Regularized Graph Laplacians for Hierarchical Spectral Partitioning
Résumé
This contribution will introduce an innovative approach to the Hierarchical Spectral Partitioning problem. The graph Laplacian will be regularized, by the scheme we are proposing, in an analytic way, by leveraging on fractional Sobolev norm realizations obtained with integral operators and by linking the Laplacian and the operators with suitably chosen mapping matrices that would connect, in the correct way, the underlying discretization spaces. In practice this will result in a multiplicative preconditioner for the graph Laplacian that, as will be detailed in the talk, will be easily obtained from matrices currently available in any standard EM boundary element implementation. Numerical results will corroborate our theoretical developments and will show the practical impact of our new technique on several realistic cases arising from applications.