The Neural Green's Operator matches exact coarse-solve iteration counts in two-level preconditioners for diffusion and advection-diffusion problems when inputs are integrated against the output basis.
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Introduces and analyzes the Δ_k-GenEO coarse space for Helmholtz problems, sharpening k-explicit GMRES convergence conditions and demonstrating scalability and robustness for low to moderate frequencies via numerical experiments.
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When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning
The Neural Green's Operator matches exact coarse-solve iteration counts in two-level preconditioners for diffusion and advection-diffusion problems when inputs are integrated against the output basis.
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Can Symmetric Positive Definite (SPD) coarse spaces perform well for indefinite Helmholtz problems?
Introduces and analyzes the Δ_k-GenEO coarse space for Helmholtz problems, sharpening k-explicit GMRES convergence conditions and demonstrating scalability and robustness for low to moderate frequencies via numerical experiments.