Boundary reduction technique and triangular differential quadrature domain decomposition method for polygonal region

The differential quadrature method (DQM) is an attractive numerical method with high efficiency and accuracy. But the conventional DQM is limited in its application to regular regions by using functional values along a mesh line to approximate derivatives. To deal with problems on irregular geometric domains, coordinate transformation has to be conducted. The triangular differential quadrature method (TDQM) proposed by Zhong [Zhong H. Triangular differential quadrature. Commun Numer Meth Eng 2000; 16:401–8; Zhong H. Triangular differential quadrature and its application to elastostatic analysis of Reissner plates. Int J Solids Struct 2001; 38:2821–32], avoid the coordinate transformation. In this paper, the domain decomposition method (DDM) is used for the elliptical boundary problems on a pentagonal region. In every sub-domain, we solve the partial differential equations with TDQM. With boundary reduction technique, the functional values on internal points can be eliminated. The system of equations, which satisfied by the boundary points, can be obtained. Numerical results show that triangular differential quadrature domain decomposition method (TDQDDM) is easy and effective for treating the problems on irregular region.