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Berkeley COMPSCI C267 - Homework

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BioI am currently an senior applied mathematics undergraduate at UC Merced, working withProfessor Mayya Tokman on modeling heat and fluid flow in a rocket stove. My currentinterests include numerical analysisClass GoalObtain some familiarity with programming parallel applications.The ProblemWeather forecasting is an important problem with obvious benefits. It also poses severaldifficulties which make it a rather computationally intensive problem to undertake. Cur-rent models simply paramaterize certain effects, as opposed to outright simulation of theunderlying phenomena, the most important of which is the convective transport of moisturefrom low to high altitudes; however, models with a more refined resolution will operate ona scale capable of handling these effects more satisfactoraly. Another serious chokingpointis the Courant-Friedrichs-Levy (CFL) condition, which requires that size of the temporaldiscretization march in line with the size of the spatial discretization.The applicationfvCAM, or the finite volume version of the Community Atmospheric Model, is a parallelapplication which seeks to model weather for climate change predictions as well as weatherforecasting. In order to create results which are useful for these applications a speedup ofabout 1000x over realtime is required. Figure 1 is a portion of a figure from [1].Figure 1: required sustained performance for a 1000x speedup over realtime at the givenresolution.1Figure 2: actual fvCAM performance at 50km resolution on different machinesYou can see that even getting to a 3km resolution is a tremendous undertaking since as ofNovember 2008 only the top 7 supercomputers in the world have a theoretical peak perfor-mance of greater than the 351.3 Tflops/s required; this is considering only peak performance,most scientific computing applications are able to only maintain about 10% of this number.Figure 2, also taken from [1], shows fvCAM performance at the 50km resolution. The 5thcolumn is particularly enlightening as it shows just how little of the peak performance isbeing wrought from these tremendous machines, and makes a case for how far away we arefrom obtaining a machine capable of operating at the super refined resolutions looked at infigure 1.fvCAM has also found some use as a benchmark for parallel machines[2]2References Shalf, John, and David Bailey. "Power Efficiency and the Top500." Top500.org. 14 Nov. 2006. <http://www.top500.org/static/lists/2006/11/bof/Top500PowerNov14.pdf>. Wehner, Michael, Leonid Oliker, and John Shalf. Towards Ultra-High Resolution Models of Climate and Weather. Tech. CRD/NERSC, Lawrence Berkeley National Laboratory, Berkeley. 31 Jan. 2009 <http://www.nersc.gov/projects/SDSA/reports/uploaded/IJHPCA06_CAM_final.pdf>.


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Berkeley COMPSCI C267 - Homework

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