论文标题
电磁腔的形状灵敏度分析
Shape sensitivity analysis for electromagnetic cavities
论文作者
论文摘要
我们研究了时间谐波麦克斯韦方程在其形状变化的腔体中的特征值的依赖性。该分析涉及所有简单和多个特征值。我们为特征值的基本对称函数的依赖性提供了分析性结果，该功能分裂了多个特征值，以及描述了相应的分叉现象的Rellich-Nagy型结果。我们还解决了一个等法问题，并表征了受到等量或等值域扰动的特征值的对称功能的关键腔，并证明球是关键的。我们在球中包括已知的特征底漆公式，并计算第一个。
We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of the elementary symmetric functions of the eigenvalues splitting a multiple eigenvalue, as well as a Rellich-Nagy-type result describing the corresponding bifurcation phenomenon. We also address an isoperimetric problem and characterize the critical cavities for the symmetric functions of the eigenvalues subject to isovolumetric or isoperimetric domain perturbations and prove that balls are critical. We include known formulas for the eigenpairs in a ball and calculate the first one.
