Computing interior eigenvalues of nonsymmetric matrices: application to three-dimensional metamaterial composites.

Area of Science:

• Numerical Analysis
• Materials Science
• Electromagnetics

Background:

• Nonsymmetric matrices pose challenges for eigenvalue and eigenvector computation.
• Traditional methods like the nonsymmetric Lanczos algorithm have limitations in accuracy for interior eigenvalues.
• Accurate analysis of metamaterials requires precise numerical methods.

Purpose of the Study:

• To develop a novel numerical method for calculating interior eigenvalues and eigenvectors of nonsymmetric matrices.
• To improve the precision and overcome limitations of existing algorithms.
• To validate the applicability of the proposed method in analyzing three-dimensional metamaterial composites.

Main Methods:

• Subspace projection technique onto an expanded Ritz subspace.
• Development of a modified algorithm addressing limitations of the nonsymmetric Lanczos algorithm.
• Application of the finite-difference frequency-domain (FDFD) algorithm for metamaterial analysis.

Main Results:

• The proposed method achieves high precision for interior eigenvalues and eigenvectors.
• Demonstrated improvement in accuracy compared to traditional methods.
• Successful application of the FDFD algorithm to analyze three-dimensional metamaterial composites.

Conclusions:

• The novel numerical method provides a robust and accurate approach for eigenvalue problems involving nonsymmetric matrices.
• The enhanced accuracy facilitates the investigation of complex material properties.
• The finite-difference frequency-domain algorithm is confirmed as suitable for analyzing metamaterial composites with the proposed numerical technique.