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.
Iterative methods by space decomposition and subspace correction
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UNVERDICTED 3representative citing papers
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.
citing papers explorer
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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.
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NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
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.
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Superconvergence in finite element method by smoothing
Smoothing iterations on finite element solutions in an enriched space produce superconvergent approximations for symmetric positive definite problems.