| Issue |
ESAIM: M2AN
Volume 59, Number 4, July-August 2025
|
|
|---|---|---|
| Page(s) | 2055 - 2079 | |
| DOI | https://doi.org/10.1051/m2an/2025046 | |
| Published online | 23 July 2025 | |
Offline-online approximation of multiscale eigenvalue problems with random defects
Institut für Numerische Simulation, Universit¨at Bonn, Friedrich-Hirzebruch-Allee 7, D-53115 Bonn, Germany
* Corresponding author: kolombag@ins.uni-bonn.de
Received:
29
November
2024
Accepted:
3
June
2025
In this paper, we consider an elliptic eigenvalue problem with multiscale, randomly perturbed coefficients. For an efficient and accurate approximation of the solutions for many different realizations of the coefficient, we propose a computational multiscale method in the spirit of the Localized Orthogonal Decomposition (LOD) method together with an offline-online strategy similar to Målqvist and Verfürth [ESAIM Math. Model. Numer. Anal. 56 (2022) 237–260]. The offline phase computes and stores local contributions to the LOD stiffness matrix for selected defect configurations. Given any perturbed coefficient, the online phase combines the pre-computed quantities in an efficient manner. We further propose a modification in the online phase, for which numerical results indicate enhanced performances for moderate and high defect probabilities. We show rigorous a priori error estimates for eigenfunctions as well as eigenvalues.
Mathematics Subject Classification: 65N25 / 65N30 / 65N12 / 65N15 / 35J15
Key words: Eigenvalue problems / multiscale method / perturbed coefficients / offline-online strategy
© The authors. Published by EDP Sciences, SMAI 2025
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