基于Haar小波包的时域多分辨分析法

Multiresolution time-domain analysis based on Haar wavelet packets

把基于Haar小波的时域多分辨分析(MRTD)推广到Haar小波包,扩展了基函数的选择范围,导出了一维小波包MRTD(WP-MRTD)的时间迭代格式,并给出WP-MRTD与传统FDTD的接口算法。计算结果显示,用小波包基作为电磁场展开函数和小波基相比可以获得能量更集中的展开系数,有利于进一步提高计算效率;对于给定级数的小波包二叉树,存在一个最佳小波包基,使得计算效率最高。该方法可直接推广到二维和三维问题。

For expanding the select range of basis functions, the Haar-wavelet- based multiresolution time-domain（MRTD） is extended to general WP-MRTD. One dimension WP-MRTD update equations are derived and the connection algorithm between WP-MRTD and FDTD is presented. The numerical results show that the Haar wavelet packets is used as basis functions of electromagnetic fields, the conefficients of field expansions are of much more energy concentrated than those obtained from Haar wavelets, and thus further reduce the computer resources. For a fixed level of binary tree, there exits a best wavelet packet basis functions that can lead to highest computational efficiency. The method proposed can be extended to 2D and 3D problems.