A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations
A new implementation of restarted Krylov subspace methods for evaluating f(A)b for a function f , a matrix A and a vector b is proposed. In contrast to an implementation proposed previously, it requires constant work and constant storage space per restart cycle. The convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given. The performance of the implementation is illustrated for three parabolic initial value problems, requiring the evaluation of exp(A)b.