A high order continuation method to locate exceptional points and to compute Puiseux series with applications to acoustic waveguides

JOURNAL OF COMPUTATIONAL PHYSICS

卷:412

Article

Nennig, Benoit¹  Perrey-Debain, Emmanuel² 

[1] Inst Super Mecan Paris SUPMECA, Lab Quartz, EA 7393, 3 Rue Fernand Hainaut, F-93407 St Ouen, France

[2] Univ Technol Compiegne, Sorbonne Univ, Lab Roberval, CNRS,UMR 7337, CS 60319, F-60203 Compiegne, France

关键词: Exceptional point;    Defective eigenvalue;    Puiseux series;    Parametric eigenvalue problem;    Duct acoustics;    Bordered matrix;   

DOI  :  10.1016/j.jcp.2020.109425

来源: Elsevier

【 摘 要 】

A numerical algorithm is proposed to explore in a systematic way the trajectories of the eigenvalues of non-Hermitian matrices in the parametric space and exploit this in order to find the locations of defective eigenvalues in the complex plane. These non-Hermitian degeneracies also called exceptional points (EP) have raised considerable attention in the scientific community as these can have a great impact in a variety of physical problems. The method requires the computation of successive derivatives of two selected eigenvalues 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. This representation, which is associated with the topological structure of Riemann surfaces allows to efficiently approximate the selected pair in a certain neighborhoodof the EP. Practical applications dealing with guided acoustic waves propagating in straight ducts with absorbing walls and in periodic guiding structures are given to illustrate the versatility of the proposed method and its ability to handle large size matrices arising from finite element discretization techniques. The fact that EPs are associated with optimal dissipative treatments in the sense that they should provide best modal attenuation is also discussed. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free