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

Uncertainty Quantification for Maxwell's Eigenproblem based on Isogeometric Analysis and Mode Tracking

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 uncertaint…

基于细分的等几何分析用于轴对称电磁问题

Subdivision-based isogeometric analysis for axisymmetric electromagnetic problems

提出基于细分的等几何方法求解轴对称Maxwell特征值问题，利用Catmull-Clark构造离散化，在TESLA 9-cell腔体上获得更平滑的数值解，收敛率与文献一致。

On the computation of analytic sensitivities of eigenpairs in isogeometric analysis

The eigenmodes of resonating structures, e.g., electromagnetic cavities, are sensitive to deformations of their shape. In order to compute the sensitivities of the eigenpair with respect to a scalar parameter, we state the Laplacian and Maxwellian eigenvalue problems and discretize the models using isogeometric analysis. Since we require the derivatives of the system matrices, we differentiate the system matrices for each setting considering the appropriate function spaces for geometry and solution. This approach allows for a straightforward computation of arbitrary higher order sensitivities …

Modelling of a Permanent Magnet Synchronous Machine Using Isogeometric Analysis

Isogeometric analysis (IGA) is used to simulate a permanent magnet synchronous machine. IGA uses non-uniform rational B-splines to parametrise the domain and to approximate the solution space, thus allowing for the exact description of the geometries even on the coarsest level of mesh refinement. Given the properties of the isogeometric basis functions, this choice guarantees a higher accuracy than the classical finite element method. For dealing with the different stator and rotor topologies, the domain is split into two non-overlapping parts on which Maxwell's equations are solved independen…

Maxwell特征值与特征模态的形状不确定性量化及其在TESLA腔体中的应用

Shape uncertainty quantification of Maxwell eigenvalues and -modes with application to TESLA cavities

本文针对TESLA腔体等不确定形状上的Maxwell特征值问题，提出基于区域映射和等几何分析的扰动方法，高效准确地近似特征对的均值与协方差，并通过三维9-cell腔体数值实验验证其优于采样和代理模型方法。

一种用于几何精确粘弹性梁的高效基于位移的等几何列式

An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams

本研究提出一种基于位移的等几何列式，将广义Maxwell模型拓展到有限位移转动的任意曲率粘弹性梁，结合配点离散、增量转动矢量更新等特性实现高效求解，可处理复杂形状梁结构，在多领域有应用潜力。