The deal.II adapter provides examples of deal.II codes, which have been coupled using preCICE. This section explains the preCICE-related code changes and introduces the Adapter class, which is located in the include/adapter directory. A step-by-step tutorial is also available on the preCICE wiki.

### Which information is needed by preCICE?

preCICE uses a black-box coupling approach, which means the solver only needs to provide a minimal set of information. In the simplest case, this includes configuration information, e.g. the name of the participant and the coordinates of the data you want to exchange (the interface mesh vertices). If you want to use a nearest-projection mapping, you need to additionally specify mesh connectivity between the vertices, which is currently not included in this adapter example.

For every multi-physics coupling, proper coupling data needs to be exchanged between all participants. In our example case, the Fluid participant calculates stresses, which are passed to the Solid participant. Using the stress for the structural calculations, the Solid participant calculates displacements, which are then passed back to the Fluid participant. As outlined above, preCICE needs coordinates of the data points you want to exchange.

## The Adapter class

This section introduces the Adapter class. This class is located in the include/adapter directory and contains various files: the files time_handler.h and adapter.h are the most important files for the adapter. The time_handler.h file contains a class to keep track of the current time step and absolute time values. There are other ways to handle this task, but we directly use its functionality in the adapter class to restore the time and therefore included it in this class. The main functionalities are, however, provided in the adapter.h file. An exhaustive documentation for all functions can be found directly in the adapter.h source code.

In order to use the adapter, we first create an adapter object:

Adapter::Adapter<dim, Vector<double>, Parameters::AllParameters> adapter(parameters, interface_boundary_id);


The first template argument specifies the coupling dimension, the second argument specifies the vector type of your simulation. The third template argument specifies the Parameter class type. The parameter object is directly passed to the constructor and all preCICE related settings are read by the adapter. In this case, required information is grouped in the parameter file in the subsection precice configuration. You can copy and insert it directly in your own parameter class or copy the class from the provided parameter class. Apart from the parameter object, the constructor needs to know your interface_boundary_id, which is the boundary_id of your deal.II triangulation. Make sure it is unique and doesn’t change during simulation.

With the adapter object and the time object, you can simply modify your time loop in the following way: This code has in large parts been copied from the linear_elasticity run() function:

// In the beginning, we create the mesh and set up the data structures
make_grid();
setup_system();
output_results(); // Output initial state
assemble_system();

// Then, we initialize preCICE i.e. we pass our mesh and coupling
// information to preCICE
// displacement and stress are the coupling data sets for FSI

// Then, we start the time loop. The loop itself is steered by preCICE. This
// line replaces the usual 'while( time < end_time)'
{
// In case of an implicit coupling, we need to store time-dependent
// data, in order to reload it later. The decision, whether it is
// necessary to store the data is handled by preCICE as well

// Afterwards, we start the actual time step computation
time.increment();

// Assemble the time dependent contribution obtained from the Fluid
// participant
assemble_rhs();

// ...and solve the system
solve();

// Update time-dependent data according to the theta-scheme
update_displacement();

// Then, we exchange data with other participants. Most of the work is
// done in the adapter: We just need to pass both data vectors with
// coupling data to the adapter. In case of FSI, 'displacement' is the
// data we calculate and pass to preCICE and 'stress' is the (global)
// vector filled by preCICE/the Fluid participant.

// Next, we reload the data we have previously stored in the beginning
// of the time loop. This is only relevant for implicit couplings and
// configuration.

Since now the coupling data is time-dependent, you need to assemble parts of your matrices/vectors in every time step, depending on your coupling problem/implementation. In most of the cases and in our example, this will be the rhs of the equations. The function assemble_rhs() uses the coupling data, namely stresses, to rebuild the rhs vector. How to apply coupling data is strongly problem-dependent. In our case, we use global data vectors to exchange data with preCICE. Afterwards, we use get_function_values() to extract the relevant data locally from the global vector. This way, we also enable to run the assembly with a shared-memory parallelization as shown in the nonlinear elastic case. More details can be found in the assemble_rhs() function in the linear elastic solver or the assemble_neumann_contribution_one_cell() function in the nonlinear elastic solver.