Abstract
A fast Poisson solver on irregular domains, based on boundary methods, is presented. The harmonic polynomial approximation of the solution of the associated homogeneous problem provides a good practical boundary method which allows a trivial parallel processing for solution evaluation or straightforward computations of the interface values for domain decomposition/embedding.
Similar content being viewed by others
References
A. Bogomolny,Fundamental solutions method for elliptic boundary value problems, SIAM J. Numer. Anal., 22 (1985), pp. 644.
A. Brandt,Multilevel computations: review and recent developments, Proc. 3d Copper Mountain Conf. on multigrid methods, 1989.
B. Buzbee, F. Dorr, A. George andG. Golub,The direct solution of the discrete Poisson equation on irregular regions, SIAM J. Numer. Anal., 8 (1971), pp. 722–736.
C. Canuto, M. Hussaini, A. Quarteroni and T. Zang,Spectral Methods in Fluid Dynamics, S-V, 1988.
P. Concus, G. Golub and D. O’Leary,A generalized conjugate gradient method for the numerical solution of partial differential equations, in J. Bunch and D. Rose, ed., Proc. Symp. on Sparse Matrix Computations, Acad. Press, 1975, pp. 309–332.
R. Dautray andJ.-L. Lions,Mathematical Analysis and Numerical Methods for Science and Technology, vol. 1, S-V, 1990.
M. Dryja and O. Widlund,Some domain decomposition algorithms for elliptic problems, in Iterative Methods for Large Linear Systems, D. Young, et al., ed., Acad. Press, 1990.
S. Eisenstat,On the rate of convergence of the Bergman-Vekua method for the numerical solution of elliptic boundary value problems, SIAM J. Numer. Anal., 11 (1974), pp. 654–680.
G. Fairweather and L. Johnston,The method of fundamental solutions for problems in potential theory, in Treatment of Integral Equations by Numerical Methods, C. Baker and G. Miller, ed., Acad. Press, 1982.
K. Gallivan, W. Jalby andU. Meier,The use of BLAS3 in linear algebra on a parallel processor with hierarchical memory, SIAM J. Sci. Stat. Comp., 11 (1987), pp. 1079–1084.
R. Glowinski, et al, ed.,Domain decomposition methods for partial differential equations, SIAM, 1991.
G. Golub andC. Van Loan,Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989.
P. Henrici,Applied and Computational Complex Analysis, V.3, Wiley, 1986.
R. Hockney,Rapid elliptic solvers, in Numerical Methods in Applied Fluid Dynamics, 1980.
Z. Li andR. Mathon,Error and stability analysis of boundary methods for elliptic problems with interfaces, Math. Comp., 54 (1990), pp. 41–61.
Z. Li, R. Mathon andP. Sermer,Boundary methods for solving elliptic problems with singularities and interfaces, SIAM J. Numer. Anal., 24 (1987), pp. 487–498.
R. Mathon andR. Johnston,The approximate solution of elliptic boundary value problems by fundamental solutions, SIAM J. Numer. Anal., 14 (1977), pp. 638–650.
A. Mayo,The fast solution of Poisson and biharmonic equations on irregular regions, SIAM J. Numer. Anal., 21 (1984), pp. 285–299.
P. Swarztrauber andR. Sweet,Efficient FORTRANsubprograms for the solution of elliptic partial differential equations, ACM Trans. Math. Software, 5 (1979), pp. 352–364.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lee, D. Boundary collocation fast poisson solver on irregular domains. Korean J. Comput. & Appl. Math. 8, 27–44 (2001). https://doi.org/10.1007/BF03011620
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03011620