Dear Jean-Paul,

Thank you very much! I had read step-45, but still have some questions:
1. How to use function "DoFTools::make_periodicity_constraints() "  only? 
if my code need not to compute parallel case.  If I choose
void DoFTools::make_periodicity_constraints ( const FaceIterator & face_1,
const typename identity 
<https://dealii.org/developer/doxygen/deal.II/structidentity.html>< 
FaceIterator >::type & face_2,
AffineConstraints 
<https://dealii.org/developer/doxygen/deal.II/classAffineConstraints.html>< 
double > & constraints,
const ComponentMask 
<https://dealii.org/developer/doxygen/deal.II/classComponentMask.html> & 
component_mask 
= ComponentMask 
<https://dealii.org/developer/doxygen/deal.II/classComponentMask.html>(),
const bool face_orientation = true,
const bool face_flip = false,
const bool face_rotation = false,
const FullMatrix 
<https://dealii.org/developer/doxygen/deal.II/classFullMatrix.html>< double 
> & matrix = FullMatrix 
<https://dealii.org/developer/doxygen/deal.II/classFullMatrix.html><double>
(),
const std::vector< unsigned int > & first_vector_components = std::vector<
unsigned int>() 
)
how to choose face1 and face2 we need there correctly? If I use 
template<typename DoFHandlerType >
void DoFTools::make_periodicity_constraints ( const std::vector< GridTools::
PeriodicFacePair 
<https://dealii.org/developer/doxygen/deal.II/structGridTools_1_1PeriodicFacePair.html>
< typename DoFHandlerType::cell_iterator >> & periodic_faces,
AffineConstraints 
<https://dealii.org/developer/doxygen/deal.II/classAffineConstraints.html>< 
double > & constraints,
const ComponentMask 
<https://dealii.org/developer/doxygen/deal.II/classComponentMask.html> & 
component_mask 
= ComponentMask 
<https://dealii.org/developer/doxygen/deal.II/classComponentMask.html>(),
const std::vector< unsigned int > & first_vector_components = std::vector<
unsigned int>() 
)
how to make a 
const std::vector< GridTools::PeriodicFacePair 
<https://dealii.org/developer/doxygen/deal.II/structGridTools_1_1PeriodicFacePair.html>
< typename DoFHandlerType::cell_iterator >> & periodic_faces
maybe I still need to use "GridTools::collect_periodic_faces" to input 
information of faces into PeriodicFacePair. If I do this,  I am not use 
"DoFTools::make_periodicity_constraints() "  only....


2. In step-45, the complete implemention is parallel case. For every step, 
it use functions used in parallel case. If I want to implement a case not 
in parallel, shall I rewrite all of them and remove the parallel parts 
(still not succeed), or use it directly, but in shell run my program via
mpirun -np 1 ./myCase


Thank you very much!

Best,
Chucui

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