An algorithm for the localization of exceptional points and the computation of Puiseux series with applications to acoustic waveguides
Résumé
Finding the defective eigenvalues of parametric non hermitian eigenvalue problem is of particular interest due to the rich physics attached to the singular behavior at the branch point. Here, a new algorithm is proposed to explore the parametric space and to locate exceptional point (EP). The method requires the computation of successive derivatives of two selected eigenpairs with respect to the parameter so that, after recombination, regular functions can be
constructed. This algebraic manipulation permits the localization of exceptional points (EP), using standard root-finding algorithms and the computation of the associated Puiseux series up to an arbitrary order.
Practical applications dealing with dissipative acoustic waveguides are given to illustrate the efficiency and the versatility of the proposed method.