A fast algorithm for particle simulations
Journal of Computational Physics
Fast, adaptive summation of point forces in the two-dimensional Poisson equation
Journal of Computational Physics
An implementation of the fast multipole method without multipoles
SIAM Journal on Scientific and Statistical Computing
A new diffusion procedure for vortex methods
Journal of Computational Physics
Modification of the carrier, Greengard, and Rokhlin FMM for independent source and target fields
Journal of Computational Physics
Yet another fast multipole method without multipoles—pseudoparticle multipole method
Journal of Computational Physics
Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry
Journal of Computational Physics
A Fast, Two-Dimensional Panel Method
SIAM Journal on Scientific Computing
Chaos and Fractals
A Fast Multipole Method for Higher Order Vortex Panels in Two Dimensions
SIAM Journal on Scientific Computing
An Object-Oriented Design for Two-Dimensional Vortex Particle Methods
ACM Transactions on Mathematical Software (TOMS)
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This paper details an efficient algorithm for particles undergoing random walks in the presence of complex, two-dimensional, solid boundaries. The scheme is developed for the simulation of vortex diffusion using the random vortex method. Both vortex blobs and sheets are handled. The relevant modifications for using the algorithm with the vorticity redistribution technique are also discussed. The algorithm is designed to be used in the framework of an existing fast multipole implementation. A measure for the geometric complexity of a body is introduced and the algorithm's efficiency is studied as various parameters are changed for bodies of varying complexity.