Reducing the bandwidth in solving linear algebraic systems arising in the finite element method

Jitka Segethová

Aplikace matematiky (1980)

  • Volume: 25, Issue: 4, page 286-304
  • ISSN: 0862-7940

Abstract

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The matrix of the system of linear algebraic equations, arising in the application of the finite element method to one-dimensional problems, is a bandmatrix. In approximations of high order, the band is very wide but the elements situated far from the diagonal of the matrix are negligibly small as compared with the diagonal elements. The aim of the paper is to show on a model problem that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced. A simple numerical example illustates the discussion.

How to cite

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Segethová, Jitka. "Reducing the bandwidth in solving linear algebraic systems arising in the finite element method." Aplikace matematiky 25.4 (1980): 286-304. <http://eudml.org/doc/15152>.

@article{Segethová1980,
abstract = {The matrix of the system of linear algebraic equations, arising in the application of the finite element method to one-dimensional problems, is a bandmatrix. In approximations of high order, the band is very wide but the elements situated far from the diagonal of the matrix are negligibly small as compared with the diagonal elements. The aim of the paper is to show on a model problem that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced. A simple numerical example illustates the discussion.},
author = {Segethová, Jitka},
journal = {Aplikace matematiky},
keywords = {reducing the bandwidth; finite element method; numerical example; reducing the bandwidth; finite element method; numerical example},
language = {eng},
number = {4},
pages = {286-304},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Reducing the bandwidth in solving linear algebraic systems arising in the finite element method},
url = {http://eudml.org/doc/15152},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Segethová, Jitka
TI - Reducing the bandwidth in solving linear algebraic systems arising in the finite element method
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 4
SP - 286
EP - 304
AB - The matrix of the system of linear algebraic equations, arising in the application of the finite element method to one-dimensional problems, is a bandmatrix. In approximations of high order, the band is very wide but the elements situated far from the diagonal of the matrix are negligibly small as compared with the diagonal elements. The aim of the paper is to show on a model problem that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced. A simple numerical example illustates the discussion.
LA - eng
KW - reducing the bandwidth; finite element method; numerical example; reducing the bandwidth; finite element method; numerical example
UR - http://eudml.org/doc/15152
ER -

References

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  1. I. Babuška, Approximation by hill functions, Comment. Math. Univ. Carolinae 11 (1970), 787-811. (1970) Zbl0215.46404MR0292309
  2. W. Feller, An introduction to probability theory and its applications, Vol. 2. Wiley, New York 1966. (1966) Zbl0138.10207MR0210154
  3. I. S. Gradštein I. M. Ryžik, Tables of integrals, sums, series, and products, (Russian). 5th edition. Nauka, Moskva 1971. (1971) 
  4. K. Segeth, Universal approximation by hill functions, Czechoslovak Math. J. 22 (1972), 612-640. (1972) Zbl0247.41011MR0310502
  5. J. Segethová, 10.1137/0709018, SIAM J. Numer. Anal. 9 (1972), 199-204. (1972) Zbl0243.65004MR0305552DOI10.1137/0709018
  6. J. H. Wilkinson, 10.1145/321075.321076, J. Assoc. Comput. Mach. 8 (1961), 281-330. (1961) Zbl0109.09005MR0176602DOI10.1145/321075.321076
  7. J. H. Wilkinson, Rounding errors in algebraic processes, HMSO, London 1963. (1963) Zbl1041.65502MR0161456

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