Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates

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References

[1] E. H Chao, S. F. Paul, R. C. Davidson and K. S. Fine, “Direct Numerical Solution of Poisson’s Equation in Cylindrical (r, z) Coordinates,” Princeton University, Princeton, 1997.

[2] H. Chen, Y. Su and B. D. Shizgal, “A Direct Spectral Collocation Poisson Solver in Polar and Cylindrical Coordinates,” Journal of Computational Physics, Vol. 160, No. 2, 2000, pp. 453-469.

http://dx.doi.org/10.1006/jcph.2000.6461

[3] I. Christopher, G. Knorr, M. Shoucri and P. Bertrand, “Solution of the Poisson Equation in an Annulus,” Journal of Computational Physics, Vol. 131, No. 2, 1997, pp. 323-326. http://dx.doi.org/10.1006/jcph.1996.5598

[4] J. C. Kalita and K. K. Ray, “A Transformation-Free HOC Scheme for Incompressible Viscous Flows Past an Impulsively Started Circular Cylinder,” Journal of Computational Physics, Vol. 228, No. 14, 2009, pp. 5207-5236.

http://dx.doi.org/10.1016/j.jcp.2009.04.016

[5] M. C. Lai and W. C. Wang, “Fast Direct Solvers for Poisson Equation on 2D Polar and Spherical Geometries,” Numerical Methods for Partial Differential Equations, Vol. 18, No. 1, 2002, pp. 56-68.

[6] P. N. Swarztrauber and R. A. Sweet, “The Direct Solution of the Discrete Poisson Equation on a Disk,” SIAM Journal on Numerical Analysis, Vol. 10, No. 5, 1973, pp. 900-907.

[7] R. C. Mittal and S. Gahlaut, “High Order Finite Difference Schemes to Solve Poisson’s Equation in Cylindrical Symmetry,” Communications in Applied Numerical Methods, Vol. 3, 1987, pp. 457-461.

[8] R. C. Mittal and S. Gahlaut, “High-Order Finite Differences Schemes to Solve Poisson’s Equation in Polar Coordinates,” IMA Journal of Numerical Analysis, Vol. 11, No. 2, 1991, pp. 261-270.

http://dx.doi.org/10.1093/imanum/11.2.261

[9] C. S. Tan, “Accurate Solution of three Dimensional Poisson’s Equation in Cylindrical Coordinate by Expansion in Chebyshev Polynomials,” Journal of Computational Physics, Vol. 59, No. 1, 1985, pp. 81-95.

http://dx.doi.org/10.1016/0021-9991(85)90108-1

[10] S. R. K. Iyengar and R. Manohar, “High Order Difference Methods for Heat Equation in Polar Cylindrical Polar Cylindrical Coordinates,” Journal of Computational Physics, Vol. 77, No. 2, 1988, pp. 425-438.

http://dx.doi.org/10.1016/0021-9991(88)90176-3

[11] S. R. K. Iyengar and A. Goyal, “A Note on Multigrid for the Three-Dimensional Poisson Equation in Cylindrical Coordinates,” Journal of Computational and Applied Mathematics, Vol. 33, No. 2, 1990, pp. 163-169.

http://dx.doi.org/10.1016/0377-0427(90)90366-8

[12] M. C. Lai and J. M. Tseng, “A Formally Fourth-Order Accurate Compact Scheme for 3D Poisson Equation in Cylindrical and Spherical Coordinates,” Journal of Computational and Applied Mathematics, Vol. 201, No. 1, 2007, pp. 175-181.

http://dx.doi.org/10.1016/j.cam.2006.02.011

[13] J. Xu, P. N. Ostroumov and J. Nolen, “A Parallel 3D Poisson Solver for Space Charge Simulation in Cylindrical Coordinates,” Computer Physics Communications, Vol. 178, No. 4, 2008, pp. 290-300.

http://dx.doi.org/10.1016/j.cpc.2007.09.008

[14] M. A. Malcolm and J. Palmer, “A Fast Method for Solving a Class of Tri-Diagonal Linear Systems,” Communications of the ACM, Vol. 17, No. 1, 1974, pp. 14-17.

http://dx.doi.org/10.1145/360767.360777

[15] R. W. Hockney, “A Fast Direct Solution of Poisson Equation Using Fourier Analysis,” JACM, Vol. 12, No. 1, 1965, pp. 95-113.

http://dx.doi.org/10.1145/321250.321259