38 citations · 89 across the 10 of their papers we have counts for
10 papers
A Kernel Based Unconditionally Stable Scheme for Nonlinear Parabolic Partial Differential Equations
Kaipeng Wang, Andrew Christlieb, Yan Jiang +1
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work…
Free-stream preserving finite difference schemes for ideal magnetohydrodynamics on curvilinear meshes
Yize Yu, Yan Jiang, Mengping Zhang
In this paper, a high order free-stream preserving finite difference weighted essentially non-oscillatory (WENO) scheme is developed for the ideal magnetohydrodynamic (MHD) equatio…
An adaptive high-order piecewise polynomial based sparse grid collocation method with applications
Zhanjing Tao, Yan Jiang, Yingda Cheng
This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional pr…
A Kernel Based High Order "Explicit" Unconditionally Stable Constrained Transport Method for Ideal Magnetohydrodynamics
Firat Cakir, Andrew Christlieb, Yan Jiang
The ideal Magnetohydrodynamics (MHD) equations are challenging because one needs to maintain the divergence free condition, $\nabla \cdot \Bv = 0$. Many numerical methods have been…
Dispersion Analysis of Finite Difference and Discontinuous Galerkin Schemes for Maxwell's Equations in Linear Lorentz Media
Yan Jiang, Puttha Sakkaplangkul, Vrushali A. Bokil +2
In this paper, we consider Maxwell's equations in linear dispersive media described by a single-pole Lorentz model for electronic polarization. We study two classes of commonly use…
A Kernel Based High Order "Explicit" Unconditionally Stable Scheme for Time Dependent Hamilton-Jacobi Equations
Andrew Christlieb, Wei Guo, Yan Jiang
In this paper, a class of high order numerical schemes is proposed for solving Hamilton-Jacobi (H-J) equations. This work is regarded as an extension of our previous work for nonli…