[Beowulf] core diameter is not really a limit

[Douglas Eadline]

>
> I've remembered to check the cluster monkey feed, and
> seen
> http://www.clustermonkey.net/Opinions/the-core-diameter.html
>
> The assumption made here is that every node needs to be able
> to talk to every other node within the assembly.

Good point, you are correct. I was using the assumption
of full bi-sectional bandwidth/latency. On thinking about it,
this feature has always a design goal for most HPC systems.
Obviously, as we reach more limits, these assumptions will need
to be reconsidered. I'll put on note on the article.

--
Doug

>
> I think there is a large class of problems where direct
> long-distance communication is not necessary. E.g. if
> you're simulating a 3d system with local interactions,
> where long-range interactions emerge by propagating
> across computational volume in a wave-like fashion
> your relativistic limits are only limited to the
> geometry of the node and its direct neighbors.
> Further nodes will be reached at next refresh,
> assuming a relativistic cut-through fabric present
> in each node, or computation where information is
> passed implicitly by change of state within
> adjacent node.
>
> Such problem classes on such node geometries have
> no intrinsic size limit to the number of nodes,
> since communication is always limited to overlapping
> light cones of subsystems.
>
> Obviously smaller nodes means higher refresh rate,
> so the system asymptotically converges towards a
> cellular automaton model, with ~nm sized cells.
> It is provably impossible to do classical computing
> faster than this. The time domain is rather ~ps
> than ~us, and maximally possible refresh rate is
> some ~100 PHz for ~nm sized cells.
>
> Obviously, ability to cool such volumes will limit
> such high refresh rates, even if the computation is
> reversible (which probably means it has to be
> adiabatic, and hence also intrinsically slower).
> It also seems that spintronics is not extremely
> fast, and spintronics/photonics/plasmonics is
> likely to be the modes of computation and
> communication used in such future systems.
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--
Doug

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