Re: [Libmesh-users] hp elements

[Daniel D. <d.d...@tu...>]

As already mentioned by Ben, there is no obstacle in the way.
Actually, here some more details that arose during the implementation
of the infinite elements (which are actually also p-FEM, but with
anisotropic p-order, therefore we have _two_ Order enums, namely the
radial_order and the base_order in FEType, when ENABLE_INFINITE_ELEMENTS
is active):


- momentarily, libmesh already offers p-FEM, but with only constant
  p-order throughout the mesh.  This order is (currently) determined
  once for all through the FEType that you have to create in the
  EquationSystems/SystemBase-child context, when you say add_variable().
  (note that there is also the simplified variant of add_variable()
   which only takes an order, and assumes LAGRANGE as family, which
   only goes up to p=2, use instead e.g. HIERARCHIC).

  In the FEType, you say what order = p you want.  This information is
  then broadcasted to all objects that may handle a degree of freedom:
  The DofObject.  Each DofObject may hold _multiple_ components per
  dof...

  E.g. you have an EDGE3, but you want to use p=3.  Then you have
  4 dof:
         o----o----o
  dof:   0   2,3   1
  node:  0    2    1

  This is also the numbering scheme in libmesh, first number the nodes
  that belong to the first-order element, then number the dofs on the
  second-order-nodes (this is particularly helpful when having a 2nd-order
  mesh, but you only want to use 1st-order shapes).
  the DofObject->n_comp() gives then for:

  Node(0) = 1
  Node(1) = 1
  Node(2) = 2

  And since both Node and Elem derive from DofObject,
  you may easily handle bubble shapes etc, consult the HIERARCHIC family.


- note that you have to --enable-expensive (or so) in ./configure to
  get the full support.


- GOOD news: the truly tedious work of coding the shapes is already
  in progress, _several_ new p-FEM families are underway: Steffen and
  Hendrik have already come a long way implementing them, like the ones
  that want to orthogonalize the stiffness matrix (integrated Legendre),
  improved variants (by Adjerid), and two more pretty interesting
  families that also seem to work well on simplices.

  I suggest you contact Steffen directly for more information.  As far
  as i know, he almost finished debugging 2D, and wants to proceed to 3D.
  So perhaps some collab' may be possible.


- extending to variable-order-p-FEM is an issue i already thought of
  in the context of the infinite elements, and also talked to Ben about
  it.  So, feel free to contact for a more detailed discussion.

Daniel

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