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.
Iterative methods by space decomposition and subspace correction
5 Pith papers cite this work. Polarity classification is still indexing.
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The paper proves feasibility of quantum domain decomposition preconditioning for FEM Poisson problems with the two-level Additive Schwarz method, supplies block-encoding bounds, derives quantum solver complexity, and details a BPX local solver choice.
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
Neural operators supply warm-start guesses that cut iteration counts and runtime by up to 90% in Krylov solvers for PDEs while retaining the original methods' convergence guarantees.
Smoothing iterations on finite element solutions in an enriched space produce superconvergent approximations for symmetric positive definite problems.
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NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.