# The method of fictitious right-hand sides

Aplikace matematiky (1984)

- Volume: 29, Issue: 5, page 384-389
- ISSN: 0862-7940

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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) Zbl0231.65083MR0292316DOI10.1137/0708066
- W. Proskurowski O. Widlund, On the numerical solution of Helmholtz's equation by the capacitance matrix method, Math. Comput. 30 (1976), 433 - 468. (1976) Zbl0332.65057MR0421102
- A. S. L. Shieh, 10.1007/BF01404568, Numer. Math., 31 (1979), 405-429. (1979) MR0516582DOI10.1007/BF01404568

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