Developing a simple program to solve the diffusion equation

[Morbius]

See? That wasn't so bad right? You see, the seminal work makes use of the stochastic method, via the Metropolis acceptance function, of sampling an ensemble of configurations. This is how everyone else in the world knows the term "Monte Carlo".

So I have Metroplis and Teller on my side here - are you so arrogant as to say them wrong too?

quetzal,

NOT AT ALL You certainly DO NOT have Metropolis and Teller on your side.

What you have obfuscated here is what type of "Monte Carlo" technique one is talking about.

We are not talking about Monte Carlo methods in general. We are talking about a particular application
of Monte Carlo to solving the neutron transport / diffusion equations and your ERRONEOUS response
that that particular application parallelized trivially.

One can use a "Monte Carlo" technique to do integrals by sampling an integrand. That type of
"Monte Carlo" does parallelize trivially because all one has to do is sample from a function; and all
those calculations are independent, and hence parallelize trivially.

However, your statement in Post #6 to a previous poster was:

the real power of parallelization comes with higher dimensional diffusion. in which case, a more efficient way of calculating diffusion is through Monte Carlo integration (since the error scales as 1/sqrt(N) rather than with the dimensionality), which indeed parallelizes trivially. for a 1D case i can't see any reason why you would parallelize.

In the above, you are advocating using a Monte Carlo technique to solve the neutron diffusion equation.

It's the Monte Carlo technique for solving neutron transport or neutron diffusion that does not
parallelize trivially; for the reasons I cited at length above.

In Post #19, you chastise me for limiting my discussion to the neutron transport problem:

It sounds like you are focusing on a very particular type of problem - neutron diffusion in some fissile material. However, keep in mind that if one was, for example, solving for a statistical mechanical observable, then doing the trivial parallelization where each processor handles a separate (indepedent) sample is appropriate

For Heavens sake, of course I was "focussing a very partucular type of problem - neutron diffusion";
because that's what we were talking about back in your Post #6.

I agree that one can trivially parallelize a Monte Carlo technique for sampling a statistical mechanical
distribution - but that doesn't solve the neutron diffusion problem - which is what you claimed could
be done trivially in Post #6.

So - it's a "Catch-22". Either the "Monte Carlo" method you recommended in Post #6 was a trivially
parallelized statistical mechanical sampling method; in which case you are WRONG in Post #6
because statistical mechanical sampling doesn't solve the neutron diffusion equation.

Or, in case you meant "Monte Carlo" to mean a method of solving the integral-differential neutron
transport and / or diffusion equations; in which case you are WRONG again because such
algorithms don't trivially parallelize.

Either way - you have OBFUSCATED what a "Monte Carlo" technique is, and how it is used.

Dr. Gregory Greenman
Physicist