研究目的
To clarify the conditions necessary for the step-by-step justification of the possibility of reduction of the homogeneous system of linear algebraic equations for the spectral problems of 2-D photonic crystals by the plane waves method, and to analyze the issues related to the algorithms and the numerical solutions of these spectral problems.
研究成果
The paper formulates conditions necessary for stable and convergent numerical schemes in solving spectral problems of 2-D photonic crystals. It demonstrates the potential of analytical regularization and suggests techniques to improve the convergence rate of results.
研究不足
The study is theoretical and does not involve experimental validation. The convergence and stability of computational schemes are analyzed mathematically, but practical implementation and verification are not covered.
1：Experimental Design and Method Selection:
The study employs the plane waves method for analyzing spectral problems of 2-D photonic crystals, focusing on the reduction of homogeneous systems of linear algebraic equations.
2：Sample Selection and Data Sources:
The research involves theoretical analysis without specific sample selection, utilizing mathematical models and algorithms.
3：List of Experimental Equipment and Materials:
Not applicable as the study is theoretical.
4：Experimental Procedures and Operational Workflow:
The methodology includes the construction of the canonical Green function for 2-D photonic crystals and the analysis of spectral problems through operator equations and matrix forms.
5：Data Analysis Methods:
The study uses mathematical analysis and numerical methods to investigate the convergence and stability of computational schemes.
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