Geodesic
The method of fictitious right-hand sides
Applications of Mathematics, Tome 29 (1984) no. 5, pp. 384-389
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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).
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).
DOI : 10.21136/AM.1984.104108
Classification : 35J05, 65F10, 65N12, 65N20, 65N22
Keywords: method of fictitious right-hand sides; fast algorithm; standard domain; convergence; numerical example; Poisson equation 
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Práger, Milan. The method of fictitious right-hand sides. Applications of Mathematics, Tome 29 (1984) no. 5, pp. 384-389. doi: 10.21136/AM.1984.104108

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