Wavelet and multiple scale reproducing kernel methods
Wavelet and multiple scale reproducing kernel methods
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DOI：
10.1002/fld.1650211010
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发表时间：
1995-11
影响因子：
1.8
通讯作者：
Wing Kam Liu;Yijung Chen
中科院分区：
文献类型：
--
作者：
Wing Kam Liu;Yijung Chen
提出了基于再生核和小波分析的多尺度方法。这些允许系统的响应被分成不同的尺度。这些尺度可以是与空间变量相对应的波数，也可以是与时间变量相对应的频率，每个尺度响应都可以单独检查。通过积分窗变换完成对未知响应的完整表征，并通过伸缩灵活的多尺度窗函数实现空间尺度和时频局部化过程。基于这种分解算法的误差估计技术是特别有用的局部网格细化和收敛性的研究。这种灵活的空间尺度窗函数可以构造成类似于著名的非结构化多重网格和hp自适应有限元方法。然而，多尺度自适应细化是通过简单地插入节点到最高小波尺度的解决方案的区域，并在同一时间缩小窗口函数。因此，类似hp的自适应细化可以在没有网格的情况下执行。
Multiple scale methods based on reproducing kernel and wavelet analysis are developed. These permit the response of a system to be separated into different scales. These scales can be either the wave numbers corresponding to spatial variables or the frequencies corresponding to temporal variables, and each scale response can be examined separately. This complete characterization of the unknown response is performed through the integral window transform, and a space-scale and time-frequency localization process is achieved by dilating the flexible multiple scale window function. An error estimation technique based on this decomposition algorithm is developed which is especially useful for local mesh refinement and convergence studies. This flexible space-scale window function can be constructed to resemble the well-known unstructured multigrid and hp-adaptive finite element methods. However, the multiple scale adaptive refinements are performed simply by inserting nodes into the highest wavelet scale solution region and at the same time narrowing the window function. Hence hp-like adaptive refinements can be performed without a mesh.