高阶均匀采样的时域伪谱算法研究

Study of Pseudo-Spectral Time-Domain Method with Higher-Order Uniform Sampling

传统的时域有限差分算法(FDTD)采用二阶中心差分格式近似计算时间微分。相对于高阶的空间离散,这种低阶的时间离散成为限制算法整体精度提高的瓶颈。利用引入高阶均匀化采样的时域伪谱方法(PSTD),消除了低阶时间离散对算法整体性能提高的制约,在提高空域分辨率的同时也消除了数值近似引起的数值波相速度各向异性和波前失真,增强了算法的适应性,提高了算法的分析精度。通过二维光子带隙结构传输系数的数值模拟,验证了高阶均匀化采样时域伪谱方法的正确性和有效性。

Traditional finite difference time domain method（FDTD） uses the second centre differential format to calculate approximate time differential.Being relative to high-order discrete time discrete space,this low-order time discrete has become the bottleneck to limit the overall accuracy of the algorithm improvement.This research uses the pseudo spectral time-domain（PSTD） method with high-order uniform sampling method introduced to eliminate the constraints of the low-order time discrete upon the overall improvement of the algorithm,the anisotropy by numerical speed phase and the wave-front distortion caused by the numerical approximation in improving high spatial domain resolution so as to enhance the algorithm adaptation and to improve analysis accuracy.This research tests the correctness and effectiveness of the pseudo-spectral time-domain method in case of high-order homogenization sampling via two-dimensional photonic band gap structure of the transmission coefficient of numerical simulation.