or in the Dirac formalism:
\langle \psi | \hat{\Omega} | \psi \rangle = \langle \psi | \omega | \psi \rangle = w \langle \psi | \psi \rangle = w
(by orthogonality of states)
but since \hat{\Omega} is Hermitian, this is equal to:
(\langle \psi | \hat{\Omega}^\dagger) | \psi \rangle = \langle...
Morbius,
I will go slow here, so that even a loud-mouth like you can understand it; I will hold your hand and together you will get through this.
Please read the following seminal paper:
JCP 21(6):1087-1092 (1953)
Equation of State Calculations by Fast Computing Machines
Nicholas...
I think that it is you who is being the STUPID one here. Open a book on Monte Carlo methods and you will see that it is for solving INTEGRALS! Guess what? That equation you have been solving all of these years via Monte Carlo is an INTEGRAL equation - did you realize that? We solve statmech...
i recognize this as obvious given that this is still the #1 machine...my point was that the WAY this was accomplished was through power/cost, etc. which you NOW also mention.
My point is this: consider this from the perspective of a teragrid user with a fixed allocation of SUs. I have access...
i think that if you stop and listen to what i am saying you will realize that what i am saying is correct.
consider, for example, a periodic system of N gas molecules contained in a specific volume at a specific temperature. Let's say we have 1000 processors available on some system. If we...
That is up to you: you obviously did not know that the goal was increased ratio of performance per watt and performance per m^2, as I pointed out (is IBM lying in their white paper which I posted the link to?)...that is how/why the #1 slot was attained since you can stuff 1024 nodes in a single...
Morbius,
I do not know anything about classified systems - I would never have guessed that such large systems would even be classified, since the current top #1 BG at LLNL is certainly not classified (actually, #1, #3 and #6, all NNSA are online at top500.org).
Q
Morbius,
Yes, I am familiar with domain decomposition methods - infact I utilize decompositions in solving for the many-bodied polarization states (iterative gauss-seidel solver with preconditioning) of my MC code.
It sounds like you are focusing on a very particular type of problem -...
the first BG/P is not expected to be operational until Spring 2008 (and only 111 TFlops at that, petascale systems will follow later) - Ranger will be up and in use sometime in December, making it #1 at least for a little while :)
Q
P.S. - i do not work for TACC, Ionly like their systems :)
I kindly disagree. If you read the BG white papers those are EXACTLY the reasons that they have used to achieve the high parallelism.
At 440 Mhz with 512 MB memory (BG/L), the motive was certainly NOT performance: it was to achieve a low power consumption footprint thus allowing higher levels...
Morbius,
you and i have something in common then: I also have implemented a Monte Carlo code in order to avoid doing many-body molecular dynamics with a potential energy function whose derivative is numerically ill-behaved! (Although, I do not get away completely unscathed since the systems...
Dr. Greenman,
ok, so you are saying that for this particular problem there is a large scaling prefactor infront of the 1/sqrt(N), and so this currently makes non-stochastic methods desirable. (However, since you say that you are developing a stochastic code I take this to mean that the high...
so what does one typically use as a scattering function? (im assuming that we're talking about solving the Boltzmann-Poisson eqn for neutron diffusion?)