  Iterative solvers preconditioned with algebraic multigrid have been devised
as an optimal technology to speed up the response of large sparse linear
systems. In this work, this technique was implemented in the framework of the
dual delineation approach. This involves a single groundwater flow solve and a
pure advective transport solve with different right-hand sides. The new solver
was compared with traditional preconditioned iterative methods and direct
sparse solvers on several two- and three-dimensional benchmark problems
spanning homogeneous and heterogeneous formations. For the groundwater flow
problems, using the algebraic multigrid preconditioning speeds up the numerical
solution by one to two orders of magnitude. Contrarily, a sparse direct solver
was the most efficient for the pure advective transport processes such as the
forward travel time simulations. Hence, the best sparse solver for the more
general advection-dispersion transport equation is likely to be P\'eclet number
dependent. When equipped with the best solvers, processing multimillion grid
blocks by the dual delineation approach is a matter of seconds. This paves the
way for routine time-consuming tasks such as sensitivity analysis. The paper
gives practical hints on the strategies and conditions under which algebraic
multigrid preconditioning for the class of nonlinear and/or transient problems
would remain competitive.
