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Title: Optimized Algorithm for Collision Probability Calculations in Cubic Geometry

Abstract

An optimized algorithm for implementing a recently developed method of computing collision probabilities (CPs) in three dimensions is reported in this work for the case of a homogeneous cube. Use is made of the geometrical regularity of the domain to rewrite, in a very compact way, the approximate formulas for calculating CPs in general three-dimensional geometry that were derived in a previous work by the author. The ensuing gain in computation time is found to be substantial: While the computation time associated with the general formulas increases as K{sup 2}, where K is the number of elements used in the calculation, that of the specific formulas increases only linearly with K. Accurate numerical results are given for several test cases, and an extension of the algorithm for computing the self-collision probability for a hexahedron is reported at the end of the work.

Authors:
 [1]
  1. HSH Scientific Computing (Brazil)
Publication Date:
OSTI Identifier:
20804935
Resource Type:
Journal Article
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 147; Journal Issue: 2; Other Information: Copyright (c) 2006 American Nuclear Society (ANS), United States, All rights reserved. http://epubs.ans.org/; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0029-5639
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; COLLISIONS; COMPUTER CALCULATIONS; GEOMETRY; PROBABILITY; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Garcia, R D.M. Optimized Algorithm for Collision Probability Calculations in Cubic Geometry. United States: N. p., 2004. Web.
Garcia, R D.M. Optimized Algorithm for Collision Probability Calculations in Cubic Geometry. United States.
Garcia, R D.M. 2004. "Optimized Algorithm for Collision Probability Calculations in Cubic Geometry". United States.
@article{osti_20804935,
title = {Optimized Algorithm for Collision Probability Calculations in Cubic Geometry},
author = {Garcia, R D.M.},
abstractNote = {An optimized algorithm for implementing a recently developed method of computing collision probabilities (CPs) in three dimensions is reported in this work for the case of a homogeneous cube. Use is made of the geometrical regularity of the domain to rewrite, in a very compact way, the approximate formulas for calculating CPs in general three-dimensional geometry that were derived in a previous work by the author. The ensuing gain in computation time is found to be substantial: While the computation time associated with the general formulas increases as K{sup 2}, where K is the number of elements used in the calculation, that of the specific formulas increases only linearly with K. Accurate numerical results are given for several test cases, and an extension of the algorithm for computing the self-collision probability for a hexahedron is reported at the end of the work.},
doi = {},
url = {https://www.osti.gov/biblio/20804935}, journal = {Nuclear Science and Engineering},
issn = {0029-5639},
number = 2,
volume = 147,
place = {United States},
year = {Tue Jun 15 00:00:00 EDT 2004},
month = {Tue Jun 15 00:00:00 EDT 2004}
}