14 citations · 18 across the 9 of their papers we have counts for
9 papers
On the Stability Barrier of Hermite Type Discretizations of Advection Equations
Xianyi Zeng
In this paper we establish a stability barrier of a class of high-order Hermite-type discretization of 1D advection equations underlying the hybrid-variable (HV) and active flux (A…
Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws
Ning Liu, Yiming Fan, Xianyi Zeng +3
Neural operators (NOs) have emerged as effective tools for modeling complex physical systems in scientific machine learning. In NOs, a central characteristic is to learn the govern…
An Explicit Fourth-Order Hybrid-Variable Method for Euler Equations with A Residual-Consistent Viscosity
Xianyi Zeng
In this paper we present a formally fourth-order accurate hybrid-variable method for the Euler equations in the context of method of lines. The hybrid-variable (HV) method seeks nu…
Equivariant Hopf Bifurcation in a Class of Partial Functional Differential Equations on a Circular Domain
Yaqi Chen, Xianyi Zeng, Ben Niu
Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differentia…
Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
Xianyi Zeng, Giovanni Stabile, Efthymios N. Karatzas +2
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background me…
On the Stability of Explicit Finite Difference Methods for Advection-Diffusion Equations
Xianyi Zeng, Md Mahmudul Hasan
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of…
On Finite Volume Discretization of Infiltration Dynamics in Tumor Growth Models
Xianyi Zeng, Mashriq Ahmed Saleh, Jianjun Paul Tian
We address numerical challenges in solving hyperbolic free boundary problems described by spherically symmetric conservation laws that arise in the modeling of tumor growth due to…
A general approach to enhance slope limiters on non-uniform rectilinear grids
Xianyi Zeng
Most slope limiter functions in high-resolution finite volume methods to solve hyperbolic conservation laws are designed assuming one-dimensional uniform grids, and they are also u…
A hybrid FD-FV method for first-order hyperbolic conservation laws on Cartesian grids: The smooth problem case
Xianyi Zeng
We present a class of hybrid FD-FV (finite difference and finite volume) methods for solving general hyperbolic conservation laws written in first-order form. The presentation focu…