Calculation of overlap integrals

[jnieg...@googlemail.com]

Hi,
I have been playing around with hermes2d and implemented a very basic waveguide mode solver. Now, for the postprocessing, I need to calculate the overlap integral of two different modes. Now, while the calculation of the two modes starts from the same parent mesh, the iterative refinement leads to very different meshes for the final modes.

I guess the proper approach would be to somehow generate a union of the two meshes, then project both solutions onto this union mesh and finally multiply and integrate on each element. I tried looking through the documentation a bit (the online version seems to be down btw) but could not really figure out how to generate this union. Can someone provide a hint or a short example?

Best regards,
Jens

[Lukas Korous]

Hello Jens,

sure, I am sorry, we are preparing a new version of both Hermes and
Agros (agros2d.org), so we are in a bit of a rush. But I marked your
messages as important, so I will get to you as quickly as I can.

Regards,
Lukas

2013/8/27 <jnieg...@googlemail.com>:

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Lukáš Korous

[jnieg...@googlemail.com]

Hi Lukas,
thanks for the quick response. There is no hurry, I am just playing around...maybe you could just quickly tell me if the calculation of overlap integrals is easily done with hermes2d or if it will require significant effort.

There is no direct connection of this question to the issues I opened on github.

Best regards,
Jens

[Lukas Korous]

Hi,

ok:
- I fixed the links to documentation earlier today, it should work
- there is no need for the union mesh, if you want to calculate an
integral taking both solutions from both meshes, the internals of
Hermes do this for you. Just pass the two (different, but coming from
a common master mesh) meshes (spaces) to the solver together with a
WeakForm containing the definition of integrals you want to evaluate.

Take a look at this example regarding this:

http://hpfem.org/hermes-doc/hermes-tutorial/html/src/hermes2d/D-adaptivity/03-system.html

Otherwise the method Traverse::construct_union_mesh could help you.

Regards,
Lukas

2013/8/27 <jnieg...@googlemail.com>:

[jnieg...@googlemail.com]

Hi Lukas,
thank you again for the quick answer and thank you for bringing the online documentation back. I might not have expressed my problem clearly (or maybe I did not understand your answer).

What I want to do is a post-processing step, i.e. I do have two solutions (two eigenmodes which belong to different eigenvalues) on different meshes and I want to form a product of those two solutions and integrate this product over the entire domain to get a single number (coupling coefficient in coupled mode theory).

I will have a look at Traverse::construct_union_mesh, it sound like what I was looking for.

Btw: some links in the online documentation are still not working, e.g. http://www.hpfem.org/hermes-doc/hermes/hermes2d/classHermes_1_1Hermes2D_1_1Traverse as linked from http://hpfem.org/hermes-doc/hermes/hermes2d/index.php is still 404


Best regards,
Jens

[Lukas Korous]

OK, let me know how it goes. I will fix the links, thanks for the hint.