On 1/14/21 10:51 AM, Karthi wrote:
I have gone through a lot of tutorials. I would like to understand the basic
relation between dof_handler and FESystem. I am trying to solve _two_ 4th
order equations on the same mesh (or triangulation). And each equation is
split into two second order equations.
FESystem<dim> fe_one, fe_two;
BlockSparseMatrix<double> system_matrix_one, system_matrix_two;
BlockVector<double> solution_one, solution_two;
BlockVector<double> old_solution_one, old_solution_two;
BlockVector<double> system_rhs_one, system_rhs_two;
Question (1) Do I need one or two dof_handler?
DoFHandler<dim> dof_handler;
Where,
fe_one(FE_Q<dim>(degree),1, FE_Q<dim>(degree),1)
fe_two(FE_Q<dim>(degree),1, FE_Q<dim>(degree),1)
Some additional information, both the fe_one and fe_two systems are
_independently solved_ in a semi-implicitly manner. Meaning system_matrix_one
is a function of old_solution_one and old_solution_two, likewise for
system_matrix_two.
No. A DoFHandler in essence just describes a function space: The triangulation
provides the subdivision of the domain into cells, the finite element provides
information about what the polynomial space is, and the DoFHandler provides an
enumeration of degrees of freedom. As a consequence, if you want to use the
same function space for your two problems, then you can use the same
DoFHandler for both of your sub-problems.
Question (2) I am assuming one block spartisty_pattern is enough and use the
same for both the system_matrix?
BlockSparsityPattern sparsity_pattern;
Correct.
Best
W.
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