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An Adaptive Fast Algorithm for Periodic Coulomb Lattice Sums in Arbitrary Unit Cells
Xuanzhao Gao, Leslie Greengard, Shidong Jiang
We present a fast algorithm for evaluating conditionally convergent Coulomb lattice sums, governed by the Laplace equation with periodic boundary conditions on arbitrary unit cells…
A fast sum-of-Gaussians algorithm for the high-dimensional fractional Fokker-Planck equation
Shidong Jiang, Dong Wang, Qi Zhou
We present a fast, high-order algorithm for the free-space fractional Fokker-Planck equation (FFPE) in arbitrary spatial dimension. Its fundamental solution, corresponding to a Dir…
Fast Ewald Summation with Prolates for Charged Systems in the NPT Ensemble
Jiuyang Liang, Libin Lu, Shidong Jiang
We present an NPT extension of Ewald summation with prolates (ESP), a spectrally accurate and scalable particle-mesh method for molecular dynamics simulations of periodic, charged…
Space-time adaptive methods for parabolic evolution equations
Jun Wang, Jie Su, Leslie Greengard +2
We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equation…
Fast summation of Stokes potentials using a new kernel-splitting in the DMK framework
Ludvig af Klinteberg, Leslie Greengard, Shidong Jiang +1
Classical Ewald methods for Coulomb and Stokes interactions rely on ``kernel-splitting," using decompositions based on Gaussians to divide the resulting potential into a near field…
Accelerating Molecular Dynamics Simulations using Fast Ewald Summation with Prolates
Jiuyang Liang, Libin Lu, Alex Barnett +2
The evaluation of long-range Coulomb interactions is a significant cost in molecular dynamics (MD), even when using Particle Mesh Ewald (PME) or Particle-Particle-Particle-Mesh (PP…
A fast spectral sum-of-Gaussians method for electrostatic summation in quasi-2D systems
Xuanzhao Gao, Shidong Jiang, Jiuyang Liang +2
The quasi-2D electrostatic systems, characterized by periodicity in two dimensions with a free third dimension, have garnered significant interest in many fields. We apply the sum-…