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5 papers · 2 filters
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…
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…
Hybrid asymptotic/numerical methods for the evaluation of layer heat potentials in two dimensions
Jun Wang, Leslie Greengard
We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that s…
Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall
Wen Yan, Michael Shelley
It is well-known that by placing judiciously chosen image point forces and doublets to the Stokeslet above a flat wall, the no-slip boundary condition can be conveniently imposed o…
A simple solver for the fractional Laplacian in multiple dimensions
Victor Minden, Lexing Ying
We present a simple discretization scheme for the hypersingular integral representation of the fractional Laplace operator and solver for the corresponding fractional Laplacian pro…