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math.NA2026
Discovery of Singularities in Partial Differential Equations Using Adaptive Numerical Discretizations
Allen Yang, Lucas Amoudruz, Petros Koumoutsakos
We compute self-similar singularity profiles of partial differential equations (PDEs) using adaptive numerical discretizations based on optimizing a discrete loss (ODIL). The field…
math.NA2026
Two Dimensional Fourier Continuation for Domains with Corners
Oscar P. Bruno, Allen Yang
This paper presents a fast "two-dimensional Fourier Continuation" (2D-FC) method for the construction of biperiodic extensions of smooth, non-periodic functions defined over genera…