Theory and numerics of subspace approximation of eigenvalue problems

Siu Wun Cheung; Youngsoo Choi; Seung Whan Chung; Jean Luc Fattebert; Coleman Kendrick; Daniel Osei-Kuffuor

doi:10.1016/j.amc.2025.129722

Theory and numerics of subspace approximation of eigenvalue problems

Siu Wun Cheung
, Youngsoo Choi
, Seung Whan Chung
, Jean Luc Fattebert
, Coleman Kendrick
, Daniel Osei-Kuffuor

Multiscale Materials

Research output: Contribution to journal › Article › peer-review

Abstract

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 some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, 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.

Original language	English
Article number	129722
Journal	Applied Mathematics and Computation
Volume	511
DOIs	https://doi.org/10.1016/j.amc.2025.129722
State	Published - Feb 15 2026

Funding

This work was supported by Laboratory Directed Research and Development (LDRD) Program by the U.S. Department of Energy (24-ERD-035). Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344. IM release number: LLNL-JRNL-867049. This manuscript has been co-authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE).

Keywords

Eigenvalue problems
Reduced order model

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10.1016/j.amc.2025.129722

Cite this

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title = "Theory and numerics of subspace approximation of eigenvalue problems",

abstract = "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 some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, 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.",

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T1 - Theory and numerics of subspace approximation of eigenvalue problems

AU - Cheung, Siu Wun

AU - Choi, Youngsoo

AU - Chung, Seung Whan

AU - Fattebert, Jean Luc

AU - Kendrick, Coleman

AU - Osei-Kuffuor, Daniel

PY - 2026/2/15

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N2 - 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 some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, 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.

AB - 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 some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, 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.

KW - Eigenvalue problems

KW - Reduced order model

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DO - 10.1016/j.amc.2025.129722

M3 - Article

AN - SCOPUS:105015514636

SN - 0096-3003

VL - 511

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 129722

ER -

Theory and numerics of subspace approximation of eigenvalue problems

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