Reducing the computational requirements of the differential quadrature method

Abstract

This article shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric, if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new skew centrosymmetric matrix is also discussed. The application of the properties of centrosymmetric and skew centrosymmetric matrices can reduce the computational effort of the DQM for calculations of the inverse, determinant, eigenvectors, and eigenvalues by 75%. This computational advantage is also demonstrated via several numerical examples.

A Lyapunov Formulation for Efficient Solution of the Poisson and Convection–Diffusion Equations by the Differential Quadrature Method

“…If N=N x =N y , about 1 3 (N -2) 6 multiplications were performed. In contrast, the present reduction approach requires about 14 1 3 (N -2) 3 multiplications. Thus, the computational effort is only about 34% in using 7×7 grid points and 6% in using 11×11 grid points as much as that in reference [1].…”

The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates

“…One of the present authors [20] proposed the following DQ formulation in matrix form for the partial derivatives of the function ψ(x,y) in two-dimensional domain:…”

Flutter prediction of cylindrical sandwich panels with saturated porous core under supersonic yawed flow

“…At the recent decades, DQM has been employed by many authors to solve the complicated engineering problems regarding static and dynamic analyses of various types of structures under different boundary conditions. [77][78][79][80][81] In the current section, a numerical solution is presented using this method (see Online Appendix C).…”