Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver

Abstract

Please cite this article in press as: A. Amritkar et al., Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver, J. Comput. Phys. (2015), http://dx. AbstractWe focus on robust and efficient iterative solvers for the pressure Poisson equation in incompressible Navier-Stokes problems. Preconditioned Krylov subspace methods are popular for these problems, with BiCGStab and GMRES(m) most frequently used for nonsymmetric systems. BiCGStab is popular because it has cheap iterations, but it may fail for stiff problems, especially early on as the initial guess is far from the solution. Restarted GMRES is better, more robust, in this phase, but restarting may lead to very slow convergence. Therefore, we evaluate the rGCROT method for these systems. This method recycles a selected subspace of the search space (called recycle space) after a restart. This generally improves the convergence drastically compared with GMRES(m). Recycling subspaces is also advantageous for subsequent linear systems, if the matrix changes slowly or is constant. However, rGCROT iterations are still expensive in memory and computation time compared with those of BiCGStab. Hence, we propose a new, hybrid approach that combines the cheap iterations of BiCGStab with the robustness of rGCROT. For the first few time steps the algorithm uses rGCROT and builds an effective recycle space, and then it recycles that space in the rBiCGStab solver.We evaluate rGCROT on a turbulent channel flow problem, and we evaluate both rGCROT and the new, hybrid combination of rGCROT and rBiCGStab on a porous medium flow problem. We see substantial performance gains on both problems.

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