A Fast Fourth-Order Cut Cell Method for Solving Elliptic Equations in Two-Dimensional Irregular Domains
Numerical Analysis
2025-04-02 v1 Numerical Analysis
Abstract
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 irregular domains is the poised lattice generation (PLG) algorithm that generates finite-volume interpolation stencils near the irregular boundary. We are able to derive high-order discretization of the elliptic operators by least squares fitting over the generated stencils. We then design a new geometric multigrid scheme to efficiently solve the resulting linear system. Finally, we demonstrate the accuracy and efficiency of our method through various numerical tests in irregular domains.
Cite
@article{arxiv.2504.00724,
title = {A Fast Fourth-Order Cut Cell Method for Solving Elliptic Equations in Two-Dimensional Irregular Domains},
author = {Yuke Zhu and Zhixuan Li and Qinghai Zhang},
journal= {arXiv preprint arXiv:2504.00724},
year = {2025}
}