A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods

Václav Červ; Karel Segeth

Aplikace matematiky (1982)

  • Volume: 27, Issue: 5, page 375-390
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Červ, Václav, and Segeth, Karel. "A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods." Aplikace matematiky 27.5 (1982): 375-390. <http://eudml.org/doc/15258>.

@article{Červ1982,
abstract = {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.},
author = {Červ, Václav, Segeth, Karel},
journal = {Aplikace matematiky},
keywords = {comparison; electromagnetic fields in geophysics; numerical experiments; accuracy; Helmholtz equation; comparison; electromagnetic fields in geophysics; numerical experiments; accuracy; Helmholtz equation},
language = {eng},
number = {5},
pages = {375-390},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
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},
url = {http://eudml.org/doc/15258},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Červ, Václav
AU - Segeth, Karel
TI - A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 5
SP - 375
EP - 390
AB - 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.
LA - eng
KW - comparison; electromagnetic fields in geophysics; numerical experiments; accuracy; Helmholtz equation; comparison; electromagnetic fields in geophysics; numerical experiments; accuracy; Helmholtz equation
UR - http://eudml.org/doc/15258
ER -

References

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  1. I. Babuška R. B. Kellog, Numerical solution of the neutron diffusion equation in the presence of corners and interfaces, Numerical Reactor Calculations. International Atomic Energy Agency, Vienna 1972, 473 - 486. (1972) 
  2. V. Bezvoda K. Segeth, Mathematical modeling of electromagnetic fields. The Use of Finite Element Method and Finite Difference Method in Geophysics, (Proceedings of Summer School, Liblice 1977.) Geofyzikální ústav ČSAV, Praha 1978, 329-332. (1977) 
  3. B. A. Carre, 10.1093/comjnl/4.1.73, Comput. J. 4 (1961), 73 - 78. (1961) Zbl0098.31405DOI10.1093/comjnl/4.1.73
  4. V. Červ, Numerical modelling of geoelectric structures using the Galerkin and finite element methods, Studia geoph. et geod. 22 (1978), 283 - 294. (1978) 
  5. V. Červ O. Praus, Numerical modelling in laterally inhomogeneous geoelectrical structures, Studia geoph. et geod. 22 (1978), 74-81. (1978) 
  6. J. H. Coggon, Electromagnetic and electrical modelling of induction effects in laterally non-uniform conductors, Phys. Earth Planet. Inter. 10 (1975), 265. (1975) 
  7. P. Concus G. H. Golub, 10.1137/0710092, SIAM J. Numer. Anal. 10 (1973), 1103 - 1120. (1973) Zbl0245.65043MR0341890DOI10.1137/0710092
  8. F. W. Dorr, 10.1137/1012045, SIAM Rev. 12 (1970), 248-263. (1970) Zbl0208.42403MR0266447DOI10.1137/1012045
  9. F. W. Jones L. J. Pascoe, A general computer program to determine the perturbation of alternating electric currents in a two-dimensional model of a region of uniform conductivity with an embedded inhomogeneity, Geophys. J. Roy. Astronom. Soc. 23 (1971), 3. (1971) 
  10. F. W. Jones A. T. Price, 10.1111/j.1365-246X.1970.tb06073.x, Geophys. J. Roy. Astronom. Soc. 20 (1970), 317. (1970) DOI10.1111/j.1365-246X.1970.tb06073.x
  11. I. Marek, On the SOR method for solving linear equations in Banach spaces, Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 11 (1969), 335-341. (1969) Zbl0221.65096MR0278086
  12. A. Ralston, A first course in numerical analysis, McGraw-Hill, New York 1965. (1965) Zbl0139.31603MR0191070
  13. G. Strong G. J. Fix, An analysis of the finite element method, Prentice-Hall, Englewood Cliffs, N. J., 1973. (1973) MR0443377
  14. R. S. Varga, Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. (1962) MR0158502
  15. J. T. Weaver, 10.1139/p63-051, Canad. J. Phys. 41 (1963), 484-495. (1963) Zbl0113.43702DOI10.1139/p63-051
  16. D. M. Young, Iterative solution of large linear systems, Academic Press, New York 1971. (1971) Zbl0231.65034MR0305568

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