On Practical Modifications to the Barnes-Hut Multipole Method for Electromagnetic Scattering

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This paper presents a simple methodology for quickly predicting and optimizing computer run time for the Barnes-Hut multipole method for boundary element electromagnetic scattering problems. The methodology is easily extended to other multipole methods (e.g., Greengard-Rokhlin) and to other physics. The idea is to simply COZM t the number of element-cell interactions, number of direct element- element interactions, and the number of cell multipole expansion creations (each expansion weighted by the number of elements in the cell), and then finally combine these three results with the associated unit costs to obtain the total computer :un-time to perform a single matrix-vector ... continued below

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Driessen, B.J. & Kotulski, J.D. October 27, 1998.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Laboratories, Albuquerque, NM, and Livermore, CA
    Place of Publication: Albuquerque, New Mexico

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Description

This paper presents a simple methodology for quickly predicting and optimizing computer run time for the Barnes-Hut multipole method for boundary element electromagnetic scattering problems. The methodology is easily extended to other multipole methods (e.g., Greengard-Rokhlin) and to other physics. The idea is to simply COZM t the number of element-cell interactions, number of direct element- element interactions, and the number of cell multipole expansion creations (each expansion weighted by the number of elements in the cell), and then finally combine these three results with the associated unit costs to obtain the total computer :un-time to perform a single matrix-vector multiply. By counting operations instead of actually performing them, the time to predict the computer run time is orders of magnitude smaller than the time to actually perform the associated calculations. This allows for very quick optimization of parameters, such as the maximum number of elements in a final generation cell of the tree. Numerical examples are presented herein in which the rate of return (time saved over time spent finding optimal parameter values) is significantly more than two orders of magnitude.

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  • Boundary Element Technology XIII, 1999; Las Vegas, NV; 06/08-10/1999

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  • Other: DE00001559
  • Report No.: SAND98-2437C
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 1559
  • Archival Resource Key: ark:/67531/metadc622604

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  • October 27, 1998

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  • June 16, 2015, 7:43 a.m.

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  • Nov. 30, 2016, 2:13 p.m.

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Driessen, B.J. & Kotulski, J.D. On Practical Modifications to the Barnes-Hut Multipole Method for Electromagnetic Scattering, article, October 27, 1998; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc622604/: accessed December 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.