Conforming finite-element assembly naturally induces element-local Gram representations, enabling black-box multilevel algebraic preconditioning for H(div), H^2, and elasticity problems where classical AMG fails.
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2026 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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A black-box, multilevel algebraic preconditioning framework for conforming finite elements
Conforming finite-element assembly naturally induces element-local Gram representations, enabling black-box multilevel algebraic preconditioning for H(div), H^2, and elasticity problems where classical AMG fails.
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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.