MiS Preprint Repository

The present paper considers the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme and its application to the special situation of the radiosity equation. It is known that the system matrix of the scheme in a wavelet basis which provides vanishing moments with respect to traces of polynomials in the space can be compressed to $\mathcal{O}(N\log N)$ relevant matrix entries, where N denotes the number of degrees of freedom. However, the presence of the visibility function in the kernel of the radiosity equation provides discontinuities for non-convex geometries, which cause trouble for most of the fast methods. Nevertheless, we have purchased a wavelet Galerkin method which is able to produce a system matrix with $\mathcal{O}(N{\log }^{3}N)$ relevant matrix coefficients for the radiosity equation on a reasonable geometry.