Mixed-Precision GPU-Multigrid Solvers with Strong Smoothers

Abstract

• Sparse iterative linear solvers are the most important building block in (implicit) schemes for PDE problems • In FD, FV and FE discretisations • Lots of research on GPUs so far for Krylov subspace methods, ADI approaches and multigrid • But: Limited to simple preconditioners and smoothing operators •Numerically strong smoothers exhibit inherently sequential data dependencies (impossible to parallelise?) • Strong smoothers required in practice: Anisotropies (mesh, operator), localised nonlinearities from the PDEs etc. increase ill-conditioning of the systems drastically •Multigrid is asymptotically optimal, all other iterative schemes suffer from h-dependencies • In our context: Multigrid = geometric multigrid