Abstract
The standard approach to calculating electrostatic forces and capacitances involves solving a surface integral equation of the first kind. However, discretizations of this problem lead to ill-conditioned linear systems and second-kind integral equations usually solve for the dipole density, which can not be directly related to electrostatic forces. This paper describes a second-kind equation for the monopole or charge density and investigates different discretization schemes for this integral formulation. Numerical experiments, using multipole accelerated matrix–vector multiplications, demonstrate the efficiency and accuracy of the new approach.
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Tausch, J., White, J. Second-kind integral formulations of the capacitance problem. Advances in Computational Mathematics 9, 217–232 (1998). https://doi.org/10.1023/A:1018973019922
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DOI: https://doi.org/10.1023/A:1018973019922