Browsing by Author "Tseng, Jui-Ming"

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A formally fourth-order accurate compact scheme for 3D Poisson equation in cylindrical coordinates
(2007-04-01)
Lai, Ming-Chih
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Tseng, Jui-Ming
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應用數學系
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Department of Applied Mathematics
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. (c) 2006 Elsevier B.V. All tights reserved.