Daubechies小波伽辽金法及其工程应用

利用Daubechies小波的性质,以Daubechies小波尺度函数作为伽辽金法的基函数,构造了基于结构工程问题的偏微分方程求解方法。由于Daubechies小波无明确的解析表达式,为了将其应用于小波伽辽金法中,关联系数的求解是关键,详细讨论了求解步骤。最后用该方法分析了两端固支轴力杆受力问题,数值算例表明,与理论解相比,构造的Daubechies小波伽辽金法具有计算精度高,收敛比较快的特点。

Daubechies Wavelet Galerkin Method and Engineering Application

By analyzing the characters of Daubechies wavelet,wavelet scaling functions are used for the basis function of wavelet-Galerkin method,which can be used to solve those differential equations based on engineering structure problems.Because the Daubechies wavelet has no obvious analytic expression,in order to apply the wavelet-Galerkin method to numerical analysis of engineering fields,how to compute the wavelet connection coefficients is the key problem,the process of computing the connection coefficients is introduced in detail.At last,the method is applied to solve the fixed-fixed axial-force beams problems,in comparison with the theory results,the resolution demonstrates that the method has better accuracy and efficiency.