Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:364

Article

Gorgizadeh, Shahnam¹  Flisgen, Thomas^1,2  van Rienen, Ursula¹ 

[1] Univ Rostock, Inst Allgemeine Elektrotech, Albert Einstein Str 2, D-18059 Rostock, Germany

[2] Helmholtz Zentrum Berlin Mat & Energie GmbH, Albert Einstein Str 15, D-12489 Berlin, Germany

关键词: Generalized eigenvalue problem;    Matrix perturbation;    Modal sensitivity analysis;    Slater's theorem;    Eigenvalue reanalysis;    Microwave cavity;   

DOI  :  10.1016/j.jcp.2018.03.012

来源: Elsevier

【 摘 要 】

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry. (C) 2018 The Author(s). Published by Elsevier Inc.

【 授权许可】

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