MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Wavelet radiosity

Ulf Kähler and Reinhold Schneider


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.

bem, wavelets, radiosity

Related publications

2007 Repository Open Access
Ulf Kähler and Reinhold Schneider

Wavelet radiosity

In: 17th International Conference on Computer Methods in Mechanics : CMM-2007, June 19-22, 2007, Lodz-Spala, Poland. Short papers / K. Dems (ed.)
Lodz : Polish Academy of Sciences / Department of Technical Sciences, 2007. - pp. 193-194