21 citations · 45 across the 4 of their papers we have counts for
5 papers
A high order multigrid-preconditioned immersed interface solver for the Poisson equation with boundary and interface conditions
James Gabbard, Andrea Paris, Wim M. van Rees
This work presents a multigrid preconditioned high order immersed finite difference solver to accurately and efficiently solve the Poisson equation on complex 2D and 3D domains. Th…
Lattice Green's Functions for High Order Finite Difference Stencils
James Gabbard, Wim M. van Rees
Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that…
A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations
Xinjie Ji, James Gabbard, Wim M. van Rees
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body prob…
An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies
James Gabbard, Thomas Gillis, Philippe Chatelain +1
We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, no…
Intransitive Dice
Brian Conrey, James Gabbard, Katie Grant +2
We consider -sided dice whose face values lie between and and whose faces sum to . For two dice and , define if it is more likely for to…