A formally fourth-order accurate compact scheme for 3D Poisson equation in cylindrical coordinates

Authors:
Ming-Chih Lai;Jui-Ming Tseng
Affiliations:
Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan;Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 5
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Abstract

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.