Re: [Swarm-Support] 3d diffusion in abm

[Scott Christley]

Hi Rick,

It can depend upon whether the number of particles diffusing is small and thus 
stochastic effects are important, or whether the number of particles is large 
enough so you can use a continuous representation.  In the former case there 
isn't a whole lot that can be done, but there are advanced approximation 
algorithms like tau-leaping to gain speedup. In the latter case then a 
diffusion PDE can be written and numerical methods used to solve the PDE over 
the grid.  It is still expensive for 3D, but a coarser grid could possibly be 
used depending upon the fidelity needed, plus many numerical methods (e.g. 
Runge-Kutta) can be parallelized.  For example in one of my models [1] I use 
GPU to solve 3D diffusion and get 100x speedup over CPU code.

cheers
Scott

[1] http://www.biomedcentral.com/1752-0509/4/107

On Feb 20, 2012, at 5:04 PM, Rick Riolo wrote:

> hi,
> some colleagues have a question about doing (3d) diffusion in an abm; they 
> say:
> 
>   we have an ABM with lots of diffusion going on and now it is in 3-D!!
>   so, it runs VERY VERY SLOWLY...we know that we need to do
>   some kind of adaptive refinement, but that is a project in itself...
>   do you happen to know of someone who has had to deal with this
>   issue or who may know about how to implement that in ABM world?
> 
> Anyone have or know of ABMs with lots of diffusion, and thus
> use some special techniques to speed things up?
> 
> thanks for any pointers/refs/etc.
> -r
> 
> Rick Riolo                           address@hidden
> Center for the Study of Complex Systems (CSCS)
> 321a West Hall
> University of Michigan         Ann Arbor MI 48109-1107
> Phone: 734 763 3323                  Fax: 734 763 9267
> http://cscs.umich.edu/~rlr
> 
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