Technical Report 2019-011

Fast Parallel Solver for the Space-Time IgA-DG Discretization of the Anisotropic Diffusion Equation

Pietro Benedusi, Paola Ferrari, Carlo Garoni, Rolf Krause, and Stefano Serra-Capizzano

November 2019

We consider the space-time discretization of the (linear) anisotropic diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a new solution method combining a suitable preconditioned GMRES (PGMRES) algorithm with a few iterations of an appropriate multigrid method. The performance of our new solution method is illustrated through numerical experiments, which show its competitiveness in terms of robustness, run-time and parallel scaling.

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