A high-efficiency rigorous approach for the solution of the two-dimensional Laplace equation with Dirichlet's boundary conditions is developed to tackle electrostatic problems involving metallic cylinders of arbitrary cross-sections. In this paper we demonstrate how this novel algorithm can be used to address the problems arising in the capacitance microscopy to provide a higher resolution in studies of micro-cavities and whiskers on the surface of metallic samples. The precise capacitance images of the probe/sample systems are presented.
Elena D. Vinogradova,
"Rigorous Approach to Calculation of Capacitance Images of Metallic Samples for Use in Capacitance Microscopy," Progress In Electromagnetics Research B,
Vol. 55, 383-399, 2013. doi:10.2528/PIERB13091002