Theory and numerics of subspace approximation of eigenvalue problems

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fide...

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Authors: Cheung, Siu Wun, Choi, Youngsoo, Chung, Seung Whan, Fattebert, Jean-Luc, Coleman, Kendrick, Osei-Kuffuor, Daniel
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Eigenvalues
Error analysis
Software
Subspaces
Online Access:Get full text
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Summary:Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fidelity systems. We provide general error estimates under non-simple eigenvalue conditions, establishing the theoretical foundations for our methodology. Numerical examples, ranging from one-dimensional to three-dimensional setups, are presented to demonstrate the efficacy of reduced basis method in handling parametric variations in boundary conditions and coefficient fields to achieve significant computational savings while maintaining high accuracy, making them promising tools for practical applications in large-scale eigenvalue computations.
ISSN:2331-8422