论文标题
关于本特征图的分析敏感性的计算
On the computation of analytic sensitivities of eigenpairs in isogeometric analysis
论文作者
论文摘要
共鸣结构的本征模，例如电磁腔，对其形状的变形敏感。为了计算特征佩对标量参数的敏感性，我们陈述了拉普拉斯和麦克斯韦特征值问题，并使用同期分析离散模型。由于我们需要系统矩阵的衍生物，因此考虑到几何和解决方案的适当函数空间，我们将每个设置的系统矩阵区分。这种方法允许在封闭形式中直接计算任意高阶灵敏度。在我们的工作中，我们证明了在小几何变形的设置中的应用，例如，用于研究电磁腔的制造不确定性以及沿形状变形的特征值跟踪中的应用。
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 in a closed-form. In our work, we demonstrate the application in a setting of small geometric deformations, e.g., for the investigation of manufacturing uncertainties of electromagnetic cavities, as well as in an eigenvalue tracking along a shape morphing.
