[khoder Alshaar]

Hello,
I'm following an open-source toolkit in OpenFoam explicitSolidDynamics, which has the following function in gradientSchemes.C :

This function takes a reference to a GeometricField, which represents the Inverse distance matrix.

void gradientSchemes::distanceMatrix
(
    GeometricField<tensor, fvPatchField, volMesh>& U 
)
{
 //Loop through internal faces (finite volume faces within the computational domain):
	forAll(own_, faceID)
    {
    
       // Get the cell IDs of the owner and neighbor cells for the current face
        const label& ownCellID = own_[faceID];
        const label& neiCellID = nei_[faceID];

	// Calculate the vector from the owner cell to the neighbor cell
        const vector& dOwn = X_[neiCellID] - X_[ownCellID];
        const vector& dNei  = X_[ownCellID] - X_[neiCellID];
      
      // Update the field U for the owner and neighbor cells with the outer product  of the vectors
        U[ownCellID] += dOwn*dOwn;
        U[neiCellID] += dNei*dNei;
        
    }
   
    //Check if the simulation is running in parallel (i.e., multiple rocessors).
    if (Pstream::parRun())
    {
        forAll(mesh_.boundary(), patchID)
        {
            if (mesh_.boundary()[patchID].coupled())
            {
                vectorField X_nei =
                  X_.boundaryField()[patchID].patchNeighbourField().ref();

                forAll(mesh_.boundary()[patchID], facei)
                {
                    const label& bCellID =
                        mesh_.boundaryMesh()[patchID].faceCells()[facei];

                    const vector& d = X_nei[facei] - X_[bCellID];
                    U[bCellID] += d*d;
                }
            }
        }

        U.correctBoundaryConditions();
    }

 
    U.primitiveFieldRef() = inv(U.internalField());
}

My question is related to the last line of the function

    U.primitiveFieldRef() = inv(U.internalField());

Could you please explain to me what it does besides the fact that it calculates the inverse of a tensor? what is the function of primitiveFieldRef() and .internalField() ?

Also, what happens to the faces at the boundary? For example, a boundary face does not have a neighboring cell, only an owner cell. So how these are evaluated:

        const vector& dOwn = X_[neiCellID] - X_[ownCellID];
        const vector& dNei  = X_[ownCellID] - X_[neiCellID];

Thank you!