In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a reduced basis approximation to bring down the computational costs. It is based on the greedy strategy from Horger et al. 2017 which considers multiple eigenvalues for elliptic eigenvalue problems. We extend this algorithm to deal with parameter-dependent domains and the Maxwell eigenvalue problem. In this setting, the reduced basis may contain spurious eigenmodes, which require special treatment. We demonstrate our algorithm in an eigenvalue tracking application for an eigenmode classification.

翻译：在许多高频仿真流程中，需要沿着参数变化进行特征值追踪。当必须反复求解耗时的特征值问题时，这可能在计算上变得难以承受。因此，我们采用降基近似来降低计算成本。该方法基于Horger等人（2017）提出的贪婪策略，该策略考虑了椭圆型特征值问题的多重特征值。我们对该算法进行了扩展，以处理参数依赖区域和麦克斯韦特征值问题。在此设定下，降基可能包含需要特殊处理的伪特征模态。我们通过一个特征模态分类中的特征值追踪应用来演示该算法。