Integral over product space

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4 years 5 months ago - 4 years 5 months ago #2735 by philipp
Dear NGSolve community,

I am having the (maybe little unusual) integral expression in a weak formulation of a problem I am interested in:
[tex]
\int_\Omega \int_\Omega f(x,y,\phi(y)) u(x) v(x) d^3y d^3x.
[/tex]
It is part of a system of equations of a time-dependent problem and both \phi and u are trial functions and v is a test function. I employ a semi-implicit Euler-scheme with Newton's methods for time integration.
To make things a little easier, I decided to take \phi explicitely, but still the only method I can think of
is to encode an integration scheme for the inner integral in the symbolic expression I give the symbolic integrator in NGSolve. I can imagine that such odd situations are not accounted for right now in NGSolve,
but still wanted to make sure I am not missing a short workaround.

I appreciate any hint, what I might do instead.

All the best,
Philipp
Last edit: 4 years 5 months ago by philipp.
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4 years 5 months ago - 4 years 5 months ago #2737 by christopher
If you take phi explicitly you can just use the gridfunction instead of the trialfunction and integrate it to get the coefficient in your form or am I missing something?
Best
Christopher
Last edit: 4 years 5 months ago by christopher.
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4 years 5 months ago - 4 years 5 months ago #2738 by philipp
Replied by philipp on topic Integral over product space
Thanks for your fast reply. Since f depends on both x and y, I need the inner integral to be a coefficient function in x. I don't know a way to do this, but symbolically write down the quadrature in y.
Maybe there is confusion because I named the points x and y which collides with the
notation in NGSolve, where x and y are coordinates. I am sorry for this. Maybe I should edit the post.

All the best,
Philipp
Last edit: 4 years 5 months ago by philipp.
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4 years 5 months ago #2739 by christopher
Ah now I got you, sry.
I guess this is an example where you would likely need to write a c++ coefficientfunction to have it somehow performant.
You can use the tutorial here:
ngsolve.org/docu/latest/mylittlengs/1_Ba...FEM/coefficient.html
from mylittlengsolve ( ngsolve.org/docu/latest/mylittlengs/1_Ba...FEM/coefficient.html )
In the evaluate you need to integrate f over the mesh with the fixed x from the mip that you get in the evaluate.
Hope this helps, if you have questions or run into problems with the cpp extension let us know.

Best
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4 years 5 months ago - 4 years 5 months ago #2749 by philipp
Replied by philipp on topic Integral over product space
I got to work on your suggestion, but sadly got stuck on the following error
that occurs when I import myngspy that I build from the code of "mylittlengsolve":
Code:
ImportError: generic_type: type "MyCoefficient" referenced unknown base type "ngfem::CoefficientFunction"
I modified the example to only implement the MyCoefficient class, so my myngspy.cpp file is slightly different (attached), but that shouldn't be the problem as far as I understand.
After some digging I suspect that it is related to the pybind-export code for CoefficientFunction not
being executed before my import, but I can't figure out how I enforce this.

Do you have any suggestions?

Thank you very much
Philipp
Attachments:
Last edit: 4 years 5 months ago by philipp.
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4 years 5 months ago #2750 by christopher
Hi,
usually the statement py::module::import("ngsolve"); sould execute the ngsolve python export.
Another option would be to do the "import ngsolve" before importing your module.
Can you zip your whole example and attach it?
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