Automatic variance reduction for Monte Carlo simulations via the local importance function transform

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The author derives a transformed transport problem that can be solved theoretically by analog Monte Carlo with zero variance. However, the Monte Carlo simulation of this transformed problem cannot be implemented in practice, so he develops a method for approximating it. The approximation to the zero variance method consists of replacing the continuous adjoint transport solution in the transformed transport problem by a piecewise continuous approximation containing local biasing parameters obtained from a deterministic calculation. He uses the transport and collision processes of the transformed problem to bias distance-to-collision and selection of post-collision energy groups and trajectories in a traditional ... continued below

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110 p.

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Turner, S.A. February 1, 1996.

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Description

The author derives a transformed transport problem that can be solved theoretically by analog Monte Carlo with zero variance. However, the Monte Carlo simulation of this transformed problem cannot be implemented in practice, so he develops a method for approximating it. The approximation to the zero variance method consists of replacing the continuous adjoint transport solution in the transformed transport problem by a piecewise continuous approximation containing local biasing parameters obtained from a deterministic calculation. He uses the transport and collision processes of the transformed problem to bias distance-to-collision and selection of post-collision energy groups and trajectories in a traditional Monte Carlo simulation of ``real`` particles. He refers to the resulting variance reduction method as the Local Importance Function Transform (LIFI) method. He demonstrates the efficiency of the LIFT method for several 3-D, linearly anisotropic scattering, one-group, and multigroup problems. In these problems the LIFT method is shown to be more efficient than the AVATAR scheme, which is one of the best variance reduction techniques currently available in a state-of-the-art Monte Carlo code. For most of the problems considered, the LIFT method produces higher figures of merit than AVATAR, even when the LIFT method is used as a ``black box``. There are some problems that cause trouble for most variance reduction techniques, and the LIFT method is no exception. For example, the author demonstrates that problems with voids, or low density regions, can cause a reduction in the efficiency of the LIFT method. However, the LIFT method still performs better than survival biasing and AVATAR in these difficult cases.

Physical Description

110 p.

Notes

INIS; OSTI as DE96008821

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  • Other Information: DN: Thesis submitted to the Univ. of Michigan, Ann Arbor, MI (US); TH: Thesis (Ph.D.)

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  • Other: DE96008821
  • Report No.: LA--13119-T
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/212579 | External Link
  • Office of Scientific & Technical Information Report Number: 212579
  • Archival Resource Key: ark:/67531/metadc672612

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Creation Date

  • February 1, 1996

Added to The UNT Digital Library

  • June 29, 2015, 9:42 p.m.

Description Last Updated

  • Feb. 29, 2016, 8:29 p.m.

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Turner, S.A. Automatic variance reduction for Monte Carlo simulations via the local importance function transform, report, February 1, 1996; New Mexico. (digital.library.unt.edu/ark:/67531/metadc672612/: accessed November 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.