48 citations · 173 across the 16 of their papers we have counts for
16 papers
High order two-grid finite difference methods for interface and internal layer problems
Zhilin Li, Kejia Pan, Juan Ruiz
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate…
High order compact schemes for flux type BCs
Zhilin Li, Kejia Pan
In this paper new innovative fourth order compact schemes for Robin and Neumann boundary conditions have been developed for boundary value problems of elliptic PDEs in two and thre…
Convergence study of IB methods for Stokes equations with no-slip boundary conditions
Zhilin Li, Kejia Pan, Juan Ruiz-Álvarez
Peskin's Immersed Boundary (IB) model and method are among one of the most important modeling tools and numerical methods. The IB method has been known to be first order accurate i…
A conservative difference scheme with optimal pointwise error estimates for two-dimensional space fractional nonlinear Schrödinger equations
Hongling Hu, Xianlin Jin, Dongdong He +2
In this paper, a linearized semi-implicit finite difference scheme is proposed for solving the two-dimensional (2D) space fractional nonlinear Schrödinger equation (SFNSE).The sche…
A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems
Xiaoqiang Yue, Kejia Pan, Jie Zhou +3
The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to…
A linearized energy--conservative finite element method for the nonlinear Schrödinger equation with wave operator
Wentao Cai, Dongdong He, Kejia Pan
In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schrödinger equation with wave operator. In this method, a modified leap-frog sch…
An efficient multigrid solver for 3D biharmonic equation with a discretization by 25-point difference scheme
Kejia Pan, Dongdong He, Runxin Ni
In this paper, we propose an efficient extrapolation cascadic multigrid (EXCMG) method combined with 25-point difference approximation to solve the three-dimensional biharmonic equ…
A three-level linearized difference scheme for the coupled nonlinear fractional Ginzburg-Landau equation
Dongdong He, Kejia Pan
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme invo…
A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers' equation
Kejia Pan, Xiaoxin Wu, Xiaoqiang Yue +1
In this paper, an efficient and high-order accuracy finite difference method is proposed for solving multidimensional nonlinear Burgers' equation. The third-order three stage Runge…
Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations
Xiaoqiang Yue, Shi Shu, Xiaowen Xu +2
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discre…
A fourth-order maximum principle preserving operator splitting scheme for three-dimensional fractional Allen-Cahn equations
Dongdong He, Kejia Pan, Hongling Hu
In this paper, by using Strang's second-order splitting method, the numerical procedure for the three-dimensional (3D) space fractional Allen-Cahn equation can be divided into thre…
Nanostructures imaging via numerical solution of a 3-d inverse scattering problem without the phase information
Michael V. Klibanov, Loc H. Nguyen, Kejia Pan
Inverse scattering problems without the phase information arise in imaging of nanostructures whose sizes are hundreds of nanometers as well as in imaging of biological cells. The g…
A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation
Dongdong He, Kejia Pan
This paper concerns the numerical study for the generalized Rosenau-Kawahara-RLW equation obtained by coupling the generalized Rosenau-RLW equation and the generalized Rosenau-Kawa…
An extrapolation cascadic multigrid method combined with a fourth order compact scheme for 3D poisson equation
Kejia Pan, Dongdong He, Hongling Hu
In this paper, we develop an EXCMG method to solve the three-dimensional Poisson equation on rectangular domains by using the compact finite difference (FD) method with unequal mes…
A new extrapolation cascadic multigrid method for 3D elliptic boundary value problems on rectangular domains
Kejia Pan, Dongdong He, Hongling Hu
In this paper, we develop a new extrapolation cascadic multigrid (ECMG) method, which makes it possible to solve 3D elliptic boundary value problems on rectangular domains…
An energy preserving finite difference scheme for the Poisson-Nernst-Planck system
Dongdong He, Kejia Pan
In this paper, we construct a semi-implicit finite difference method for the time dependent Poisson-Nernst-Planck system. Although the Poisson-Nernst-Planck system is a nonlinear s…