一维区间B样条小波单元的构造研究

基于区间B样条小波及小波有限元理论,提出了一种区间B样条小波有限元方法。传统有限元多项式插值被一维区间B样条小波尺度函数取代,进而构造形状函数和单元。与小波Galer-kin方法不同,本文构造的区间B样条小波单元通过转换矩阵将无明确物理意义的小波插值系数转换到物理空间。转换矩阵在小波单元构造过程中起到关键作用,为了保证求解的稳定性,转换矩阵必须非奇异。构造了以区间B样条尺度函数为插值函数的一系列一维区间B样条小波单元。数值算例表明,本文构造的区间B样条小波单元与传统有限元方法相比,在求解变截面,变载荷等问题时具有收敛快和精度高等优势;有效地丰富了小波有限元法单元库。

Construction of One-Dimensional Elements with B-Spline Wavelet

Adopting the scaling function of BSWI as trial functions,a new finite element method of B-Spline wavelet on the interval(FEM BSWI) is presented.Instead of traditional polynomial interpolation,scaling functions at the certain scale was utilized to form the shape functions and construct wavelet-based elements.Unlike the process of direct wavelets adding in the previous work,the elemental displacement field represented by the coefficients of wavelets expansions was transformed into edges and internal modes via the constructed transformation matrix which serves as the key to constructing elements freely as the nonsigularity gets ensured to construct a class of one-dimensional elements.The numerical examples indicate that the BSWI elements have higher efficiency and accracy in solving problems with variable boundary conditions and structural shapes than the traditional finite element methods.