On Total Reuse of Krylov Subspaces for an iterative FETI-solver in multirate integration

Abstract

Recycling techniques for Krylov subspaces in parallel FETI-solvers are able to increase efficiency of solution processes with repeated right-hand-sides. One simple technique consists in a Total Reuse of the Krylov Subspace (TRKS) provided by conjugate directions generated during the solution of previous problems. This applies especially for linear structural dynamics and recycling also reduced global iterations for nonlinear structural dynamics. The structure of the interface-operator's eigenvalues governs the possible efficiency-gain. Only if high clustered eigenvalues are captured early enough, global FETI iterations will be reduced accordingly. Besides these advances, multirate integrators have been proposed, that enable adapted time-step-sizes on each substructure and are expected to accelerate the parallel simulation of nonlinear dynamic simulations with local highly nonlinear processes, e.g. damaging. Based on the linear BGC-macro and nonlinear PH-method, a nonlinear BGC-macro method has been proposed and on the other hand a more flexible and accurate multirate-integrator has been derived from the variational principle. These multirate-integration schemes require several local integration-steps in each global iteration, leading to a non-symmetric structure of the linearized local problems and the local boundary conditions are altered compared to FETI for standard singlerate integration. So, we have to solve the global interface-problem with a GMRes-solver. In this contribution, we show our recent results on the eigenvalues and application of a TRKS to these new problems.