Electrostatic Forces on Conductors with Boundary Element Methods in 3D

In this work we are concerned with computing local/global electrostatic forces and torques on perfect electrical conductors using the boundary element method (BEM). Classical boundary based force functionals are not continuous on energy trace spaces and therefore offer low accuracy and convergence rates. Following the work [P. Panchal and R. Hiptmair, Electrostatic Force Computation with Boundary Element Methods, the SMAI journal of computational mathematics, 8 (2022), pp. 49–74], we derive a similar force expression starting from a floating potential problem for conducting bodies. The computations are done by employing the Virtual Work Principle using shape calculus and the adjoint method. The final expression is structurally simple and can be evaluated without explicitly computing the adjoint solution. It enjoys superior accuracy and convergence rates compared to standard formulas which is demonstrated by means of numerical experiments.