Fast Poisson solvers for problems with sparsity
Author:
Alexandra Banegas
Journal:
Math. Comp. 32 (1978), 441446
MSC:
Primary 65F10; Secondary 65N20
MathSciNet review:
0483338
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Fast Poisson solvers, which provide the numerical solution of Poisson's equation on regions that permit the separation of variables, have proven very useful in many applications. In certain of these applications the data is sparse and the solution is only required at relatively few mesh points. For such problems this paper develops algorithms that allow considerable savings in computer storage as well as execution speed. Results of numerical experiments are given.
 [1]
James
R. Bunch and Donald
J. Rose (eds.), Sparse matrix computations, Academic Press
Inc. [Harcourt Brace Jovanovich Publishers], New York, 1976. MR 0448792
(56 #7097)
 [2]
O. BUNEMAN, A Compact Noniterative Poisson Solver, Rep. SUIPR294, Inst. Plasma Research, Stanford Univ., 1969.
 [3]
B.
L. Buzbee, G.
H. Golub, and C.
W. Nielson, On direct methods for solving Poisson’s
equations, SIAM J. Numer. Anal. 7 (1970),
627–656. MR 0287717
(44 #4920)
 [4]
J. W. COOLEY, P. A. W. LEWIS & P. D. WELCH, "The fast Fourier transform algorithm: Programming consideration in the calculation of sine, cosine and Laplace transform," J. Sound Vib., v. 12, 1970, pp. 315337.
 [5]
Ȧke
Björck and Germund
Dahlquist, Numerical methods, PrenticeHall Inc., Englewood
Cliffs, N.J., 1974. Translated from the Swedish by Ned Anderson;
PrenticeHall Series in Automatic Computation. MR 0368379
(51 #4620)
 [6]
D.
Fischer, G.
Golub, O.
Hald, C.
Leiva, and O.
Widlund, On FourierToeplitz methods for
separable elliptic problems, Math. Comp. 28 (1974), 349–368.
MR
0415995 (54 #4072), http://dx.doi.org/10.1090/S00255718197404159952
 [7]
R.
W. Hockney, A fast direct solution of Poisson’s equation
using Fourier analysis, J. Assoc. Comput. Mach. 12
(1965), 95–113. MR 0213048
(35 #3913)
 [8]
R. W. HOCKNEY, "The potential calculation and some applications," Methods in Computational Physics, Vol. 9, Academic Press, New York, 1970.
 [9]
D. P. O'LEARY & O. WIDLUND, ERDANYU report. (To appear.)
 [10]
W. PROSKUROWSKI, Numerical Solution of Helmholtz's Equation by Implicit Capacitance Matrix Methods, Report 6402, Lawrence Berkeley Laboratory, February 1977.
 [11]
Wlodzimierz
Proskurowski and Olof
Widlund, On the numerical solution of
Helmholtz’s equation by the capacitance matrix method, Math. Comp. 30 (1976), no. 135, 433–468. MR 0421102
(54 #9107), http://dx.doi.org/10.1090/S00255718197604211024
 [12]
P. SWARZTRAUBER & R. SWEET, Efficient FORTRAN Subprograms for the Solution of Elliptic Partial Differential Equations, Report NCAR1N/1A109, National Center for Atmospheric Research, Boulder, Colorado, 1975.
 [13]
O. WIDLUND, "On the use of fast methods for separable finite difference equations for the solution of general elliptic problems," Sparse Matrices and Their Applications (D. J. Rose and R. A. Willoughby, Editors), Plenum Press, New York, 1972.
 [14]
O. WIDLUND, Capacitance Matrix Methods for Helmholtz' Equation on General Bounded Regions, Proc. from a July 1976 Meeting in Oberwolfach. (To appear.)
 [1]
 R. E. BANK, Marching Algorithms and Gaussian Elimination, Proc. Sympos. on Sparse Matrix Computations, Argonne National Lab., Sept. 1975 (J. R. Bunch and D. J. Rose, Editors), Academic Press, New York, 1976. MR 0448792 (56:7097)
 [2]
 O. BUNEMAN, A Compact Noniterative Poisson Solver, Rep. SUIPR294, Inst. Plasma Research, Stanford Univ., 1969.
 [3]
 B. L. BUZBEE, G. H. GOLUB & C. W. NIELSON, "On direct methods for solving Poisson 's equation," SIAM J. Numer. Anal., v. 7, 1970, pp. 627656. MR 0287717 (44:4920)
 [4]
 J. W. COOLEY, P. A. W. LEWIS & P. D. WELCH, "The fast Fourier transform algorithm: Programming consideration in the calculation of sine, cosine and Laplace transform," J. Sound Vib., v. 12, 1970, pp. 315337.
 [5]
 G. DAHLQUIST, A. BJÖRCK & N. ANDERSON, Numerical Methods, PrenticeHall, Englewood Cliffs, N. J., 1974. MR 0368379 (51:4620)
 [6]
 D. FISCHER, G. GOLUB, O. HALD, C. LEIVA & O. WIDLUND, "On FourierToeplitz methods for separable elliptic problems," Math. Comp., v. 28, 1974, pp. 349368. MR 0415995 (54:4072)
 [7]
 R. W. HOCKNEY, "A fast direct solution of Poisson's equation using Fourier analysis," J. Assoc. Comput. Mach., v. 12, 1965, pp. 95113. MR 0213048 (35:3913)
 [8]
 R. W. HOCKNEY, "The potential calculation and some applications," Methods in Computational Physics, Vol. 9, Academic Press, New York, 1970.
 [9]
 D. P. O'LEARY & O. WIDLUND, ERDANYU report. (To appear.)
 [10]
 W. PROSKUROWSKI, Numerical Solution of Helmholtz's Equation by Implicit Capacitance Matrix Methods, Report 6402, Lawrence Berkeley Laboratory, February 1977.
 [11]
 W. PROSKUROWSKI & O. WIDLUND, "On the numerical solution of Helmholtz's equation by the capacitance matrix method," Math. Comp., v. 30, 1976, pp. 433468. Appeared also as an ERDANYU report COO307799. MR 0421102 (54:9107)
 [12]
 P. SWARZTRAUBER & R. SWEET, Efficient FORTRAN Subprograms for the Solution of Elliptic Partial Differential Equations, Report NCAR1N/1A109, National Center for Atmospheric Research, Boulder, Colorado, 1975.
 [13]
 O. WIDLUND, "On the use of fast methods for separable finite difference equations for the solution of general elliptic problems," Sparse Matrices and Their Applications (D. J. Rose and R. A. Willoughby, Editors), Plenum Press, New York, 1972.
 [14]
 O. WIDLUND, Capacitance Matrix Methods for Helmholtz' Equation on General Bounded Regions, Proc. from a July 1976 Meeting in Oberwolfach. (To appear.)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65F10,
65N20
Retrieve articles in all journals
with MSC:
65F10,
65N20
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197804833388
PII:
S 00255718(1978)04833388
Article copyright:
© Copyright 1978 American Mathematical Society
