Guaranteed lower bounds to effective stiffness

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F23%3A00367531" target="_blank" >RIV/68407700:21110/23:00367531 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/pamm.202300098" target="_blank" >https://doi.org/10.1002/pamm.202300098</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/pamm.202300098" target="_blank" >10.1002/pamm.202300098</a>

Result language
angličtina
Original language name
Guaranteed lower bounds to effective stiffness
Original language description
We present a numerical scheme for obtaining guaranteed (reliable) and arbitrarily close two sided bounds to effective (homogenized) parameters of the linearelasticity problem. For the upper bounds, we use standard finite element (FE) discretization of the so-called primal problem with preconditioning based on the fast discrete Fourier transformation (FFT). For the lower bounds, we use the dual formulation and some smoother FE approximation spaces. Moreover, instead of solving the discretized dual problem, we can only compute an ????2-orthogonal projection of an auxiliary field built from the primal solution. The projection can becomputed easily by FFT and provides a lower bound of almost the same qualityas that obtained as the exact solution of the discretized dual problem. In addition, a simple low-dimensional optimization improves the projected solution. Numerical examples are presented to support the theoretical developments.
Czech name
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Czech description
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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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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