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math.NA2025
Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method
Yuwei Geng, Junqi Yin, Eric C. Cyr +2
While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional…
math.NA2025
Learning Singularity-Encoded Green's Functions with Application to Iterative Methods
Qi Sun, Shengyan Li, Bowen Zheng +2
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-f…
math.NA2025
Optimal error estimates of the diffuse domain method for parabolic equations
Wenrui Hao, Lili Ju, Yuejin Xu
In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann bounda…