The application of Krylov subspace methods for solution of linear systems of equations arising in nonlinear structural finite element analysis is presented. It is shown, that - with appropriate preconditioners - iterative methods can be developed which are efficient even for problems with ill conditioned stiffness matrix K. For parallelization mesh partitioning methods are used. On each processor a partial stiffness matrix K_i is computed. Parallel preconditioning is based on complete or incomplete factorizations of the partial stiffness matrices K_i. For ill-conditioned linear systems with multiple right hand sides direct methods usually are superior to the iterative ones, but they are hard to parallelize. For this class of problems a Schur complement method where the Schur complement system is solved by a Krylov subspace iteration with preconditioning of the local Schur complements is more efficient. Two examples are presented, and the efficiency of the presented methods is discussed.

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