Edge asymptotics for the radiosity equation over polyhedral boundaries

Abstract

In the present paper we consider the radiosity equation over the boundary of a polyhedral domain. Similarly to corresponding results on the double-layer potential equation, the solution of the second kind integral equation with non-compact integral operator is piecewise continuous. The partial derivatives, however, are not bounded. In the present paper we derive the first term in the asymptotic expansion of the solution in the vicinity of an edge. Note that, knowing this term, optimal mesh gradings can be designed for the numerical solution of this equation.