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

Johan C.-E. Stén and Hanno Essén

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 205, issue C, 987-996

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.

Keywords: Electrostatic interaction energy; Coulomb singularity; Volume charge density distribution; Cubical elements (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:205:y:2023:i:c:p:987-996

DOI: 10.1016/j.matcom.2022.10.035

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