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

  • Authors:

  • Predrag Lazić;Hrvoje Štefančić;Hrvoje Abraham

  • Affiliations:

  • Theoretical Physics Division, Rudjer Bošković Institute, Bijenička Cesta 54, P.O. Box 180, HR-10002 Zagreb, Croatia;Theoretical Physics Division, Rudjer Bošković Institute, Bijenička Cesta 54, P.O. Box 180, HR-10002 Zagreb, Croatia;Theoretical Physics Division, Rudjer Bošković Institute, Bijenička Cesta 54, P.O. Box 180, HR-10002 Zagreb, Croatia

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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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^@a, where @a