Numerical solution for Poisson problems by using differential quadrature method
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Abstract
This article presents a meshless method called Differential Quadrature Method for solving the Poisson problems. Solving the Poisson problem is one of the important steps for calculating flow dynamics, electric field, and heat transfer. This method estimates the derivatives directly so there is no need to deal with integration process. The selected Poisson’s problems were analyzed in a unit square domain. The numerical solutions were compared with the analytical solutions in five cases. The overall error in all cases were less than one percent.
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Belytschko T, Lu, YY and Gu, L. Element-Free Galerkin Methods. International Journal of Numerical Methods in Engineering. 1994;37: 229-256.
Atluri SN and Zhu T. A New Meshless Local Petrov-Galerkin (MLPG) Approach in Computational Mechanics. Computational Mechanics. 1998;22: 117-127.
Kansa E J. Multiquartics-A Scattered Data Approximation with Applications to Computational Fluid Dynamics-II: Solutions to Parabolic, Hyperbolic, and Elliptic Partial Differential Equations. Computers and Mathematics with Applications. 1990;19: 147-161.
Goldberg MA. The Method of Fundamental Solutions for Poisson’s Equation. Engineering Analysis with Boundary Elements. 1995;16: 205-213.
Shu C, Ding H and Yeo, KS. Local Radial Basis Function-Based Differential Quadrature Method and Its Application to Solve Two-Dimensional Incompressible Navier-Stokes. Computer Methods in Applied Mechanics and Engineering. 2003;192: 941-954.
Monaghan JJ. Smooth Particle Hydrodynamics. Annual Review of Astronomy and Astrophysics. 1992;30: 543-574.
Liu WK, Jun S and Belytschko T. Reproducing Kernel Particle Methods. International Journal of Numerical Methods in Fluid. 1995;20: 1081-1106.
Chantasiriwan S. Meshless Methods: Future of Engineering Computations. In: The 17th Conference of Mechanical Engineering Network; 15-17 October 2003.