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</o:shapelayout></xml><![endif]--></head><body lang=DE link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span lang=EN-US>Hello everybody,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>in my recent research on parallelization of a 2D unstructured flow model code I came upon a question on domain decomposition techniques in “grids”. Maybe someone knows of any previous results on this?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Typically, when doing large simulations with many unknowns, the problem is distributed to many computer nodes and solved in parallel by some iterative method. Many of these iterative methods boil down to a large number of distributed matrix-vector multiplications (in the order of the number of iterations). This means there are many synchronization points in the algorithms, which makes them tightly coupled. This has been found to work well on clusters with fast networks.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Now my question:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>What if there is a small number of very powerful nodes (say less than 10), which are connected by a slow network, e.g. several computer clusters connected over the internet (some people call this “grid computing”). I expect that the traditional iterative methods will not be as efficient here (any references?).<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>My guess is that a solution method with fewer synchronization points will work better, even though that method may be computationally more expensive than traditional methods. An example would be a domain composition approach with direct solution of the Schur complement on the interface. This requires that the interface size has to be small compared to the subdomain size. As this algorithm basically works in three decoupled phases (solve the subdomains for several right hand sides, assemble and solve the Schur complement system, correct the subdomain results) it should be suited well, but I have no idea how to test or otherwise prove it. Has anybody made any thoughts on this before, possibly dating back to the 80ies and 90ies, where slow networks were more common?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Best regards<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>Stefan<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p></div></body></html>