[khoder Alshaar]

Hello,
I'm using an opensource solver with OpenFOAM explicitSolidDynamics, which has the following function in gradientSchemes.C.

The function calculates the Inverse Distance Matrix for each domain's owner and neighbor cell of each face:

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 processors).
    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();
    }
    
    //Compute the inverse of the internal field of `U` and assign it to the primitive field:
    U.primitiveFieldRef() = inv(U.internalField());
}

1- My first question is primarily related to the last line:

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

Could you please explain the function of primitiveFieldRef() and internalField() in this context?

2- I understand that a boundary face has only an owner cell and does not have a neighbor cell. In this case, how are these getting evaluated:

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

I would like to understand how openFoam deals with calculations related to boundary cells, for example, calculating the gradient.