Advanced Differential Quadrature Methods

ISBN: 9781138117907 出版年：2009 页码：363 Zong, Zhi Zhang, Yingyan CRC Press

Approximation and Differential Quadrature Approximation and best approximation Interpolating bases Differential quadrature (DQ) Direct DQ method Block marching in time with DQ discretization Implementation of boundary conditions Conclusions Complex Differential Quadrature Method DQ in the complex plane Complex DQ method for potential problems Complex DQ method for plane linear elastic problems Conformal mapping-aided complex DQ Conclusions Triangular Differential Quadrature Method Triangular DQ method in standard triangle Triangular DQ method in curvilinear triangle Geometric transformation Governing equations of Reissner-Mindlin plates on Pasternak foundation Conclusions Multiple Scale Differential Quadrature Method Multi-scale DQ method for potential problems Solutions of potential problems Successive over-relaxation (SOR)-based multi-scale DQ method Asymptotic multi-scale DQ method DQ solution to multi-scale poroelastic problems Conclusions Variable Order Differential Quadrature Method Direct DQ discretization and dynamic numerical instability Variable order approach Improvement of temporal integration Conclusions Multi-Domain Differential Quadrature Method Linear plane elastic problems with material discontinuity A multi-domain approach for numerical treatment of material discontinuity Multi-domain DQ method for irregular domain Multi-domain DQ formulation of plane elastic problems Conclusions Localized Differential Quadrature Method DQ and its spatial discretization of the wave equation Stability analysis Coordinate-based localized DQ Spline-based localized DQ method Conclusions Mathematical Compendium Gauss elimination SOR method One-dimensional band storage Runge-Kutta method (constant time step) Complex analysis QR algorithm Codes DQ for numerical evaluation of function cos(x) Complex DQ for harmonic problem Localized DQ method References Index