电磁谐振腔的形状灵敏度分析
Shape sensitivity analysis for electromagnetic cavities
摘要：
本文研究了腔体中时谐麦克斯韦方程组的本征值随腔体形状变化的关系。分析涉及所有的特征值，包括简单的和多重的。我们提供解析结果的依赖性的特征值分裂的多重特征值的基本对称函数，以及Rellich-Nagy型的结果描述相应的分岔现象。我们还解决了一个等周问题和特征的对称函数的特征值的临界腔等体积或等周域扰动，并证明球是关键的。我们包括已知的公式的本征对在一个球和计算第一个。
英文摘要：
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.
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