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Title: The Robin Hood method - A novel numerical method for electrostatic problems based on a non-local charge transfer

Abstract

We introduce a novel numerical method, named the Robin Hood method, of solving electrostatic problems. The approach of the method is closest to the boundary element methods, although significant conceptual differences exist with respect to this class of methods. The method achieves equipotentiality of conducting surfaces by iterative non-local charge transfer. For each of the conducting surfaces, non-local charge transfers are performed between surface elements, which differ the most from the targeted equipotentiality of the surface. The method is tested against analytical solutions and its wide range of application is demonstrated. The method has appealing technical characteristics. For the problem with N surface elements, the computational complexity of the method essentially scales with N {sup {alpha}}, where {alpha} < 2, the required computer memory scales with N, while the error of the potential decreases exponentially with the number of iterations for many orders of magnitude of the error, without the presence of the Critical Slowing Down. The Robin Hood method could prove useful in other classical or even quantum problems. Some future development ideas for possible applications outside electrostatics are addressed.

Authors:
 [1];  [2];  [3]
  1. Theoretical Physics Division, Rudjer Boskovic Institute, Bijenicka Cesta 54, P.O. Box 180, HR-10002 Zagreb (Croatia). E-mail: plazic@thphys.irb.hr
  2. Theoretical Physics Division, Rudjer Boskovic Institute, Bijenicka Cesta 54, P.O. Box 180, HR-10002 Zagreb (Croatia). E-mail: shrvoje@thphys.irb.hr
  3. Theoretical Physics Division, Rudjer Boskovic Institute, Bijenicka Cesta 54, P.O. Box 180, HR-10002 Zagreb (Croatia). E-mail: ahrvoje@thphys.irb.hr
Publication Date:
OSTI Identifier:
20767034
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 213; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2005.08.006; PII: S0021-9991(05)00371-2; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; BOUNDARY ELEMENT METHOD; ELECTROSTATICS; ERRORS; ITERATIVE METHODS; SLOWING-DOWN; SURFACES

Citation Formats

Lazic, Predrag, Stefancic, Hrvoje, and Abraham, Hrvoje. The Robin Hood method - A novel numerical method for electrostatic problems based on a non-local charge transfer. United States: N. p., 2006. Web. doi:10.1016/j.jcp.2005.08.006.
Lazic, Predrag, Stefancic, Hrvoje, & Abraham, Hrvoje. The Robin Hood method - A novel numerical method for electrostatic problems based on a non-local charge transfer. United States. doi:10.1016/j.jcp.2005.08.006.
Lazic, Predrag, Stefancic, Hrvoje, and Abraham, Hrvoje. Mon . "The Robin Hood method - A novel numerical method for electrostatic problems based on a non-local charge transfer". United States. doi:10.1016/j.jcp.2005.08.006.
@article{osti_20767034,
title = {The Robin Hood method - A novel numerical method for electrostatic problems based on a non-local charge transfer},
author = {Lazic, Predrag and Stefancic, Hrvoje and Abraham, Hrvoje},
abstractNote = {We introduce a novel numerical method, named the Robin Hood method, of solving electrostatic problems. The approach of the method is closest to the boundary element methods, although significant conceptual differences exist with respect to this class of methods. The method achieves equipotentiality of conducting surfaces by iterative non-local charge transfer. For each of the conducting surfaces, non-local charge transfers are performed between surface elements, which differ the most from the targeted equipotentiality of the surface. The method is tested against analytical solutions and its wide range of application is demonstrated. The method has appealing technical characteristics. For the problem with N surface elements, the computational complexity of the method essentially scales with N {sup {alpha}}, where {alpha} < 2, the required computer memory scales with N, while the error of the potential decreases exponentially with the number of iterations for many orders of magnitude of the error, without the presence of the Critical Slowing Down. The Robin Hood method could prove useful in other classical or even quantum problems. Some future development ideas for possible applications outside electrostatics are addressed.},
doi = {10.1016/j.jcp.2005.08.006},
journal = {Journal of Computational Physics},
number = 1,
volume = 213,
place = {United States},
year = {Mon Mar 20 00:00:00 EST 2006},
month = {Mon Mar 20 00:00:00 EST 2006}
}