Adding Time Discretization Schemes to OpenCMP

The OpenCMP code base is designed such that new time discretization schemes can be added without significantly modifying the main code base. The time discretization schemes are defined in “time_integration_schemes.py”, but the actual simulation run is controlled by a solver, the general hierarchy of which is shown below:

For more information on the differences between multi-step and Runge-Kutta time discretization schemes see Time Discretization Schemes.

To add a new time discretization scheme, add it as a new function in “time_integration_schemes.py”. Then determine whether it is a multi-step or Runge-Kutta scheme and modify the initialization of “solvers/base_solver.py” appropriately. Add the order of the scheme and its time step coefficients to scheme_order and scheme_dt_coef at the top of “solvers/base_solver.py”. The order of the scheme is the number of previous time steps used by the scheme. For example, Crank-Nicolson uses only the one previous time step to solve for the next time step so has a scheme order of 1. The time step coefficients are only non-unity for Runge-Kutta schemes and indicate the portion of the full time step to use during each intermediate step. Fixed time step schemes can then simply be added to the _create_linear_and_bilinear_forms method of TransientMultiStepSolver or TransientRKSolver. Finally, add the scheme to “solvers/misc.py”.

Adaptive time-stepping schemes should inherit from either BaseAdaptiveTransientMultiStepSolver or BaseAdaptiveTransientMultiStepSolver. The exact implementation will vary depending on the scheme, but existing adaptive time-stepping schemes may provide some guide. The final class must be added to “solvers/adaptive_transient_solvers/__init__.py” and to “solvers/misc.py”.