Monte Carlo Method on Parallel Computing. Jongsoon Kim

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1 Monte Carlo Method on Parallel Computing Jongsoon Kim

2 Introduction Monte Carlo methods Utilize random numbers to perform a statistical simulation of a physical problem Extremely time-consuming Inherently parallel Each particle history simulate independently Recent increase in accessibility of advanced computer * Parallel Monte Carlo methods have been interested

3 Multiple instruction multiple data (MIMD) Several processors operate in parallel. Each processor has its own instruction stream and its own data stream. They operate asynchronously. Depending on memory structure, Distributed-memory parallel processors Shared-memory parallel processors

4 Distributed memory parallel processors P M P M P M P M Regular array of large number of processors They have their own private memory Interconnected by communication link Communicate by passing message along them

5 Shared memory parallel processors Global Memory Shared bus P P P P Utilize a shared bus to connect processors with memory Some use high-speed bus Most successful commercial parallel processors

6 Limiting factors of parallel algorithm Balanced workload Obvious goal for efficient algorithm All processors should keep busying Communications Serious concern for distributed memory processors Relatively slow inter-processor communication Shared memory processor memory interface

7 Limiting factors of parallel algorithm (cont.) Synchronization Lead to inefficiencies Processors are waiting for one another Unavoidable

8 Monte Carlo method Radiation Transport Monte Carlo method A particle emitted from a source routine Transported through the medium interested Processed through whatever collisions or interactions As a history finish, result of simulation are accumulated (tallies) Simulation continues until the particle is terminated; absorbed, escape etc.

9 Monte Carlo on parallel architecture Monte Carlo method is inherently parallel Parallel algorithm can be developed with minimal change of conventional Monte Carlo Critical parts of parallel algorithm Sufficient memory Parallel random number generator Must provide uncorrelated random number

10 Domain decomposition scheme To reduce excessive memory demand Partitioning by geometry Assign specific zone to processors Partitioning by energy Assign specific energy group to processors Substantial saving in memory Increase inter-processor communications

11 Random number generator Most critical part of parallel Monte Carlo Should make sure statistical independence Two alternative approaches Parameterization Recursion Linear congruential generator, shift register generator, and lagged-fibonacci generators Splitting Long period is split into a number of substreams

12 Parallel Virtual Machine (PVM) Portable message passing programming system Link separate machines to create a virtual machine as a single manageable computing source

13 Massively Parallel Processors (MPP) IOP PE PE PE PE IOP MP IOP IOP

14 Massively Parallel Processors (MPP) (cont.) S Speedup is the ratio of the CPU time taken on a single processor to on a number of machines = T T 1 S N N Speedup achieves nearly linear performance

15 Schematic view of cluster system HDD 1GB SCSI-2 I/O Compute 1 Compute 2 Router 8x8 HS Link Compute 3 Ethernet PCI Entry Compute 4 SCSI-1 LAN Compute 6 Compute 5 HDD 2GB

16 Cluster system (cont.) Speedup Number of computing s Linear decrease of computing time with the number of computing s

17 Architecture of network of workstations Node 1 Node 2 Node 8 Node 3 PE PE Node Mb Fast Ethernet Node 4 Cach Bus Cach Memory Network Node 6 Node 5

18 Conclusion Monte Carlo methods are necessary tools in radiation dosimetry and shielding design Both parallel architecture (MPP and distributed workstation) are suitable and effective A mixture of PCs and workstations May more cheaper

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