Incorrect combination of implicit and explicit schemes

[fsimonis]

Describe your setup

preCICE Version: 3.0.0 (since #1453)

Describe the problem

The current method of handling compositional coupling schemes with implicit coupling schemes is the following:

1. run all explicit schemes
2. run the implicit scheme

Then rerun the implicit schemes until it achieves convergence and move to the next time-window.

The implicit scheme defines a fixed-point problem on the interface, which is accelerated using the configured acceleration schemes.
This problem changes every time window, until the implicit scheme reaches convergence.

As explicit schemes run during the first iteration along the implicit scheme, they also exchange data.
Even if the exchanged data via the explicit scheme is not used in the implicit scheme, it may change available readData of the solver and thus changes the fixed-point problem.
Hence, the fixed-point problem of the first iteration is different than following iterations.
This numerically doesn't make sense.

Furthermore, a serial explicit scheme where the participant with the implicit scheme runs first sends the data of the first iteration to the coupling partner. This data should really be the data of the converged iteration.

Expected behaviour

The implicit coupling scheme should run until convergence is achieved without any interference from explicit schemes. Only when the implicit scheme converges, should the explicit schemes run.

For serial schemes, where the participant with the implicit scheme

• comes first: the data of the converged iteration should be sent to the coupling partner.
• comes second: the data of the coupling partner should be received before the implicit scheme starts iterating.

Example

A-B parallel-implicit; A-C serial-explicit

Top is our currently incorrect method. Bottom is the expected way of handling this.

Additional context
This means that splitting the former CouplingScheme::advance() into substeps is more complex as assumed.
This makes remeshing for serial coupling significantly more difficult to implement, while remeshing for parallel participants should be largely unaffected.