3 papers
math.NA2026
A Fourth-Order Cut-cell Multigrid Method for Solving Elliptic Equations on Arbitrary Domains
Jiyu Liu, Zhixuan Li, Jiatu Yan +2
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) gen…
math.NA2025
A Fast Fourth-Order Cut Cell Method for Solving Elliptic Equations in Two-Dimensional Irregular Domains
Yuke Zhu, Zhixuan Li, Qinghai Zhang
We propose a fast fourth-order cut cell method for solving constant-coefficient elliptic equations in two-dimensional irregular domains. In our methodology, the key to dealing with…
math.NA2024
An AI-aided algorithm for multivariate polynomial reconstruction on Cartesian grids and the PLG finite difference method
Qinghai Zhang, Yuke Zhu, Zhixuan Li
Polynomial reconstruction on Cartesian grids is fundamental in many scientific and engineering applications, yet it is still an open problem how to construct for a finite subset $K…