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Abstract. In this work we benchmark the performance of a preconditioned iterative method, used in large scale computer simulations of a geophysical application, namely, the elastic Glacial Isostatic Adjustment model. The model is discretized using the finite element method that gives raise to algebraic systems of equations with matrices that are large, sparse, nonsymmetric, indefinite and with a saddle point structure. The efficiency of solving systems of the latter type is crucial as it is to be embedded in a time-evolution procedure, where systems with matrices of similar type have to be solved repeatedly many times. The implementation is based on available open source software packages -Deal.II, Trilinos, PARALUTION and AGMG. These packages provide toolboxes with state-of-the-art implementations of iterative solution methods and preconditioners for multicore computer platforms and GPU. We present performance results in terms of numerical and the computational efficiency, number of iterations and execution time, and compare the timing results against a sparse direct solver from a commercial finite element package, that is often used by applied scientists in their simulations.