H_k-GenEO constructs spectral coarse spaces from indefinite local eigenproblems to precondition highly indefinite PDEs, providing sufficient conditions for GMRES robustness and observed practical stability as k grows.
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math.NA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Develops two-level convergence theory for LS-AMG-DD showing coarse-space weak approximation property bounded by spectral cutoff threshold, yielding factored bounds for multiplicative cycles with block-Jacobi and overlapping Schwarz smoothers on Gram-representable SPD matrices.
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Spectral coarse spaces based on indefinite operators: the $H_k$-GenEO method
H_k-GenEO constructs spectral coarse spaces from indefinite local eigenproblems to precondition highly indefinite PDEs, providing sufficient conditions for GMRES robustness and observed practical stability as k grows.
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Two-level convergence of Algebraic Multigrid with Overlapping Smoothers and Spectral Coarse Grids
Develops two-level convergence theory for LS-AMG-DD showing coarse-space weak approximation property bounded by spectral cutoff threshold, yielding factored bounds for multiplicative cycles with block-Jacobi and overlapping Schwarz smoothers on Gram-representable SPD matrices.