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This is a Quantitative Study study.

October 15, 2025Open Access

Optimal Spectral Approximation in the Overlaps for Generalized Finite Element Methods

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Analysis reveals nearly exponential convergence of approximation errors in spectral computations, indicating robustness in method performance.

The proposed method achieves nearly exponential decay in approximation errors, enhancing computational efficiency.
A significant reduction in matrix bandwidth and problem size facilitates faster spectral computations.
The method can function as a preconditioner, optimizing convergence rates in iterative processes.
Numerical experiments validate the method's effectiveness and demonstrate robustness against varying coefficients.

Alber et al. (2025) studied this question.

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Analysis reveals nearly exponential convergence of approximation errors in spectral computations, indicating robustness in method performance.