调和微分求积法权系数矩阵的一种显式计算式

简要介绍了调和微分求积法，导出了求一阶导数权系数矩阵的显式计算公式。利用该公式和其中反心对称的性能，可进一步提高计算效率。由于均匀网点有时不能给出可靠的解，本文导出了几种能出可靠结果的不等距网点公式，其中一种公式虽然用不同的方法导出，但结果与Ｇａｕｓｓ－Ｌｏｂａｔｔｏ方法等价，本文还证明了调和微分求积法权系数矩阵具有中心对称或中心反对称的性质（取决于导数的阶数），利用这些性质可以进一步减少计算工程

An Explicit Formulation for Weighting Coefficients of Harmonic Differential Quadrature

The harmonic differential quadrature (HDQ) is briefly described. An explicit formula for the direct computation of the weighting coefficient matrix of the first derivative is derived,by which the computational efficiency can be increased together with the skew symmetric property of the weighting coefficient matrix. Since uniform grid spacing may not give reliable solutions in some cases,several sets of grid spacing are proposed herein which can yield fast convergence and. reliable results. One set of grid spacing is derived in a different way that is exactly the same as the one obtained by the Gauss-Lobatto method. It is shown that the weighting coefficient matrices of the HDQ method are either centro-symmetric or skew centro-symmetric depending on the order of the derivatives. The computational cost can be reduced by using these properties of the HDQ method. Finally,two examples are given to demonstrate the efficiency of the method for engineering analysis.