Preconditioning of Krylov subspace methods using recycling in Lattice QCD computations

Many applications in computational science and engineering require the solution of sequences of slowly changing linear systems. We focus on problems arising in Lattice QCD simulations. In order to generate an ensemble of configurations from which the values of physical observables can be obtained, we have to solve a linear system with a Dirac operator in each time step of the hybrid Monte-Carlo simulations. This operator changes just slightly from time step to time step. While recycling subspace information from the previous system like described in [1] reduces the number of necessary matrix-vector multiplications, the systems are still expensive to solve. To overcome this limitation, we include preconditioning in our implementation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)