کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4642515 | 1341346 | 2007 | 7 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A formally fourth-order accurate compact scheme for 3D Poisson equation in cylindrical coordinates A formally fourth-order accurate compact scheme for 3D Poisson equation in cylindrical coordinates](/preview/png/4642515.png)
In this paper, we extend our previous work (M.-C. Lai, A simple compact fourth-order Poisson solver on polar geometry, J. Comput. Phys. 182 (2002) 337–345) to 3D cases. More precisely, we present a spectral/finite difference scheme for Poisson equation in cylindrical coordinates. The scheme relies on the truncated Fourier series expansion, where the partial differential equations of Fourier coefficients are solved by a formally fourth-order accurate compact difference discretization. Here the formal fourth-order accuracy means that the scheme is exactly fourth-order accurate while the poles are excluded and is third-order accurate otherwise. Despite the degradation of one order of accuracy due to the presence of poles, the scheme handles the poles naturally; thus, no pole condition is needed. The resulting linear system is then solved by the Bi-CGSTAB method with the preconditioner arising from the second-order discretization which shows the scalability with the problem size.
Journal: Journal of Computational and Applied Mathematics - Volume 201, Issue 1, 1 April 2007, Pages 175–181