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Multi-level preconditioners for Discontinuous Galerkin (DG) discretizationsare widely used to solve elliptic equations, and a main ingredient of suchsolvers is the interpolation operator to transfer information from the coarseto the fine grid. Classical interpolation operators give continuousinterpolated values, but since DG solutions are naturally discontinuous, onemight wonder if one should not use discontinuous interpolation operators for DGdiscretizations. We consider a discontinuous interpolation operator with aparameter that controls the discontinuity, and determine the optimal choice forthe discontinuity, leading to the fastest solver for a specific 1D symmetricinterior penalty DG discretization model problem. We show in addition that ouroptimization delivers a perfectly clustered spectrum with a high geometricmultiplicity, which is very advantageous for a Krylov solver using the methodas its preconditioner. Finally, we show the applicability of the optimal choiceto higher dimensions.

Should multilevel methods for discontinuous Galerkin discretizations use discontinuous interpolation operators?