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RANGE DECOMPOSITION WITH ADAPTIVE MESH REFINEMENT FOR PETA AND EXASCALE COMPUTING

David Appelhans

Applied Mathematics,Ìý

Date and time:Ìý

Tuesday, November 19, 2013 - 10:00am

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ECCR 257

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Range decomposition combined with adaptive mesh refinement reduces many 1-to-1 communications in exchange for a single all-to-all communication, albeit at the cost of more local computation. The target application is peta- and exascale machines where traditional parallel numerical PDE communication patterns stifle scalability. Range decomposition uses a partition of unity to assign each processor a forcing function that is zero outside of the processor's region of interest. After each processor solves a decomposed system with its own version of the right-hand side, the sum of such solutions from each processors represents the solution to the global problem in that region of interest. The computational advantages of this approach are that adaptive mesh refinement achieves minimal error in each processors region of responsibility and the decomposed problems can be solved in parallel without any communication until the solutions need to be summed. This offers potential advantages in the paradigm of expensive communication but very cheap computation.