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On the evaluation of electrostatic energy of volume charge distributions and the role of the Coulomb singularity

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  • Stén, Johan C.-E.
  • Essén, Hanno

Abstract

Methods for evaluating electrostatic interaction energy of volume distributions of charge of different shapes and densities are studied. In our numerical method, a cubic integration volume is divided into smaller sub-cubes, whereupon the pertinent double volume integral is turned into a six-fold sum from which all self-interaction terms exhibiting the Coulomb singularity are duly extracted. More precision is gained by optimising the values of the partial integrals corresponding to the nearest interacting sub-cubes obtained by different discretisation of a cube. Further insight is obtained by modelling a sphere, a cylinder and a cube with cubical elements, for which analytical results are available. We also consider spheres with different radially dependent charge density functions, whose interaction energy is known exactly.

Suggested Citation

  • Stén, Johan C.-E. & Essén, Hanno, 2023. "On the evaluation of electrostatic energy of volume charge distributions and the role of the Coulomb singularity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 987-996.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:987-996
    DOI: 10.1016/j.matcom.2022.10.035
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