  The coupled simulations of dynamic interactions between the well, hydraulic
fractures and reservoir have significant importance in some areas of petroleum
reservoir engineering. Several approaches to the problem of coupling between
the numerical models of these parts of the full system have been developed in
the industry in past years. One of the possible approaches allowing formulation
of the problem as a fixed-point problem is studied in the present work.
Accelerated Anderson's and Aitken's fixed-point algorithms are applied to the
coupling problem. Accelerated algorithms are compared with traditional Picard
iterations on the representative set of test cases including ones remarkably
problematic for coupling. Relative performance is measured, and the robustness
of the algorithms is tested. Accelerated algorithms enable a significant (up to
two orders of magnitude) performance boost in some cases and convergent
solutions in the cases where simple Picard iterations fail. Based on the
analysis, we provide recommendations for the choice of the particular algorithm
and tunable relaxation parameter depending on anticipated complexity of the
problem.
