3 papers
math.NA2026
Neural Green's Function Accelerated Iterative Methods for Solving Indefinite Boundary Value Problems
Shengyan Li, Qi Sun, Xuejun Xu +1
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space o…
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
Two-level hybrid Schwarz Preconditioners for The Helmholtz Equation with high wave number
Peipei Lu, Xuejun Xu, Bowen Zheng +1
In this work, we propose and analyze two two-level hybrid Schwarz preconditioners for solving the Helmholtz equation with high wave number in two and three dimensions. Both precond…