Second-kind integral formulations of the capacitance problem

The standard approach to calculating electrostatic forces and ca-pacitances involves solving a surface integral equation of the rst 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 diierent discretization schemes for this integral formulation. Numerical experiments, using multipole accelerated matrix-vector multiplications, demonstrate the eeciency and accuracy of the new approach.