Block Krylov Subspace Recycling: Theory and Application in a Newton Iteration

Description

The GCRODR algorithm (GMRES with subspace recycling) for linear systems, presented by Parks and colleagues [SIAM J. Sci Comput, 2006] has been shown to offer significant acceleration of convergence over restarted GMRES. The method is particularly effective when solving a slowly- changing sequence of linear systems. Block Krylov methods are a generalization of Krylov methods to the setting of linear systems with multiple right-hand sides. Block Krylov methods are attractive in the setting of next-generation exascale supercomputers, as they can exhibit lower data movement costs, a limiting factor of computations on such machines. We derive a version of GCRODR for use in the block Krylov setting. We call this method block GCRODR (block GMRES with recycling). We then demonstrate this method's effectiveness as a solver embedded in a Newton iteration arising in uid density functional theory, where we use our method to accelerate each Newton step through the introduction of random right-hand sides, generating a block Krylov subspace. We have implementations in Matlab and Trilinos C++ library.

Period	20 Jun 2013
Event title	International Conference On Preconditioning Techniques For Scientific And Industrial Applications
Event type	Conference
Location	United KingdomShow on map