapid and accurate 2.5D simulations and generate databases when considering arbitrary 2D Earth models.Numerical results show that we can generate a meaningful synthetic database composed of 100,000 Earth models with the corresponding measurements in 56 hours using a workstation equipped with two CPUs.

show abstract

IsoGeometric approximations for electromagnetic problems in axisymmetric domains

Cited by 12 publications

References 18 publications

Freeform shape optimization of a compact DC photo-electron gun using isogeometric analysis

Freeform shape optimization of a compact DC photo-electron gun using isogeometric analysis

Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries

Massive database generation for 2.5D borehole electromagnetic measurements using refined isogeometric analysis

Contact Info

Product

Resources

About