Block Krylov Subspace Recycling: Theory and Application in a Newton Iteration
Sprache des Vortragstitels:
International Conference On Preconditioning Techniques For Scientific And Industrial Applications
Sprache des Tagungstitel:
The GCRODR algorithm (GMRES with subspace recycling) for linear systems, presented by Parks
and colleagues [SIAM J. Sci Comput, 2006] has been shown to oer signicant acceleration of
convergence over restarted GMRES. The method is particularly eective 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 eectiveness 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.