Capacitances and singularities of the unit triangle, square, tetrahedron and cube

Abstract

The boundary element method has been used to obtain the electrical capacitances of the unit equilateral triangle, square, regular tetrahedron and cube. For each of these objects, a series of values of the number N of segments has been used and then empirical formulae have been used to extrapolate N to infinity. The singularities of the charge densities at the edges and corners of these objects can be characterised by power laws, the relevant exponents of which have also been determined.

Citation

Read, F.H. (2004), "Capacitances and singularities of the unit triangle, square, tetrahedron and cube", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 23 No. 2, pp. 572-578. https://doi.org/10.1108/03321640410510758