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| A Legendre spectral element method for solving Poisson-type equation in polar coordinates |
| Received:June 07, 2011 Revised:December 03, 2011 |
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| DOI：10.7511/jslx20125001 |
| KeyWord:spectral element method legendre polynomials Legendre Gauss Radau Legendre Gauss Lobatto polar coordinate Poisson equations |
| Author | Institution |
| 梅欢 |
重庆大学 资源及环境科学学院 工程力学系, 重庆 |
| 曾忠 |
重庆大学 资源及环境科学学院 工程力学系, 重庆 ;重庆大学 煤矿灾害动力学与控制国家重点实验室, 重庆 |
| 邱周华 |
重庆大学 资源及环境科学学院 工程力学系, 重庆 |
| 姚丽萍 |
重庆大学 资源及环境科学学院 工程力学系, 重庆 |
| 李亮 |
重庆大学 资源及环境科学学院 工程力学系, 重庆 |
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| Abstract: |
| The key to solve Poisson-type equations in polar coordinates is its singularity at r=0.In this paper,a Legendre spectral element method (SEM) based on the Galerkin variational formulation for solving the Poisson-type equations in polar coordinates was proposed.The physical domain was divided into a number of elements and the Legendre polynomials were adopted in every computational element.Further,the Legendre-Gauss-Radau (LGR) quadrature points were used in the elements which involved the origin while Legendre-Gauss-Lobatto (LGL) quadrature points in the others in the radial direction,so that the 1/r coordinate singularity was avoided successfully.As to the azimuthal direction,the LGL quadrature points were employed.The clustering of collocation points near the pole could be prevented through the technique of domain decomposition.Finally,the method was applied to several Poisson-type equations subject to a Dirichlet or Neumann boundary condition.The numerical results demonstrate that the SEM has high accuracy. |
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