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Localized subspace iteration methods for multiscale problems
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DOI：10.1016/j.jcp.2025.114559.png)
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Abstract
En 中文
This paper introduces a novel localized subspace iteration (LSI) method for constructing generalized finite element basis functions, designed to address multiscale problems on complex domains without scale separation. The proposed method synergistically combines operator localization with subspace iteration applied to local spectral problems. Localization is achieved by employing local homogeneous Dirichlet boundary conditions in conjunction with partition-of-unity functions. We subsequently develop two computationally efficient implementations: the localized standard subspace iteration (LSSI) and the localized krylov subspace iteration (LKSI), founded on standard and Krylov subspaces, respectively. Furthermore, from a unifying theoretical perspective, we demonstrate that several established multiscale methods can be reinterpreted as specific instances of subspace iteration for approximating the eigenspaces of these local spectral problems. A rigorous convergence analysis is provided to substantiate the method’s theoretical foundations. Finally, numerical experiments confirm the robustness and high efficiency of our method, showcasing its superior capability in handling challenging scenarios such as long-channel configurations in fractured media.
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