# 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

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topHetmaniuk, 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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- 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.
- 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
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