Simultaneous solution of large-scale linear systems and eigenvalue problems with a parallel GMRES method

A method for simultaneous solution of large and sparse linearized equation sets and the corresponding eigenvalue problems is presented. Such problems arise from the discretization and the solution of nonlinear problems with the finite element method and Newton iteration. The method is based on a parallel version of the preconditioned GMRES( m ) by deflation. The parallel code exploits the architecture of the computational clusters using the MPI (Message Passing Interface). The convergence rate, the parallel speedup and the memory requirements of the proposed method are reported and evaluated.