The method of fictitious right-hand sides
Aplikace matematiky (1984)
- Volume: 29, Issue: 5, page 384-389
- ISSN: 0862-7940
Access Full Article
top
Abstract
topHow to cite
topPráger, Milan. "The method of fictitious right-hand sides." Aplikace matematiky 29.5 (1984): 384-389. <http://eudml.org/doc/15369>.
@article{Práger1984,
abstract = {The paper deals with the application of a fast algorithm for the solution of finite-difference systems for boundary-value problems on a standard domain (e.g. on a rectangle) to the solution of a boundary-value problem on a domain of general shape contained in the standard domain. A simple iterative procedure is suggested for the determination of fictitious right-hand sides for the system on the standard domain so that its solution is the desired one. Under the assumptions that are usual for matrices obtained by discretization of elliptic boundary-value problems, the convergence of this procedure for all sufficiently small positive values of a parameter is proved. The method is illustrated by a simple numerical example (solution of the Poisson equation on an $L$-shaped domain).},
author = {Práger, Milan},
journal = {Aplikace matematiky},
keywords = {method of fictitious right-hand sides; fast algorithm; standard domain; convergence; numerical example; Poisson equation; method of fictitious right-hand sides; fast algorithm; standard domain; convergence; numerical example; Poisson equation},
language = {eng},
number = {5},
pages = {384-389},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The method of fictitious right-hand sides},
url = {http://eudml.org/doc/15369},
volume = {29},
year = {1984},
}
TY - JOUR
AU - Práger, Milan
TI - The method of fictitious right-hand sides
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 5
SP - 384
EP - 389
AB - The paper deals with the application of a fast algorithm for the solution of finite-difference systems for boundary-value problems on a standard domain (e.g. on a rectangle) to the solution of a boundary-value problem on a domain of general shape contained in the standard domain. A simple iterative procedure is suggested for the determination of fictitious right-hand sides for the system on the standard domain so that its solution is the desired one. Under the assumptions that are usual for matrices obtained by discretization of elliptic boundary-value problems, the convergence of this procedure for all sufficiently small positive values of a parameter is proved. The method is illustrated by a simple numerical example (solution of the Poisson equation on an $L$-shaped domain).
LA - eng
KW - method of fictitious right-hand sides; fast algorithm; standard domain; convergence; numerical example; Poisson equation; method of fictitious right-hand sides; fast algorithm; standard domain; convergence; numerical example; Poisson equation
UR - http://eudml.org/doc/15369
ER -
References
top- B. L. Buzbee F. W. Dorr J. A. George G. H. Golub, 10.1137/0708066, SIAM J. Numer. Anal. 8 (1971), 722 -736. (1971) MR0292316DOI10.1137/0708066
- W. Proskurowski O. Widlund, On the numerical solution of Helmholtz's equation by the capacitance matrix method, Math. Comput. 30 (1976), 433 - 468. (1976) MR0421102
- A. S. L. Shieh, 10.1007/BF01404568, Numer. Math., 31 (1979), 405-429. (1979) MR0516582DOI10.1007/BF01404568
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.