Monte Carlo simulations

The most simple but very powerful technique to solve the probabilistic problem is a Monte Carlo technique. The same problem is solved many times, each time with different fields of random variables generated according to prescribed parameters.

The whole problem is solved in the following steps:

1. Generate random fields according to Sec. 3.7.1 using control_distribute command as many times as many variables are treated as random. In principle, any variable can be related as random. For example material parameters, unknowns (e.g., history variables), etc.
2. Solve the problem using finite element method. Collect required results of each Monte Carlo realisation into an output file. The user can prescribe any result to be collected into an output file using control_repeat_save command (e.g., time_current, final displacement of a selected point, etc.).
3. Repeat items 1. and 2. $m$-times, where $m$ is a prescribed number of Monte Carlo realisations. $m$ value is specified in Tochnog input file using control_repeat command.
4. Evaluate results statistically. More complex statistical evaluation is done by the user, calculation of mean value and standard deviation can be done in Tochnog using control_repeat_save_calculate command.