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Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems

机译：扩散对流问题的双互易性边界元方法解中的最小二乘差分正交时间积分方案

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摘要

Least-squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in diffusive-convective type problems with variable coefficients. The DRBEM enables us to use the fundamental solution of Laplace equation, which is easy to implement computation ally. The terms except the Laplacian are considered as the nonhomogeneity in the equation, which are approximated in terms of radial basis functions. The application of DQM for time derivative discretization when it is combined with the DRBEM gives an overdetermined system of linear equations since both boundary and initial conditions are imposed. The least squares approximation is used for solving the overdetermined system. Thus, the solution is obtained at any time level without using an iterative scheme. Numerical results are in good agreement with the theoretical solutions of the diffusive-convective problems considered. (C) 2006 Elsevier Ltd. All rights reserved.
机译：最小二乘微分求积法（DQM）用于及时求解常微分方程，该方程是从对等变分型问题的对等空间边界导数对偶边界元方法（DRBEM）的应用获得的。 DRBEM使我们能够使用Laplace方程的基本解，该解易于在计算上实现。除拉普拉斯算子外的其他项均视为等式中的非均质性，它们是根据径向基函数近似的。当DQM与DRBEM结合用于时间导数离散化时，由于施加了边界条件和初始条件，因此该应用程序给出了线性方程组的超定系统。最小二乘近似用于求解超定系统。因此，无需使用迭代方案即可在任何时间级别获得解决方案。数值结果与所考虑的扩散对流问题的理论解非常吻合。 （C）2006 Elsevier Ltd.保留所有权利。

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