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spatial derivatives in material properties?

Posted 30 sept. 2013, 10:16 UTC−4 Version 4.1, Version 4.2, Version 4.2a, Version 4.3, Version 4.3a, Version 4.3b 4 Replies

Andriy Gorbach
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Hi,

I am trying to model a material with non-local response. Particularly, I need a non-local electric permittivity, but I guess it does not really matter for this discussion, as the question is quite general. The easiest way to introduce such non-locality in equations is to replace the usual (local) property epsilon with the operator:

epsilon = epsilon_0 + epsilon_1 (d/dx) + epsilon_2 (d^2/dx^2)

It is easy on a paper, but is it at all possible in COMSOL?
4 Replies Last Post 1 oct. 2013, 07:07 UTC−4
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago 30 sept. 2013, 12:52 UTC−4
Why not would just input epsilon as a function of x?
Why not would just input epsilon as a function of x?
Andriy Gorbach
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Posted: 1 decade ago 30 sept. 2013, 13:52 UTC−4
No, it's not the same! Non-locality means that the material response (polarization) in any point of space x0 is defined by the external electromagnetic field within a certain area surrounding this point.

Local response: P(x)=epsilon(x) E(x)

Non-local response: P(x)=integral_0^infinity epsilon(x,delta) E(x-delta) d delta

Physically epsilon(x,delta) is localized in its second argument (delta). In this case, the above integral can be replaced with derivatives, as in my original post
No, it's not the same! Non-locality means that the material response (polarization) in any point of space x0 is defined by the external electromagnetic field within a certain area surrounding this point. Local response: P(x)=epsilon(x) E(x) Non-local response: P(x)=integral_0^infinity epsilon(x,delta) E(x-delta) d delta Physically epsilon(x,delta) is localized in its second argument (delta). In this case, the above integral can be replaced with derivatives, as in my original post
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago 30 sept. 2013, 18:35 UTC−4
Oh, a nonlocal response. That’s not trivial to implement in FEA in my opinion. There is a similar issue in solid mechanics in the implementation of nonlocal elasticity formulations such as “Cosserat” elasticity.
Oh, a nonlocal response. That’s not trivial to implement in FEA in my opinion. There is a similar issue in solid mechanics in the implementation of nonlocal elasticity formulations such as “Cosserat” elasticity.
Jesus Lucio
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Posted: 1 decade ago 1 oct. 2013, 07:07 UTC−4
Hi,

This thread is similar to this one:
www.comsol.com/community/forums/general/thread/25040/
where spatial integrals are also discussed. Look for the "dest" operator at documentation.

Regards.
Jesus.
Hi, This thread is similar to this one: http://www.comsol.com/community/forums/general/thread/25040/ where spatial integrals are also discussed. Look for the "dest" operator at documentation. Regards. Jesus.

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