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.mexample 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 ([email protected]) 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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