Coupling

The coupling class takes two timestepping schemes and executes them alternatingly. It sets divides the total time span in smaller time spans. For each of the smaller time spans \([t_i,t_{i+1}]\), it does the following:

• set time span \([t_i,t_{i+1}]\) in time stepping scheme 1

• solve time stepping scheme 1 (call advanceTimeSpan())

• transfer data from time stepping scheme 1 to 2

• set time span \([t_i,t_{i+1}]\) in time stepping scheme 2

• solve time stepping scheme 2 (call advanceTimeSpan())

• transfer data from time stepping scheme 2 to 1

The Coupling is itself a timestepping scheme and has all options listed on the (TimeSteppingSchemesOde) page.

It is equivalent to Operator Splitting, but with the keyword “Coupling” instead of “GodunovSplitting”.

Note that usually data should be transferred between the two solvers. This is done with the settings connectedSlotsTerm1To2 and connectedSlotsTerm2To1. See the notes on Connector Slots.

C++ code:

Control::Coupling<
  /*first timestepping scheme*/,
  /*second timestepping scheme*/
>

Python settings:

"Coupling": {
  "numberTimeSteps": 1,
  "timeStepWidth": 1e-1,
  "endTime": 10.0,
  "logTimeStepWidthAsKey": "dt_3D",
  "durationLogKey": "duration_total",
  "timeStepOutputInterval": 10,

  "connectedSlotsTerm1To2": [0],  # list of slots of term 2 that are connected to the slots of term 1
  "connectedSlotsTerm2To1": [0],  # list of slots of term 1 that are connected to the slots of term 2

  "Term1": {
    "ExplicitEuler" : {  # these are the properties for the first timestepping
    }
  },
  "Term2": {
    "ImplicitEuler" : {  # these are the properties for the second timestepping
    }
  }
}

MultipleCoupling

If you need more than two child solvers that should be executed in a row, you can use MultipleCoupling.

Without this, a nested structure of Coupling schemes would be needed. For example, for 3 solvers A, B and C, you would do something like:

Control::Coupling<
  A,
  Control::Coupling<
    B,
    C
  >
>

with settings

"Coupling": {
  "Term1": {
    # settings for A
  },
  "Term2": {
    "Coupling": {
      "Term1": {
        # settings for B
      },
      "Term2": {
        # settings for C
      }
    }
  }
}

The MultipleCoupling abstracts this construction for any number of subsolvers. The usage is

Control::MultipleCoupling<
  A,B,C, //...   any number of subsolvers (at least 2)
>

This is more convenient than the construction with the nested Coupling schemes. Also the Python settings are simplified:

"MultipleCoupling": {
  "endTime":                variables.end_time,           # end time of the simulation
  "timeStepWidth":          variables.dt_neuron_transfer, # time step width of the data transfer between the sub solvers
  "logTimeStepWidthAsKey":  "dt_neuron_transfer",         # string under which the timestep width will be stored in the log file
  "durationLogKey":         "duration_total",             # string under which the total duration will be stored in the log file
  "timeStepOutputInterval": 500,                          # how often to print the current time step
  "connectedSlotsTerm1To2": None,                         # this would be the connected slots for a normal Coupling scheme, but here it should be set to None, use global option "connectedSlots" instead
  "connectedSlotsTerm2To1": None,                         # this would be the connected slots for a normal Coupling scheme, but here it should be set to None, use global option "connectedSlots" instead

  "Term1": {
    # settings for A
  },
  "Term2": {
    # settings for B
  },
  "Term3": {
    # settings for C
  },
  // etc.
}

Internally, MultipleCoupling constructs the tree of nested Coupling schemes. It is implemented using variadic templates and therefore works for any number of nested solvers.

The settings for MultipleCoupling are shared for all constructed Coupling schemes. This means that the set timestep width is reused for all terms of the coupling. The options "connectedSlotsTerm1To2" and "connectedSlotsTerm2To1" should be set to None. The slots should be connected using the “connectedSlots” option, for details see Connector Slots. The settings for the nested solvers can be given under “Term1”, “Term2”, “Term3”, etc., as with the normal Coupling scheme.