On the discretisation of the double layer integral operator for surfaces of revolution

摘要

The double layer integral operator W, occuring in many potential problems, is discretised in the following form: WV(P)∼(2π)-1∑j=1NV(Pj)Ω(P,Δj), P∈S, where Ω(P, Δ) is the solid angle of a piece Δj of the surface S seen from P and Pj is a point in Δj.It is shown that Ω(P, Δj) depends only on the boundary of Δj. For axisymmetric problems, each Δj is a zone of the surface of revolution, Ω(P, Δj) is a complete elliptic integral of the third kind which can be computed by the Bartky-Bulirsch algorithm.An application to the dielectric resonances of a truncated sphere is presented.