14 citations · 85 across the 27 of their papers we have counts for
21 papers · 1 filter
Compressing the memory variables in constant-Q viscoelastic wave propagation via an improved sum-of-exponentials approximation
Xu Guo, Shidong Jiang, Yunfeng Xiong +1
Earth introduces strong attenuation and dispersion to propagating waves. The time-fractional wave equation with very small fractional exponent, based on Kjartansson's constant-Q th…
A Dual-space Multilevel Kernel-splitting Framework for Discrete and Continuous Convolution
Shidong Jiang, Leslie Greengard
We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the…
A new version of the adaptive fast Gauss transform for discrete and continuous sources
Leslie Greengard, Shidong Jiang, Manas Rachh +1
We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave…
An accurate and efficient scheme for function extensions on smooth domains
Charles L. Epstein, Fredrik Fryklund, Shidong Jiang
A new scheme is proposed to construct an n-times differentiable function extension of an n-times differentiable function defined on a smooth domain D in d-dimensions. The extension…
Periodic Fast Multipole Method
Ruqi Pei, Travis Askham, Leslie Greengard +1
A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmh…
Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries
Johan Helsing, Shidong Jiang
A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The…
On time-domain NRBC for Maxwell's equations and its application in accurate simulation of electromagnetic invisibility cloaks
Bo Wang, Zhiguo Yang, Lilian Wang +1
In this paper, we present analytic formulas of the temporal convolution kernel functions involved in the time-domain non-reflecting boundary condition (NRBC) for the electromagneti…
Fast integral equation methods for linear and semilinear heat equations in moving domains
Jun Wang, Leslie Greengard, Shidong Jiang +1
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant ad…
A fast Gauss transform in one dimension using sum-of-exponentials approximations
Shidong Jiang
We present a fast Gauss transform in one dimension using nearly optimal sum-of-exponentials approximations of the Gaussian kernel. For up to about ten-digit accuracy, the approxima…
Evaluation of Abramowitz functions in the right half of the complex plane
Zydrunas Gimbutas, Shidong Jiang, Li-Shi Luo
A numerical scheme is developed for the evaluation of Abramowitz functions in the right half of the complex plane. For , the scheme utilizes series expan…
An Integral Equation Method for the Cahn-Hilliard Equation in the Wetting Problem
Xiaoyu Wei, Shidong Jiang, Andreas Kloeckner +1
We present an integral equation approach to solving the Cahn-Hilliard equation equipped with boundary conditions that model solid surfaces with prescribed Young's angles. The discr…
Explicit unconditionally stable methods for the heat equation via potential theory
Alex H. Barnett, Charles L. Epstein, Leslie Greengard +2
We study the stability properties of explicit marching schemes for second-kind Volterra integral equations that arise when solving boundary value problems for the heat equation by…
On the accurate evaluation of unsteady Stokes layer potentials in moving two-dimensional geometries
Leslie Greengard, Shidong Jiang, Jun Wang
Two fundamental difficulties are encountered in the numerical evaluation of time-dependent layer potentials. One is the quadratic cost of history dependence, which has been success…
Multiscale Hydrophobic Lipid Dynamics Simulated by Efficient Integral Equation Methods
Szu-Pei P. Fu, Rolf J. Ryham, Andreas Klöckner +3
In this paper, we first develop a mathematical model for long-range, hydrophobic attraction between amphiphilic particles. The non-pairwise interactions follow from the first varia…
A new mixed potential representation for the equations of unsteady, incompressible flow
Leslie Greengard, Shidong Jiang
We present a new integral representation for the unsteady, incompressible Stokes or Navier-Stokes equations, based on a linear combination of heat and harmonic potentials. For velo…
Second Kind Integral Equation Formulation for the Mode Calculation of Optical Waveguides
Jun Lai, Shidong Jiang
We present a second kind integral equation (SKIE) formulation for calculating the electromagnetic modes of optical waveguides, where the unknowns are only on material interfaces. T…
Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations
Shidong Jiang, Jiwei Zhang, Qian Zhang +1
We present an efficient algorithm for the evaluation of the Caputo fractional derivative of order , which can be expressed as a convolution of …
Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT
Weizhu Bao, Shidong Jiang, Qinglin Tang +1
We present efficient and accurate numerical methods for computing the ground state and dynamics of the nonlinear Schrödinger equation (NLSE) with nonlocal interactions based on a f…
Fast and Accurate Evaluation of Nonlocal Coulomb and Dipole-Dipole Interactions via the Nonuniform FFT
Shidong Jiang, Leslie Greengard, Weizhu Bao
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 con…
Efficient sum-of-exponentials approximations for the heat kernel and their applications
Shidong Jiang, Leslie Greengard, Shaobo Wang
In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel…
The solution of the scalar wave equation in the exterior of a sphere
Leslie Greengard, Thomas Hagstrom, Shidong Jiang
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our form…