Re: using level-set for inclusions/non homogeneity

[Yves Renard]

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

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  Yves Renard (Yves.Renard@insa-lyon.fr)       tel : (33) 04.72.43.87.08
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