Guaranteed lower bounds to effective stiffness
Abstract: We present a numerical scheme for obtaining guaranteed (reliable) and arbitrarily close two sided bounds to effective (homogenized) parameters of the linear elasticity 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 L2-orthogonal projection of an auxiliary field built from the primal solution. The projection can be computed easily by FFT and provides a lower bound of almost the same quality as 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
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
-
Online-Ressource
- Sprache
-
Englisch
- Anmerkungen
-
PAMM : proceedings of applied mathematics and mechanics. - 23, 2 (2023) , e202300098, ISSN: 1617-7061
- Ereignis
-
Veröffentlichung
- (wo)
-
Freiburg
- (wer)
-
Universität
- (wann)
-
2024
- Urheber
- DOI
-
10.1002/pamm.202300098
- URN
-
urn:nbn:de:bsz:25-freidok-2548493
- Rechteinformation
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
-
14.08.2025, 10:46 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Gaynutdinova, Liya
- Ladecký, Martin
- Pultarová, Ivana
- Zeman, Jan
- Universität
Entstanden
- 2024
Ähnliche Objekte (12)
Guaranteed lower bounds to effective stiffness
Guaranteed lower bounds for eigenvalues
Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates
Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds
Comparison of guaranteed lower eigenvalue bounds with three skeletal schemes
Direct guaranteed lower eigenvalue bounds with quasi-optimal adaptive mesh-refinement
Nonobtuse meshes with guaranteed angle bounds
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method
(Un)conventional policy and the effective lower bound
Unconventional monetary policies at the effective lower bound
Expectation and duration at the effective lower bound
Guaranteed lower bounds to effective stiffness
Guaranteed lower bounds for eigenvalues
Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates
Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds
Comparison of guaranteed lower eigenvalue bounds with three skeletal schemes
Direct guaranteed lower eigenvalue bounds with quasi-optimal adaptive mesh-refinement
Nonobtuse meshes with guaranteed angle bounds
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method
(Un)conventional policy and the effective lower bound
Unconventional monetary policies at the effective lower bound
Expectation and duration at the effective lower bound
Guaranteed lower bounds to effective stiffness
Guaranteed lower bounds for eigenvalues
Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates
Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds
Comparison of guaranteed lower eigenvalue bounds with three skeletal schemes
Direct guaranteed lower eigenvalue bounds with quasi-optimal adaptive mesh-refinement
Nonobtuse meshes with guaranteed angle bounds
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method
(Un)conventional policy and the effective lower bound
Unconventional monetary policies at the effective lower bound