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I've heard this in distributed computing circles. I'm no mechanical engineer. Can you tell why this is so? And are there any solutions to this?

P.S: can I use the Finite Element method as a solution?

Sreejith Ramakrishnan
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    There are multiple levels on which this can be answered, the most basic being that parallel processing is pretty much _always_ difficult when you're dealing with mutable data. — How detailed / fluid-dynamics–specific would you like it to be? – leftaroundabout Apr 14 '13 at 19:03
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    Basically the problem is that the finite elements influence each other. That is, the results of one have to wait for the other to finish and thus the process is inherently sequential. – Lars Kotthoff Apr 14 '13 at 19:13
  • Can it be accomplished using numerical techniques such as the Finite Element method to find approximate solutions? – Sreejith Ramakrishnan Apr 14 '13 at 19:21
  • leftaroundabout, I'm generally interested in knowing the limitations of distributed computing. But, specifically, I would love a mathematical proof. – Sreejith Ramakrishnan Apr 14 '13 at 19:50
  • Probably best moved to the math site, or better, numerical computing. –  Apr 14 '13 at 19:54
  • woodchips, If a move would yield better answers, I'd love that. Sorry if I posted this in the wrong place. – Sreejith Ramakrishnan Apr 14 '13 at 19:56
  • There's nothing deeply mathematical about it -- it's just the nature of the problem. If you model how something spreads across a number of finite elements, they are by definition not independent and the potential for parallelisation is limited. – Lars Kotthoff Apr 14 '13 at 19:57
  • http://scicomp.stackexchange.com/ –  Apr 14 '13 at 20:27
  • Moved: http://scicomp.stackexchange.com/questions/6852/why-are-computational-fluid-dynamics-problems-difficult-to-solve-in-parallel-pro – Sreejith Ramakrishnan Apr 14 '13 at 21:30
  • I've been told that the matching equation yields sometimes chaotic results -- called turbulence. I think this happens only if you enter a certain parameter area -- I think if you put too much pressure on such a system it becomes chaotic. –  Nov 03 '13 at 21:23

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There are some fundamental difficulties in getting a solution for the laplace equation, but it looks like you're asking specifically about extending cfd to parallel. In my experience (Master's in Aerospace, 2 years developing a plasma simulator), the fundamental concepts for solving CFD in parallel aren't too hard. Unfortunately, there's a never-ending stream of edge cases that will cause your solution to explode. We ran into sign errors at processor boundaries, variables that were uninitialized on certain processors under certain conditions, and a host of other "we should have thought of that"s. If by Difficult you mean Slow, then the issue is a little domain specific, but it boils down to 1) high communication overhead between processors and 2) short time steps for (explicit solutions) or high iteration counts per time step (implicit solutions) which are pretty hard to avoid when solving an elliptic PDE.

A lot of tools use finite element. It's pretty powerful/flexible.

Malcolm White
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