In this work we emphasize some aspects of the numerical and computational performance of block preconditioners for systems with matrices of saddle point form. We discuss the quality of a sparse approximation of the related Schur complement for constructing an efficient preconditioner and the achieved numerical efficiency in terms of number of iterations. We also present a performance study of the computational efficiency of the corresponding preconditioned iterative solution methods, implemented using publicly available numerical linear algebra software packages, both on multicore CPU and GPU devices. We show that the presently available GPU accelerators can be very efficiently used in computer simulations involving inner-outer solution methods and hierarchical data structures. The benchmark problem originates from a geophysical application, namely, the elastic Glacial Isostatic Adjustment model, discretized using the finite element method.
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