Regularized formulations for spectral graph partitioning

In this paper, we introduce a novel regularization technique for the spectral partitioning of a mesh that relies on a efficient preconditioning of the associated graph Laplacian. The regularization is obtained by leveraging on fractional order Sobolev norms obtained with integral operators and by linking the Laplacian and the operators with suitably chosen Gram matrices that connect the underlying discretization spaces. The numerical results support the developed theory when applied to some of the realistic examples arising in Computational Electro-magnetics applications.