Hi,
First, thank you for your fast answer. After, multiple tries, I found
that the number of timesteps has also an influence on the solution but
not the number of elements nor the refinement's deep. I can't figure
out the convergence mecanism with Neumann whereas it seems obvious
with Dirichlet.
Quoting Roy Stogner :
> I can't tell for sure, but it looks like there may be a bit of conflict
> between your time discretization and your Neumann boundary conditions?
> Make sure you're really solving "du/dx|xmax = g", not "d^2 u/dxdt|xmax = g"
You are right, the Neumann condition returns good results in static
mode but not in transient. As I was using the theta method, I tried
with the Newmark system (from ex. 8) to figure out a way to implement
this Neumann boundary, but the problem still exists. Therefore, I
replaced the Dirichlet condition in the dirichlet function by a
Neumann condition.
// ------------------------------------------------------ //
if (fabs(curr_node(0)-Xmax) < TOLERANCE)
{
unsigned int dn = curr_node.dof_number(0,0,0);
double neumann_value = 1.0;
force.add(dn,neumann_value);
}
// ------------------------------------------------------ //
Now, it seems that the derivative value at the upper side only depends
on Xmax (not on dt). In that way, the good result is obtained with on
approximative value of Xmax=55. Then, the same phenomenon occurs, if
Xmax < 55, the upper derivative is > 1 and if Xmax > 55, the upper
derivative is < 1.
Another way to proceed would prefer the use of infinite elements but
some restrictions have been made in 1D as it is explained in
InfElemBuilder class :
"00572 // 1D infinite elements not supported"
So, the questions are :
How to construct a free Neumann condition ?
Is there any way to circumvent restrictions and use infinite elements in 1D ?
Thanks a lot,
Maxime
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