A Direct Spectral Collocation Poisson Solver in Polar and Cylindrical Coordinates

Journal of Computational Physics

Volumn 160, Issue 2, 2000, Pages 453-469

  Chen, Heli ^a   Su, Yuhong ^a   Shizgal, Bernie D ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Cylindrical coordinates; Poisson solver; Polar coordinates; Spectral collocation

Indexed keywords

CYLINDERS (SHAPES);

CYLINDRICAL COORDINATES; DIFFERENT DOMAINS; POISSON SOLVERS; POLAR COORDINATE; POLE CONDITION; SPECTRAL ACCURACY; SPECTRAL COLLOCATION; SPECTRAL COLLOCATION METHOD; UNIT DISK; WEIGHTED INTERPOLATION;

POISSON EQUATION;

EID: 0042683304     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6461     Document Type: Article

References (33)

1. Birdsall C. K., Langdon A. B. Plasma Physics via Computer Simulation. 1985.
2. Roth J. R. Industrial Plasma Engineering. 1995.
3. Birney J., Tremaine S. Galactic Dynamics. 1987.
4. Canuto C., Hussaini M. Y., Quarteroni A., Zang T. A. Spectral Methods in Fluid Dynamics. 1987.
5. Serikov V. V., Nanbu K. Spatio-temporal variations in a three-dimensional DC glow discharge via particle-in-cell simulation. IEEE Trans. Plasma Sci. 27:1999;84.
6. Miller P. A., Riley M. E. Dynamics of collisionless plasma sheaths. J. Appl. Phys. 82:1997;3689.
7. Grapperhuis M. J., Kushner M. J. A semiananlytic radio frequency sheath model integrated into two dimensional hybrid model for plasma processing reactors. J. Appl. Phys. 81:1997;569.
8. Christopher I., Knorr G., Shoucri M., Bertrand P. Solution of the Poisson equation in an annulus. J. Comput. Phys. 131:1997;323.
9. Braverman E., Israeli M. A fast 3D Poisson solver of arbitrary order accuracy. J. Comput. Phys. 144:1998;109.
10. Averbuch A., Israeli M., Vozovoi I. A fast Poisson solver of arbitrary order accuracy in rectangular regions. SIAM J. Sci. Comput. 19:1998;933.
11. Bouaoudia B., Marcus P. S. Fast and accurate spectral treatment of coordinate singularities. J. Comput. Phys. 96:1991;217.
12. Karageorghis A. Conforming spectral methods for Poisson problems in cuboidal domains. J. Sci. Comput. 9:1994;341.
13. Huang W., Sloan D. M. Pole condition for singular problems: The pseudospectral approximation. J. Comput. Phys. 107:1993;254.
14. Dang-Vu H., Delcarte C. An accurate solution of the Poisson equation by the Chebyshev collocation method. J. Comput. Phys. 104:1993;211.
15. Eisen H., Heinrichs W., Witsch K. Spectral methods and polar coordinate singularities. J. Comput. Phys. 96:1991;241.
16. Shen J. Efficient spectral-Galerkin methods III: Polar and cylindrical geometries. SIAM J. Sci. Comput. 18:1997;1583.
17. Tan C. S. Accurate solution of three-dimensional Poisson's equation in cylindrical coordinate by expansion in Chebyshev polynomials. J. Comput. Phys. 59:1985;81.
18. Zhao S., Yedlin M. J. A new iterative Chebyshev spectral method for solving the elliptic equation. J. Comput. Phys. 113:1994;215.
19. Bernardi C., Karageorghis A. Spectral method in a part of a disk. Numer. Math. 73:1996;265.
20. Gottlieb D., Orszag S. Numerical Analysis of Spectral Methods: Theory and Applications. 1977.
21. Orszag S. A. Fourier series on spheres. Mon. Weather Rev. 102:1974;56.
22. Matsushima T., Marcus P. S. A spectral method for polar coordinates. J. Comput. Phys. 120:1995;365.
23. Lynch R. E., Rice J. R., Thomas D. H. Direct solution of partial different equations by tensor product methods. Numer. Math. 6:1964;185.
24. Haidvogel D. B., Zang T. The accurate solution of Poisson's equation by expansion in Chebyshev polynomials. J. Comput. Phys. 30:1979;167.
25. D. Gottlieb, M. Y. Hussaini, and, S. A. Orszag, Introduction, theory and applications of spectral methods, in, Spectral Methods for Partial Differential Equation, edited by, Voigt, Gottlieb, and Yousuff, SIAM, Philadelphia, 1984.
26. Zang T. A., Wang Y. S., Hussaini M. Y. Spectral multigrid methods for elliptic equations. J. Comput. Phys. 48:1982;485.
27. J. A. C. Weideman, Spectral methods based on non-classical orthogonal polynomials, in Approximations and Computation of Orthogonal Polynomials, edited by, Gautschi, Golub, and Opfer, Intern. Ser. Numer. Math. 131, 239, 1999.
28. Su Y. Collocation Spectral Methods in the Solution of Poisson Equation. 1998.
29. Peyret R. Von Karman Institute Lecture Series 1986-04. Introduction to Spectral Methods. 1986.
30. Chen H., Shizgal B. D. The quadrature discretization method (QDM) in the solution of the Schrödinger equation. J. Math. Chem. 24:1998;321.
31. Shizgal B. D., Chen H. The quadrature discretization method in the solution of the Fokker-Planck equation with nonclassical basis functions. J. Chem. Phys. 107:1997;8051.
32. Shizgal B. D., Chen H. The quadrature discretization method (QDM) in the solution of the Schrödinger equation with nonclassical basis functions. J. Chem. Phys. 104:1996;4137.
33. Gautschi W. Orthogonal polynomials-constructive theory and applications. J. Comput. Appl. Math. 12, 13:1985;61.