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Electrostatic Force Computation with Boundary Element Methods

by R. Hiptmair and P. Panchal

(Report number 2021-21)

Abstract
Boundary element methods are a well-established technique for solving linear boundary value problems for electrostatic potentials. In this context we present a novel way to approximate the forces exerted by electrostatic fields on conducting objects. Like the standard post-processing technique employing surface integrals derived from the Maxwell stress tensor the new approach solely relies on surface integrals, but, compared to the former, offers better accuracy and faster convergence. The new formulas arise from the interpretation of forces fields as shape derivatives, in the spirit of the virtual work principle, combined with the adjoint approach from shape optimization. In contrast to standard formulas, they meet the continuity and smoothing requirements of abstract duality arguments, which supply a rigorous underpinning for their observed superior performance.

Keywords: Electrostatics, electromagnetic forces, shape derivative, boundary integral equations, boundary element method.

@Techreport{HP21_963,
  author = {R. Hiptmair and P. Panchal},
  title = {Electrostatic Force Computation with Boundary Element
Methods},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-21},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-21.pdf },
  year = {2021}
}

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