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The Monte Carlo method is seen to be particularly well suited for parallel computers. However the probabilistic nature of the method imposes certain limitations. Parameter studies, for example, prove to be impossible if the differences of the sampled responses are the same size as the uncertainties. Two methods for the calculation of small parameter variations are described, one based on correlation techniques and the other on differential operator sampling. Fundamental aspects of correlated sampling and differential operator procedures applied to integrals and systems of linear equations modelling Markov processes are investigated. Algorithms providing sensitivities (gradients, Jacobians) and perturbations estimates obtained by a single simulation experiment are described and a mathematical proof is provided showing that, for most conditions, a finite relative variance can be obtained for arbitrarily small parameter variations. In the case of differential operator sampling, the execution time can be substantially shortened if the score of the Jacobian is calculated by a vector processor.

Additional information

Authors: RIEF H, JRC Ispra (IT)
Bibliographic Reference: Paper presented: Mathematical Methods and Supercomputing in Nuclear Applications, Karlsruhe (DE), April 19-23, 1993
Availability: Available from (1) as Paper EN 37316 ORA
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