[case] IterationNumberBasedTimeStepping

Iteration number based adaptive time stepping.

This algorithm estimates a time step size depending on the number of iterations (e.g. of iterative linear solvers, nonlinear methods, partitioned coupling) needed in the last time step (see Hoffmann (2010) for Newton-Raphson case). The new time step \(\Delta t_{n+1}\) size is calculated as

\[ \Delta t_{n+1} = \alpha \Delta t_n \]

with the previous time step size \(\Delta t_{n}\) and a multiplier coefficient \(\alpha\) depending on the iteration number. Note that a time step size is always bounded by the minimum and maximum allowed value.

\[ \Delta t_{\min} \le \Delta t \le \Delta t_{\max} \]

For example, users can setup the following time stepping strategy based on the iteration number of the Newton-Raphson method in the last time step.

Num. of Newton steps0-23-67-89<
Time step size multiplier1. (repeat time step)
Upper and lower bound\( 1. \le \Delta t \le 10.\)

A time step size is increased for the small iteration number, and decreased for the large iteration number. If the iteration number exceeds a user-defined threshold (e.g. 9), a time step is repeated with a smaller time step size.


  • Hoffmann J (2010) Reactive Transport and Mineral Dissolution/Precipitation in Porous Media:Efficient Solution Algorithms, Benchmark Computations and Existence of Global Solutions. PhD thesis. pp82. Friedrich-Alexander-Universität Erlangen-Nürnberg.

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Used in the following test data files