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Title: A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods (English)
Author: Červ, Václav
Author: Segeth, Karel
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 27
Issue: 5
Year: 1982
Pages: 375-390
Summary lang: English
Summary lang: Czech
Summary lang: Russian
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Category: math
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Summary: The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical experiments performed are studied from the point of view of the time and storage requirements and the achieved accuracy of the solution. (English)
Keyword: comparison
Keyword: electromagnetic fields in geophysics
Keyword: numerical experiments
Keyword: accuracy
Keyword: Helmholtz equation
MSC: 35J05
MSC: 65F05
MSC: 65F10
MSC: 65N20
MSC: 65N22
MSC: 86A25
idZBL: Zbl 0511.65074
idMR: MR0674982
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Date available: 2008-05-20T18:20:11Z
Last updated: 2015-07-08
Stable URL: http://hdl.handle.net/10338.dmlcz/103983
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Reference: [12] A. Ralston: A first course in numerical analysis.McGraw-Hill, New York 1965. Zbl 0139.31603, MR 0191070
Reference: [13] G. Strong G. J. Fix: An analysis of the finite element method.Prentice-Hall, Englewood Cliffs, N. J., 1973. MR 0443377
Reference: [14] R. S. Varga: Matrix iterative analysis.Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 0158502
Reference: [15] J. T. Weaver: The electromagnetic field within a discontinuous conductor with reference to geomagnetic micropulsations near a coastline.Canad. J. Phys. 41 (1963), 484-495. Zbl 0113.43702, 10.1139/p63-051
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