Year: 2024
Type: preprint
Abstract: 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, Verfürth, ESIAM Math. Model. Numer. Anal., 56(1):237-260, 2022]. 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.
Source: arXiv (Cornell University)
Authors: Kolombage, Dilini, Verfürth, Barbara
Institution: University of Bonn
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4405030671