Rajat,
1. My problem involves the mesh movement in every time step. But with
adaptive mesh refinement and automatic repartitioning, I found that the
mesh becomes non-conforming, even when the displacements that I add to
the mesh are conforming (I call hanging node constraints . distribute to
make displacements conforming on the new mesh). I read this post
https://groups.google.com/forum/#!searchin/dealii/mesh$20refinement$20move$20%7Csort:relevance/dealii/HGnGKX8Gbo0/6BtK6pg8vKcJ
<ttps://groups.google.com/forum/#!searchin/dealii/mesh$20refinement$20move$20%7Csort:relevance/dealii/HGnGKX8Gbo0/6BtK6pg8vKcJ>
It says that the instead of mesh movement with conforming displacements,
store the coordinates of the mesh, then interpolate the mesh coordinates
using solution transfer like other vectors, and then set the coordinates
of the new mesh to this "transferred mesh coordinate vector". This works
for me. The new mesh is conforming. But I dont understand why this
works? I also tried the note
https://www.dealii.org/8.5.0/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation.html#a247598f1323a9f847832e60d6c840469 but
even this did not work.
I don't know the answer to this question. You will need to construct a
small testcase with just a few cells that demonstrates the issue and
that people can look at.
2. I want to apply boundary conditions on my domain. Lets say that the
domain is rectangular and I am solving for displacements on this domain.
I want to fix dofs that correspond to bottom left corner (x and y both
fixed), and "x dof" on bottom right corner is fixed. Without AMR, I
get the 3 dofs by looping over cells and even when the mesh moves, the
dofs are the same. But now, with AMR, the mesh moves as well the dofs
are changed.
So, I want to ask that is there any way I can know, the map from the
vertex/dof in the old configuration to the vertex/dof in the new
configuration. Configuration here refers to mesh+dofs before and after
refinement.
You could store the cell->vertex_index() that corresponds to these
corner points at the beginning of the computation. Later, you would then
go over all cells, over all vertices of the cell, and compare the
vertex_index. The vertex_index is a piece of geometric information and
has nothing to do with the DoF index.
3. This is most important question of all (for me :), pardon me if I am
unable to explain this well). [...]
In such a case, we cannot say that the value at the hanging node (middle
one) is just the average of the value at the end nodes of the
single element to begin with.
The argument you are making above is the wrong one. You are thinking in
terms of nodal values and degrees of freedom, but you should be thinking
of functions of x,y that happen to be parameterized by nodal values but
at the end of the day are still just functions.
So, a constraint that says that the sum of the nodal values should be
zero does not make sense. What you want is that the *average* (or
integral) of the function is zero; this happens to be equivalent to the
sum of nodal values if you have a uniform mesh, but on adaptive meshes
the nodes are weighted differently (as are, by the way, nodes at the
boundary).
Similarly, if you want to think of the finite element function as
*continuous*, then the *only way of achieving this* is by requiring that
the hanging node in the middle is the average of the two adjacent ones.
If it does not satisfy this property, then the function is not continuous.
In your example, you are representing the *displacement* as a continuous
function, but the *traction* is related to the derivative of the
displacement and consequently is not, in general, continuous -- so it
should not have hanging nodes, and the 1/2 rule does not apply.
Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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