Implementation of the bisection method with macro commands in the input file in the dockSIM research code

J. Boungard, J. Wackerfuß

The bisection method is a numerical method for the exact determination of breakdown and bifurcation points. Since the method is based on the same calculation steps and variables as the Newton-Raphson method with load increase (homotopy method), it is not necessary to implement the bisection method as a completely new numerical method within the framework of the dockSIM research cocde. Instead, the method can be mapped with macro commands at the level of the input data set. The same commands are used as for controlling the Newton-Raphson method with load increase. In addition, there are commands for querying the number of non-positive eigenvalues, for controlling the load step size and if-else queries for checking the convergence criterion. This illustrates the great flexibility offered by the dockSIM research code. This flexibility enables the clever combination of different numerical methods and also allows efficient implementation. Thus, by implementing the bisection method with macro commands in the input data set, it is not necessary to implement new functions to incorporate boundary and constraint conditions, as is otherwise required in the case of a new numerical method.