Thanks for the great feedback. I will proceed with the DUNE solvers and I might compare to the Eigen solvers for a simple setup.
I also considered PETSc as I use TAO (part of PETSc) to carry out optimization, though I think it is easier to use DUNE together with the Eigen SparseMatrix format. Regarding the DuneMatrix object <http://www.opm-project.org/documentation/master/opm-autodiff/html/class_opm_1_1_dune_matrix.php>, it seems that it takes a SparseMatrix<double Eigen::RowMajor> object as input, whereas the M object <http://www.opm-project.org/documentation/master/opm-autodiff/html/class_opm_1_1_auto_diff_block.php> from the AutoDiffBlock class is of type SparseMatrix<double>, i.e. using the default <http://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.html> Eigen::ColumnMajor as the _Options input. Could this be a problem?
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