A special finite element method based on component mode synthesis

Ulrich L. Hetmaniuk; Richard B. Lehoucq

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 3, page 401-420
  • ISSN: 0764-583X

Abstract

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The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.

How to cite

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Hetmaniuk, Ulrich L., and Lehoucq, Richard B.. "A special finite element method based on component mode synthesis." ESAIM: Mathematical Modelling and Numerical Analysis 44.3 (2010): 401-420. <http://eudml.org/doc/250776>.

@article{Hetmaniuk2010,
abstract = { The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions. },
author = {Hetmaniuk, Ulrich L., Lehoucq, Richard B.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Eigenvalues; modal analysis; multilevel; substructuring; domain decomposition; dimensional reduction; finite elements; eigenvalues; domain decomposition; Poisson equation; second order linear elliptic operator; highly oscillating coefficients; numerical experiments},
language = {eng},
month = {4},
number = {3},
pages = {401-420},
publisher = {EDP Sciences},
title = {A special finite element method based on component mode synthesis},
url = {http://eudml.org/doc/250776},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Hetmaniuk, Ulrich L.
AU - Lehoucq, Richard B.
TI - A special finite element method based on component mode synthesis
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/4//
PB - EDP Sciences
VL - 44
IS - 3
SP - 401
EP - 420
AB - The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.
LA - eng
KW - Eigenvalues; modal analysis; multilevel; substructuring; domain decomposition; dimensional reduction; finite elements; eigenvalues; domain decomposition; Poisson equation; second order linear elliptic operator; highly oscillating coefficients; numerical experiments
UR - http://eudml.org/doc/250776
ER -

References

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  5. J.K. Bennighof and R.B. Lehoucq, An automated multilevel substructuring method for eigenspace computation in linear elastodynamics. SIAM J. Sci. Comput.25 (2004) 2084–2106.  Zbl1133.65304
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  8. R.R. Craig, Jr. and M.C.C. Bampton, Coupling of substructures for dynamic analysis. AIAA J.6 (1968) 1313–1319.  Zbl0159.56202
  9. Y. Efendiev and T. Hou, Multiscale Finite Element Methods: Theory and Applications, Surveys and Tutorials in the Applied Mathematical Sciences4. Springer, New York, USA (2009).  Zbl1163.65080
  10. U. Hetmaniuk and R.B. Lehoucq, Multilevel methods for eigenspace computations in structural dynamics, in Domain Decomposition Methods in Science and Engineering, Lect. Notes Comput. Sci. Eng.55, Springer-Verlag (2007) 103–114.  
  11. T. Hou and X. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys.134 (1997) 169–189.  Zbl0880.73065
  12. W.C. Hurty, Vibrations of structural systems by component-mode synthesis. J. Eng. Mech. Division ASCE86 (1960) 51–69.  
  13. J. Nolen, G. Papanicolaou and O. Pironneau, A framework for adaptive multiscale methods for elliptic problems. Multiscale Model. Simul.7 (2008) 171–196.  Zbl1160.65342
  14. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations – Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford, UK (1999).  Zbl0931.65118

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