skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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}
}
  • In a simple tight-binding approach, we consider the role of charge transfer and entropy in the semiconductor-to-metal transition which may occur upon melting group IV elements and their isoelectronic III-V and II-VI compounds. In the liquid state, entropy is shown to destabilise the diamond structure in favor of a metallic simple cubic-like local order, while charge transfer tends to keep the semiconducting tetrahedral local order of the solid state. These results are consistent with neutron diffraction data.
  • A new coarse-mesh computational method for the numerical solution of heat conduction and fluid flow problems is formally developed and applied to sample problems. The method is based upon formal use of Green's functions, which are defined locally over subdomains of the original system under consideration. The formal development of the local Green's function method for the solution of heat conduction problems is presented and discussed. Numerical solutions of sample problems for one-dimensional heat conduction with constant thermal conductivity, one-dimensional heat conduction with temperature-dependent thermal conductivity, and two-dimensional heat conduction with constant thermal conductivity are given, and these results aremore » compared with results obtained using the finite difference and finite element methods. The formal development of the local Green's function method for the solution of fluid flow problems is then also presented and discussed; the numerical solution of a sample problem for simple one-dimensional incompressible fluid flow with viscous heating is also given.« less
  • Purpose: Sparse-view computed tomography (CT) reconstruction is an effective strategy to reduce the radiation dose delivered to patients. Due to its insufficiency of measurements, traditional non-local means (NLM) based reconstruction methods often lead to over-smoothness in image edges. To address this problem, an adaptive NLM reconstruction method based on rotational invariance (RIANLM) is proposed. Methods: The method consists of four steps: 1) Initializing parameters; 2) Algebraic reconstruction technique (ART) reconstruction using raw projection data; 3) Positivity constraint of the image reconstructed by ART; 4) Update reconstructed image by using RIANLM filtering. In RIANLM, a novel similarity metric that is rotationalmore » invariance is proposed and used to calculate the distance between two patches. In this way, any patch with similar structure but different orientation to the reference patch would win a relatively large weight to avoid over-smoothed image. Moreover, the parameter h in RIANLM which controls the decay of the weights is adaptive to avoid over-smoothness, while it in NLM is not adaptive during the whole reconstruction process. The proposed method is named as ART-RIANLM and validated on Shepp-Logan phantom and clinical projection data. Results: In our experiments, the searching neighborhood size is set to 15 by 15 and the similarity window is set to 3 by 3. For the simulated case with a resolution of 256 by 256 Shepp-Logan phantom, the ART-RIANLM produces higher SNR (35.38dB<24.00dB) and lower MAE (0.0006<0.0023) reconstructed image than ART-NLM. The visual inspection demonstrated that the proposed method could suppress artifacts or noises more effectively and preserve image edges better. Similar results were found for clinical data case. Conclusion: A novel ART-RIANLM method for sparse-view CT reconstruction is presented with superior image. Compared to the conventional ART-NLM method, the SNR and MAE from ART-RIANLM increases 47% and decreases 74%, respectively.« less
  • The interaction of light with metallic nanostructures is increasingly attracting interest because of numerous potential applications. Sub-wavelength metallic structures, when illuminated with a frequency close to the plasma frequency of the metal, present resonances that cause extreme local field enhancements. Exploiting the latter in applications of interest requires a detailed knowledge about the occurring fields which can actually not be obtained analytically. For the latter mentioned reason, numerical tools are thus an absolute necessity. The insight they provide is very often the only way to get a deep enough understanding of the very rich physics at play. For the numericalmore » modeling of light-structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models, e.g. Drude or Drude–Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equations coupled to Maxwell's equations. However, recent experiments have shown that the repulsive interaction between electrons inside the metal makes the response of metals intrinsically non-local and that this effect cannot generally be overlooked. Technological achievements have enabled the consideration of metallic structures in a regime where such non-localities have a significant influence on the structures' optical response. This leads to an additional, in general non-linear, system of partial differential equations which is, when coupled to Maxwell's equations, significantly more difficult to treat. Nevertheless, dealing with a linearized non-local dispersion model already opens the route to numerous practical applications of plasmonics. In this work, we present a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell's equations coupled to a linearized non-local dispersion model relevant to plasmonics. While the method is presented in the general 3D case, numerical results are given for 2D simulation settings.« less
  • In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to model in volumetric modeling techniques such as smoothed particle hydrodynamics (SPH). A new SPH method for diffusion type equations subject to Neumann or Robin boundary conditions is proposed. The new method is based on the continuum surface force model [1] and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method for geometrically complex boundaries.more » The paper discusses the details of the method and the criteria needed to apply the model. The model is used to simulate diffusion and surface reactions and its accuracy is demonstrated through test cases for boundary conditions describing different surface reactions.« less