6 papers
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-,…
Fourth- and higher-order finite element methods for the incompressible Navier-Stokes equations with Dirichlet boundary conditions
Yang Li, Heyu Wang, Qinghai Zhang
Inspired by the unconstrained pressure Poisson equation (PPE) formulation [Liu, Liu, \& Pego, Comm. Pure Appl. Math. 60 (2007): 1443-1487], we previously proposed the generic proje…
Lagrangian Particle Classification and Lagrangian Flux Identities for a Moving Hypersurface
Lingyun Ding, Shuang Hu, Baiyun Huang +1
For a moving hypersurface in the flow of a nonautonomous ordinary differential equation in -dimensional Euclidean spaces, the fluxing index of a passively-advected Lagrangian pa…
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…
MetaRuleGPT: Recursive Numerical Reasoning of Language Models Trained with Simple Rules
Kejie Chen, Lin Wang, Qinghai Zhang +1
Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-l…