6 papers
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…
Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-dimensional Advection Equation on Arbitrarily Complex Domains
Yunxia Sun, Kaiyi Liang, Yuke Zhu +2
To numerically solve the two-dimensional advection equation, we propose a family of fourth- and higher-order semi-Lagrangian finite volume (SLFV) methods that feature (1) fourth-,…
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…
A fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries
Kaiyi Liang, Yuke Zhu, Jiyu Liu +1
We propose a fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries on a Cartesian grid. We employ the ARMS technique to g…
A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains
Yixiao Qian, Weizhen Li, Yan Tan +1
We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable…
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…