摘要
小波理论为有限元方法提供了许多不同的基函数和多尺度分析方法,需要根据具体分析问题进行选择.本文首先介绍了Daubechies小波函数、尺度函数,给出了尺度函数高阶导数的改进求解方法.利用尺度函数作为基函数得到了小波伽辽金有限元法.用此方法求解弹性地基上的有限长梁,从结果对比可以看出其解具有良好的精确性和收敛性.此求解步骤可以应用到通常的微分方程求解中.
Wavelet theory provides various basis functions and multi-resolution methods for finite element method, which will be selected in solving different problems. At first, this paper introduces the wavelet function, scaling function of Daubechies wavelet and the modified solving methods of derivative of higher order for scaling functions are given. The scaling functions are used as basis functions to construct the wavelet Galerkin finite element method. The finite-length beam on elastic foundation is solved by the wavelet Galerkin finite element method. In comparison with the analytical results, the solution has better accuracy and convergence. Those steps can be used to solve usually differential equations.
出处
《西安建筑科技大学学报（自然科学版）》
CSCD
2004年第4期413-416,共4页
Journal of Xi'an University of Architecture & Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(59978038)
关键词
小波函数
高阶导数
有限元
有限长梁
wavelet function
derivative of higher order
finite element method
finite-length beam
