Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F15%3A43926412" target="_blank" >RIV/49777513:23520/15:43926412 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21110/15:00233279 RIV/61989100:27740/15:86095971
Result on the web
<a href="http://dx.doi.org/10.1016/j.cma.2015.09.003" target="_blank" >http://dx.doi.org/10.1016/j.cma.2015.09.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cma.2015.09.003" target="_blank" >10.1016/j.cma.2015.09.003</a>

Result language
angličtina
Original language name
Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method
Original language description
Guaranteed upper-lower bounds on homogenized coefficients, arising from the periodic cell problem, are calculated in a scalar elliptic setting. Our approach builds on the recent variational reformulation of the Moulinec-Suquet (1994) Fast Fourier Transform (FFT) homogenization scheme by Vondřejc et al. (2014), which is based on the conforming Galerkin approximation with trigonometric polynomials. Upper-lower bounds are obtained by adjusting the primal-dual finite element framework developed independently by Dvořák (1993) and Wi?ckowski (1995) to the FFT-based Galerkin setting. We show that the discretization procedure differs for odd and non-odd number of grid points. Thanks to the Helmholtz decomposition inherited from the continuous formulation, the duality structure is fully preserved for the odd discretizations. In the latter case, a more complex primal-dual structure is observed due to presence of the trigonometric polynomials associated with the Nyquist frequencies. These theoretical findings are confirmed with numerical examples. To conclude, the main advantage of the FFT-based approach over conventional finite-element schemes is that the primal and the dual problems are treated on the same basis, and this property can be extended beyond the scalar elliptic setting.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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