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math.NA2025
On the Pre-Asymptotic Stability and Inverse Structure of Extended-Domain Spectral Methods
Po-Yi Wu
The extended-domain method is a strategy for applying spectral methods to complex geometries. Its stability is complicated by the ill-conditioning of the Fourier extension frame. T…
math.NA2025
Convergent Operator-Splitting Scheme for Viscosity Solutions: A Foundation for Learning Domain-to-Solution Maps
Po-Yi Wu
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order par…