准消失矩变阶小波Galerkin边界元法

迄今为止,所有关于小波边界元法的报道中均采用严格满足消失矩特性的小波.文章提出了准消失矩小波的概念及其在边界单元划分上的构造方法.将此小波用于非标准型Galerkin边界元的矩阵压缩.在给定小波矩误差的情况下,建立了矩阵元素的估值公式.分析表明,准消失矩小波在保证精度的前提下可以降低小波边界元法的复杂度.空间非光滑边界问题算例证实了理论结果.

Further Reducing Considerably Complexity of Galerkin BEM (Boundary Element Method) while Retaining Adequate Accuracy

Aim.Existing papers have reduced the complexity of Galerkin BEM through using variable-order vanishing moment wavelets.We propose reducing considerably the complexity further through using variable-order quasivanishing moment wavelets.Section 1 of the full paper constructs the variable order quasi-vanishing moment wavelets and uses the threshold of singular values given in eq.(6) for controlling the accuracy of the BEM (to be explained in section 2).Section 2 explains how to compress the matrix of the Galerkin BEM further and discusses the convergence of the underlying Galerkin scheme; in it,Theorem 2 stipulates the conditions under which the threshold of singular values given in eq.(6) can control the accuracy of the BEM and under which the convergence of the underlying Galerkin BEM is not affected.Section 3 analyzes the complexity of the Galerkin BEM.Section 4 presents a numerical example; the results,given in Tables 1 and 2,and their analysis show preliminarily that we,using variable order quasi-vanishing moment wavelets,can reduce the complexity of non-standard form wavelet Galerkin BEM considerably while retaining adequate accuracy.