Dear All,
I just got some concerns about the efficiency after reading the example
misc.ex5. It may be due to my misunderstanding of the libmesh or the DG
scheme. Would you guys please help me clear it.
In this example, the Laplace equation is solved using DG with interior
penalty method. So the main job is to compute the mass matrix from the
element volume integration and surface jump integration. It is done element
by element with the help of element iterator. I know all of the
elements organized as a quad-forest and only the active items need to be
looped.
so does this mean when we need to reach to the next active
element, const_element_iterator++ need to go through the quad-forest and
pass several non-active parent elements then get to the correct element
pointer to the next active element? If the answer is true. Is it too
expensive to find an element in a solver?
The other thing is the metrics computing such as Jacobian, xi_x xi_y eta_x
eta_y and face normal etc. Do those metrics computed several times using
FE::FEMap? If the mesh is fixed in space, we only need to compute them once
and store them somewhere.
Same thing happens when computing quadrature points in physical domain and
value of shape function/ its derivation at those points in computational
domain. I think those are computed in
----------------------
fe->reinit(elem)
----------------------
Those values do not change during the calculation and should be computed
only once. I think they are in the deepest loop and will eat a lot of cpu
time.
Last one, to compute the flux jump at flux points on the common surface of
two cells with different h levels. The coordinates and normals of the flux
quadrature points on the both side of element are computed several times
if we use a residual based scheme. It does not change at each refinement
level. Is there any efficient way to handle those kind of situation: flux
jump calculation at a surface with hanging node?
Or those are just for demo only. Those efficiency problem get even worse
for a scheme need residual jacobian at each time step. Do we need to use
FEMap explicitly and store the metrics for each element/face? So we don't
need to compute them more than once.
Thanks a lot for your time.
Sincerely Yours,
Lei Shi
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