Phononic Crystals - Plane Wave Expansion Method

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Resource Overview

Adapted from the plane wave expansion method used for photonic crystals. This technique expands parameters such as elastic constants and density into Fourier series, combines with Bloch's theorem, and expresses the elastic wave equation in reciprocal lattice space as a superposition of plane waves. The program provides a detailed implementation with comprehensive annotations for easy understanding, including key algorithmic steps and function descriptions for Fourier coefficient calculations and eigenvalue problem solving.

Detailed Documentation

Inspired by the plane wave expansion method applied to photonic crystals, we can expand parameters like elastic constants and density using Fourier series and incorporate Bloch's theorem to formulate the elastic wave equation in reciprocal lattice space as a superposition of plane waves. This methodology forms the basis for the program implementation, which features detailed annotations and clear structure for enhanced comprehension. The code includes algorithms for Fourier coefficient computation, matrix diagonalization for eigenvalue problems, and dispersion relation calculation. This approach finds applications across various domains including materials science and physics, enabling deeper insights and more accurate results. Further exploration of this method's potential may reveal additional application scenarios and optimization opportunities.

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