STUDY OF PARALLEL MONTE CARLO SIMULATION TECHNIQUES OBJECTIVES PROJECT FRAMEWORK FUTURE PLAN To solve practical application problems using MONTE CARLO simulation . To provide a range of possible results in cases when it is impossible to arithmetically calculate just one solution. Judging the solution obtained upon parameter of accuracy and time taken for computation To perform various processing techniques over the practical application problem and composing the results with serial and benchmarked programs. To apply Monte Carlo techniques over these application problems to reduce the average computation time. Monte Carlo techniques Acceptance-Rejection techniques Likelihood weighing Localization technique Game tree search Graphical analysis and interpretation of each technique If time permits, then we will try to apply MPI techniques also. Applications used Mathematics Estimation of ∏(pi) value. Multi-dimensional integral estimation (∫∫∫..dxdydz) Curve tracing. Random walks. Financial planning Black scholes option valuation. Autonomous robotics Maze solver. Games a) Game of Tantrix. PURPOSE Monte Carlo exploits the power of randomness and we can sometime converge very quickly. problem solved using parallelization of Monte Carlo simulation increases accuracy to a great degree, as we can combine results obtained from multiple nodes and choose the solution value PROGRESS PLATFORM Serial c code for ∏ ,multi-dimensional integral estimation. Optimizations No of samples /experiment=108. Time of execution a)Basic code 2-3 minutes. b)Optimized(parallelized file i/o)3-5 sec Accuracy=3.14156 Precision(std. dev.)=0.0000164 Linux GCC compiler I/O library parallelization support Open MP P threads Multi core system GUIDE: Dr. S. R. SATHE DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING VISVESVARAYA NATIONAL INSTITUTE OF TECHNOLOGY, NAGPUR PRAKHAR SINGH (BT09ECE055) SHEETAL BORKAR (BT09ECE003) NIPUN AGRAWAL (BT09ECE051) DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING