Prize-winning research on Snapchat – the meaning of mobile imagery

The following post is a summary of Alexander Hebels’ winning entry for the 2014 Polis Social Media Prize

A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries

In this paper we consider a piecewise linear collocation method for the solution of the double layer potential equation corresponding to Laplace's equation over polygonal domains. We give a wavelet algorithm for the computation of the corresponding stiffness matrix and for the solution of the arising matrix equation with no more than O(N x [logN]"8) arithmetic operations. The error of the resulting approximate solution is of order O(N"-"2 x [logN]"6). Finally, we give some remarks on the generalization of the algorithm to the piecewise cubic collocation and present numerical tests. (orig.)Available from TIB Hannover: RR 5549(106)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman