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.
Galyna Safonova,
and
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
