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Three-dimensional phononic band gap calculations using the FDTD method and a PC cluster system.
Po-Feng Hsieh1, Tsung-Tsong Wu, Jia-Hong Sun
1Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan.
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
|February 14, 2006
Summary
This study investigates three-dimensional phononic crystals, predicting band gaps using the finite difference time domain (FDTD) method and parallel computing. Results offer insights into acoustic wave propagation and material design.
Area of Science:
- Materials Science
- Acoustics
- Computational Physics
Background:
- Phononic crystals offer unique wave manipulation properties.
- Understanding band gap phenomena is crucial for device applications.
- Three-dimensional phononic crystals present significant computational challenges.
Purpose of the Study:
- To study the band gap phenomena in three-dimensional phononic crystals.
- To apply Bloch's theorem and the finite difference time domain (FDTD) method.
- To utilize a PC cluster system for enhanced computational efficiency.
Main Methods:
- Application of Bloch's theorem to wave equations and boundary conditions.
- Calculation of displacement variations and discrete Fourier transform for resonances.
- Implementation of parallel FDTD programs on a PC cluster system.
Main Results:
- Obtained dispersion relations for bulk acoustic waves.
- Predicted band gaps in three-dimensional phononic crystals.
- Analyzed numerical calculations for steel/epoxy phononic crystals.
Conclusions:
- The FDTD method combined with parallel computing effectively predicts phononic band gaps.
- PC cluster systems are essential for handling large-scale 3D phononic crystal simulations.
- The study provides valuable data on band gap phenomena in 2D and 3D phononic crystals.