Aplicación del método de descomposición matricial y la transformada rápida de Fourier a la solución de la ecuación de Poisson
DOI:
https://doi.org/10.22199/S07160917.1983.0004.00002Keywords:
Transformada de Fourier discreta, AlgortimoAbstract
Se presenta un algoritmo para resolver numéricamente la ecuación de Poisson, basado en el método de "Descomposición matricial" o "Separación discreta de Variables" con el uso de la Transformada Rápida de Fourier. El método se describe y analiza para condiciones de borde del tipo Dirichlet en regiones rectangulares. Se dan ejemplos y se presentan los programas computacionales que permiten aplicar el método.References
B. L. Buzbee, G. M. Golub, C. W. Nielson. : "On direct methods for solving Poisson's equations". Siam Journal on Numerical Analysis. Vol. December 1970.
E. Gray Brigham.: "The fast Fourier Transform". Prentice-Hall, Inc. U.S.A. 1974.
Alexandra Banegas.: "Fast Poisson solvers for problems with sparsity". Mathematics of Computation, Volume 32, Number 142. Aprib 1978.
D. Fischer, G. Golub, O. Hald., C. Leiva y O. Widlund. "On Fourier-Toeplitz methods for separable elliptic problems". Mathematics of Computation, Vol. 28, 1974.
R. W. Hockney.: "A Fast Direct Solution of Poisson's Equation Using Fourier Analysis". J. Computation Machine, Vol. 12. 1965.
O. Widlund. "On the use of fast methods for separable finite difference equations for general elliptic problems". Editado por Rose Willoughby Plenum Press, New York, 1972.
Elliptic problems solvers. Proceedings of the Elliptic Problem Solvers Conference, held in Santa Fe. New Mexico, June 30- July 2, 1980. Editado por Martin Schultz. Academic Press.
William Ames.: "Numerical methods for partial differencial equations". Academic Press - 1977.
E. Gray Brigham.: "The fast Fourier Transform". Prentice-Hall, Inc. U.S.A. 1974.
Alexandra Banegas.: "Fast Poisson solvers for problems with sparsity". Mathematics of Computation, Volume 32, Number 142. Aprib 1978.
D. Fischer, G. Golub, O. Hald., C. Leiva y O. Widlund. "On Fourier-Toeplitz methods for separable elliptic problems". Mathematics of Computation, Vol. 28, 1974.
R. W. Hockney.: "A Fast Direct Solution of Poisson's Equation Using Fourier Analysis". J. Computation Machine, Vol. 12. 1965.
O. Widlund. "On the use of fast methods for separable finite difference equations for general elliptic problems". Editado por Rose Willoughby Plenum Press, New York, 1972.
Elliptic problems solvers. Proceedings of the Elliptic Problem Solvers Conference, held in Santa Fe. New Mexico, June 30- July 2, 1980. Editado por Martin Schultz. Academic Press.
William Ames.: "Numerical methods for partial differencial equations". Academic Press - 1977.
Published
2018-03-27
How to Cite
[1]
Óscar L. Rojo Jeraldo, R. L. Soto Montero, and L. Valdivia Reyes, “Aplicación del método de descomposición matricial y la transformada rápida de Fourier a la solución de la ecuación de Poisson”, Proyecciones (Antofagasta, On line), vol. 2, no. 4, pp. 23-53, Mar. 2018.
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