计算力学学报2012，Vol.29Issue(5)：641-645,674,6.
极坐标系下的Legendre谱元方法求解Poisson-型方程
A Legendre spectral element method for solving Poisson-type equation in polar coordinates
摘要
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.关键词
谱元法/Legendre多项式/Legendre/Gauss/Radau/Legendre/Gauss/Lobatto/极坐标/Poisson方程Key words
spectral element method/legendre polynomials/Legendre Gauss Radau/Legendre Gauss Lobatto/polar coordinate/Poisson equations分类
数理科学引用本文复制引用
梅欢,曾忠,邱周华,姚丽萍,李亮..极坐标系下的Legendre谱元方法求解Poisson-型方程[J].计算力学学报,2012,29(5):641-645,674,6.基金项目
国家自然科学基金（10872222,50921063）资助项目. （）
