High performance computing using threads and mpi for massively parallel processing
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High performance computing using threads and mpi for massively parallel processing

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High performance computing using threads and mpi for massively parallel processing High performance computing using threads and mpi for massively parallel processing Presentation Transcript

  • Monte-Carlo Simulations on n-dimensional hyper-spheres Lalit Azad 12/08/2008
  • Problem description• Applying monte-carlo simulations to n- dimensional hyper-spheres.• Checking the performances against threads and MPI instructions.
  • Approach• The first program takes number of dimensions and number of points as command line arguments.• The outputs are saved into 2 files. One having execution time and other having simulation results.• In second part, threading is used to monitor the increase in performance.• In third part, MPI instructions are used for further parallel processing.
  • Simulation results• ndim:2 Observed_value_PI:3.141588 percentage_error:0.000369• ndim:3 Observed_value_PI:3.142579 percentage_error:-0.031150• ndim:4 Observed_value_PI:3.141115 percentage_error:0.030892• ndim:5 Observed_value_PI:3.142416 percentage_error:-0.051931• ndim:6 Observed_value_PI:3.14325 percentage_error:-0.157805• ndim:7 Observed_value_PI:3.139468 percentage_error:0.203435•  ndim:8 Observed_value_PI:3.140882 percentage_error:0.091410• ndim:9 Observed_value_PI:3.141970 percentage_error:-0.047180• ndim:10 Observed_value_PI:3.139775 percentage_error:0.290059
  • Performance graph of normal execution
  • Effect of threading on performance
  • Effect of threading on increasing dimensions
  • Effect of MPI on monte-carlo simulations
  • Effect of MPI on increasing dimensions
  • Conclusions• As number of dimensions increase , error in calculation increases.• The time required to compute the value increases.• Threading has a performance scaling w.r.t normal single threaded execution by a factor of 13• MPI parallelizes the execution and a 18 times faster performance is seen.