Creating CoefficientFunctions or GridFunctions Using Integration

Hello!

I am new to NGSolve and would like to follow up on a similar question .

I am solving a three dimensional problem and as part of my weak form, I need to implement a vector valued quantity that arises through integration of a coefficient function defined on the bottom of my domain. The integration is wrt z and the result should be a CoefficientFunction or a GridFunction defined on the whole domain.

To do this, I am trying to implement numerical integration myself and essentially create a CoefficientFunction holding the result (though I am not certain this is the most convenient way to do this either). Therefore I would need to create a CoefficientFunction or a GridFunction from a vector or array holding the values from the numerical integration.

My questions are:

1. Is there a better way to do this numerical integration?
2. How could I go about setting a GridFunction or CoefficientFunction containing the results if there is no better way?

Thanks in advance,
Josie

Could you provide a short mathematical description of what you want to do? Maybe with a sketch or something? From what I would understand you can do something like:
Best
Christopher

Hello Christopher,

sorry for being unclear. A rough explanation of my problem is that my bilinear form is a convection operator and I was having trouble implementing the vector that acts as the wind.
This is because each component of the wind arises through integration of a function (that we will call phi), i.e. The expression for the wind is actually more complicated, but my question is about evaluating this type of integral: Is there a nicer way to evaluate this integral using NGSolve than by writing a numerical integration scheme myself?
Thanks,
Josie

Hi Josie,
you could use another Python package, for example scipy.integrate for that.
Best Christopher