CArl
Code Arlequin / C++ implementation
Coupling matrices assembly

Now that we have the mesh intersections, we can use them to build the coupling matrices. Three matrices will be constructed:

  • Two $ n_{\mbox{Med}} \times n_l$ coupling matrices, noted as $C_l$ ( $m = 1,2$).
  • One $ n_{\mbox{Med}} \times n_{\mbox{Med}}$ matrix, noted as $C_{\mbox{Med}}$.

$ n_{\mbox{Med}} $ and $ n_l $ are the number of degrees of freedom of the mediator and the model $ m $ meshes, respectively. The $C_l$ matrices are the coupling matrices between the models and the mediator space used by the Arlequin method. The $C_{\mbox{Med}}$ is completely defined inside the mediator space, and it is used by the conjugate gradient solver preconditioners. By default, the restricted mesh of the Macro / A model is used as the mediator.

Submiting scripts/PBS_FETI_test_assemble_coupling_matrices_traction_test_1k.pbs or executing scripts/LOCAL_FETI_test_assemble_coupling_matrices_traction_test_1k.sh will run the command 

mpirun -n 4 ./CArl_assemble_coupling -i examples/coupled_traction_test/FETI_solver/brick_traction_1k/assemble_coupling_1k.txt

Note: the CArl_assemble_coupling MUST be executed with the same number of processors as the intersection construction case. This is because each processor does most of the coupling matrices calculations independently, reading only one of the [nb. of processors] intersection meshes.

Input

File: examples/coupled_traction_test/FETI_solver/brick_traction_1k/assemble_coupling_1k.txt 

### Coupling matrices assembly parameters
# - Model meshes
MeshA examples/coupled_traction_test/meshes/test_brick_A_1k.msh
MeshB examples/coupled_traction_test/meshes/test_brick_B_1k.msh

# - Intersection meshes and table files
InterBase examples/coupled_traction_test/intersection/output/inter_1k/inter

### Coupling parameters
# - Coupling region width (same unit as the meshes)
CouplingWidth 0.5

# - Coupling rigidity (in MPa, if mm was used for the meshes)
CouplingRigidity 2e5

# - Output folder path
OutputFolder examples/coupled_traction_test/FETI_solver/brick_traction_1k/coupling_matrices

Input file parameters:

  • MeshA, MeshB: as before, paths to the two model meshes.
  • InterBase: common filename for the intersection and restriction meshes.
  • CouplingWidth: width of the coupling region (same unit as the meshes, $e$ in the $L_2$ coupling term).
  • CouplingRigidity: rigidity used for the coupling matrix (in MPa, if mm was used for the meshes, $\kappa$ in both the $L_2$ and $H_1$ terms).
  • OutputFolder: folder where the coupling matrices will be saved.

Other optional parameters (not used here) include the paths to the restricted meshes and their mappings with the model meshes, and the choice of the mediator mesh. Those options are described at CArl_assemble_coupling.cpp.

Output

After running the coupling assembly program, the three matrices will be created inside the OutputFolder: 

coupling_matrix_micro.petscmat
coupling_matrix_macro.petscmat
coupling_matrix_mediator.petscmat

These matrices are saved using PETSc's binary format. The extension .petscmat is arbitrary. Three other files, named ***.info, contain some information on how PETSc should read these files (mainly, the matric block size).