Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems
Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems
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DOI：
10.1016/j.jcp.2018.03.012
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Shahnam Gorgizadeh;T. Flisgen;U. Rienen
中科院分区：
文献类型：
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作者：
Shahnam Gorgizadeh;T. Flisgen;U. Rienen
广义特征值问题是计算科学中的标准问题。它们可以在电磁场中由例如有限元法（FEM）对亥姆霍兹方程的离散化产生。结构的几何摄动导致了一个新的广义特征值问题，不同的系统矩阵。几何扰动可能由制造公差、苛刻的操作条件或在形状优化期间产生。直接求解每个扰动的本征值问题在计算上是昂贵的。扰动的特征对可以近似使用特征对导数。本文讨论了计算本征对导数的两种常用方法，即模态叠加法和直接代数法。基于直接代数方法，提出了一种由未扰动几何的特征值和特征向量有效计算扰动几何的特征值和特征向量的迭代算法。
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.