Several strategies for solving a nonlinear eigenvalue problem are evaluated. This problem stems from the boundary integral equation solution of propagation in photonic crystal fibers. The origin and specificities of the eigenvalue problem are recalled before considering the solution of this eigenvalue problem. The first strategy, which is the starting point to illustrate the difficulties, is to solve the problem using Muller’s method. We then look at more recent techniques based on contour integrals or a rational interpolant that can be used to compute several eigenmodes simultaneously and considerably reduce the volume of computations.

中文翻译：

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通过边界元法离散化光子晶体光纤应用中的非线性特征值问题的求解


评估了解决非线性特征值问题的几种策略。该问题源于光子晶体光纤中传播的边界积分方程解。在考虑该特征值问题的解决方案之前，先回顾一下特征值问题的起源和特殊性。第一个策略，是说明困难的起点，是用穆勒方法解决问题。然后，我们研究基于轮廓积分或有理插值的最新技术，这些技术可用于同时计算多个本征模并大大减少计算量。