Dear Yves, thank you for responding!
Looks like I am getting closer to my goal.
But there is a collision with continuity at the
interface condition
If I use something like Interior Point condition for
example
'((u-Interpolate(u,neighbour_elt))*Normal).((Test_u-Interpolate(Test_u,neighbour_elt))*Normal)'
there is no level-set zero level faces to apply in mesh
linked to
mim_ls_bound integration method i use in assembly
gf.asm('generic',
mim_ls_bound, 2, blueExpression,
INNER_FACES, 'u', 1, mfls, 0)
here
mim_ls_bound =
gf.MeshIm('levelset', mls, 'BOUNDARY',
gf.Integ("IM_TRIANGLE(3)"))
mfls =
gf.MeshFem('levelset',mls,mfu)
where mls is
mls =
gf.MeshLevelSet(m)
mls.add(ls1)
mls.adapt()
for some
ls1 =
gf.LevelSet(m, 2, 'x-.25')
lagrangian MeshFem
mfu and mesh m
If i use
gf.asm('generic',
mim_ls_bound, 2, purpleExpression, -1,
'u', 1, mfls, 0)
I can't use Interpolate(*,
neighbour_elt
) term in
purleExpression since there is no convex faces in
defined region
This one is not empty : gf.asm('generic', mim_ls_bound,
2, 'Test_u.u', -1,
'u', 1, mfls, 0)
but how to express a jump on interface?
Do you have any thoughts on this? Could you advise
me how to implement continuity at the
interface condition term properly from your
perspective?
I attached a small solid python script as well
Regards, Egor
Dear Egor,
This is of course possible. The best way, I
think, is to define two different fields for the
matrix and the inclusion by defining an
integration method inside the inclusion and
outside (If you take only one field for the
inclusion and the matrix, you will have some
locking effect on the interface). Then you can
ensure the continuity at the interface either with
a multiplier (but with some possible non
satisfaction of the inf-sup condition) or in a
better way with Nitsche's method (see Hansbo's
publications for instance).
Best regards,
Yves
On 16/03/2021 18:40, Egor Vtorushin wrote:
Dear Yves,
Could you please provide me with a hint on
how to implement an inclusion with level set.
I want to implement an
inversion/optimization problem with a given
conductive homogeneous medium.
There is a dipole source with given
frequency, power and location and i am
modeling a field via Helmholtz equation or
MaxwelL equation
Then i want to put an anomalous object
(that has different non zero conductivity/k
^2) inside the media such a way so field
propagation and frequency resolution is
sensitive to the anomalia.
My optimization problem is to find the
anomalia's position and shape to minimize a
misfit with the measured field. It is close
to structural_optimization.m example
but i don't need holes i need an inclusion.
It still seems to me that it is very
reasonable to use a LevelSet based technique
to describe the anomalia and its changings.
But using the level-set raises the variable
jump immediately instead of the operator
coefficient jump that i need for.
I looked through some other examples(like
fictitious domains) but still have no way to
come up with.
Please share with me some hints if you have
one.
Regards, Egor Vtorushin
--
Yves Renard (Yves.Renard@insa-lyon.fr) tel : (33) 04.72.43.87.08
INSA-Lyon
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE
http://math.univ-lyon1.fr/~renard
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