Effective computation of restoring force vector in finite element method

Martin Balazovjech; Ladislav Halada

Kybernetika (2007)

  • Volume: 43, Issue: 6, page 767-776
  • ISSN: 0023-5954

Abstract

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We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and equations.

How to cite

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Balazovjech, Martin, and Halada, Ladislav. "Effective computation of restoring force vector in finite element method." Kybernetika 43.6 (2007): 767-776. <http://eudml.org/doc/33894>.

@article{Balazovjech2007,
abstract = {We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and equations.},
author = {Balazovjech, Martin, Halada, Ladislav},
journal = {Kybernetika},
keywords = {FEM; stiffness matrix; restoring force vector; computational efficiency of algorithm; e-invariants; numerical examples; stiffness matrix; restoring force vector; algorithm; computational efficiency; elastodynamic equation; finite element method; finite difference method},
language = {eng},
number = {6},
pages = {767-776},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Effective computation of restoring force vector in finite element method},
url = {http://eudml.org/doc/33894},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Balazovjech, Martin
AU - Halada, Ladislav
TI - Effective computation of restoring force vector in finite element method
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 6
SP - 767
EP - 776
AB - We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and equations.
LA - eng
KW - FEM; stiffness matrix; restoring force vector; computational efficiency of algorithm; e-invariants; numerical examples; stiffness matrix; restoring force vector; algorithm; computational efficiency; elastodynamic equation; finite element method; finite difference method
UR - http://eudml.org/doc/33894
ER -

References

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  1. Archuleta R. J., Experimental and Numerical Three-dimensional Simulations of Strike-slip Earthquakes, Ph.D. Thesis. University of California, San Diego 1976 
  2. Felippa C. A., Introduction to Finite Element Methods (ASEN 5007), Lecture notes. University of Colorado, Boulder 2005 
  3. Moczo P., Kristek, J., Bystrický E., 10.1142/S0218396X01000681, J. Comp. Acoustics 9(2) (2004), 593–609 MR1853644DOI10.1142/S0218396X01000681
  4. Reddy J. N., An Introduction to the Finite Element Method, McGraw-Hill, New York 199 

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