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- Shidong Jiang, L Greengard
- 2004

We present a fast algorithm for the evaluation of the exact nonreflecting boundary conditions for the SchrSdinger equation in one dimension. The exact nonrefleeting boundary condition contains a nonloeal term which is a convolution integral in time, with a kernel proportional to 1/v~. The key observation is that this integral can be split into two parts: a… (More)

- Zhi Liang, Zydrunas Gimbutas, Leslie Greengard, Jingfang Huang, Shidong Jiang
- J. Comput. Physics
- 2013

A second kind integral equation formulation is presented for the Dirichlet problem for the Laplace equation in two dimensions, with the boundary conditions specified on a collection of open curves. The performance of the obtained apparatus is illustrated with several numerical examples. The formulation is a simplification of the equation previously… (More)

A detailed analysis is presented of all pseudo-differential operators of orders up to 2 encountered in classical potential theory in two dimensions. Each of the operators under investigation turns out to be a sum of one or more of standard operators (second derivative, derivative of the Hilbert transform, etc.), and an integral operator with smooth kernel.… (More)

- Yanming Wang, Shidong Jiang, +6 authors Yong Huang
- Chemical communications
- 2013

An anisotropic biocompatible composite PCL-PTFE film was used to guide smooth muscle cell outgrowth along defined directions.

- Shidong Jiang, Shravan K. Veerapaneni, Leslie Greengard
- SIAM J. Scientific Computing
- 2012

We present an integral equation formulation for the unsteady Stokes equations in two dimensions. This problem is of interest in its own right, as a model for slow viscous flow, but perhaps more importantly, as an ingredient in the solution of the full, incompressible Navier-Stokes equations. Using the unsteady Green's function, the velocity evolves… (More)

- Shidong Jiang, Leslie Greengard, Weizhu Bao
- SIAM J. Scientific Computing
- 2014

We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel U (x) and a density function ρ(x) = |ψ(x)| 2 for some complex-valued wave function ψ(x), permitting the formal use of Fourier methods. These are… (More)

We present a fast algorithm for the evaluation of exact nonreflecting boundary conditions for the time-dependent Schrödinger equation in two dimensions on the unit circle. After separation of variables, the exact outgoing condition for each Fourier mode contains a nonlocal term which is a convolution integral in time. The kernel for that convolution is the… (More)

- Shidong Jiang, Zhi Liang, Jingfang Huang
- Math. Comput.
- 2013

- Matthew F. Causley, Peter G. Petropoulos, Shidong Jiang
- J. Comput. Physics
- 2011