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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