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math.NA2025
General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance
Daniel V. Leibovici, Oscar P. Bruno
This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of…
math.NA2025
General-domain FC-based shock-dynamics solver I: Basic elements
Oscar P. Bruno, Daniel V. Leibovici
This contribution, Part I in a two-part article series, presents a general-domain version of the FC-SDNN (Fourier Continuation Shock-detecting Neural Network) spectral scheme for t…
math.NA2021
FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment
Oscar P. Bruno, Jan S. Hesthaven, Daniel V. Leibovici
This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in non-periodic domains under arbitrary boundary conditions. The approach relies on…