Quadrature over part of a mesh

[ethrelfall]

Dear community,

I've got a 2D domain on which I have a scalar function. I know how to integrate the function over the entire domain in Firedrake, but it is possible to integrate it over the entire range of y but a particular range in x (e.g. from x0 to x1), please?

I don't think I want to do it by multiplying the scalar function by a window function BTW.

Search for matching discussions done.

Thanks!

[colinjcotter]

For that you need to generate a mesh (eg using gmsh or netgen) so that the subdomain you want to integrate over is tagged. Then you provide the subdomain tag to the dx measure: dx(<tag>) On 28 Jan 2024, at 20:44, ethrelfall ***@***.***> wrote:  Dear community, I've got a 2D domain on which I have a scalar function. I know how to integrate the function over the entire domain in Firedrake, but it is possible to integrate it over the entire range of y but a particular range in x (e.g. from x0 to x1), please? I don't think I want to do it by multiplying the scalar function by a window function BTW. Search for matching discussions done. Thanks! — Reply to this email directly, view it on GitHub<#3365>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4XAMKYGYIUWXXZZ5KLYQ22DNAVCNFSM6AAAAABCON7L32VHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZWGE2DINJRGM>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[ethrelfall]

Many thanks. I don't think the suggested will work for what I'm trying to do (kinetics, viz.

wh. f and phi are scalars in a 2D domain coordinatized by (x,v)).

In the same vein, I assume I can't do a line integral (e.g. along a vertical line in a 2D domain) without meshing the line and identifying it as a domain.

So OK, I think I can't do the above problem in FD without using fudges or being capable enough to add new features (which I'm not).

Cheers,

Ed.

[colinjcotter]

Ah, you are talking about the projection in Vlasov. I have a few approaches to that, probably best if we meet for a chat instead of Github discussions as it depends on discretisation choices. I’m running an MSc project on kinetics with Firedrake currently. Re: the line. This can be discretised as a quadrature sum, and implemented using vertex only mesh. But it might be better for us to discuss what you want to do. On 29 Jan 2024, at 08:00, ethrelfall ***@***.***> wrote:  Many thanks. I don't think the suggested will work for what I'm trying to do (kinetics, viz. image.png (view on web)<https://github.com/firedrakeproject/firedrake/assets/77395015/32e8e84e-72ff-4a46-9433-4e118792e130> wh. f and phi are scalars in a 2D domain coordinatized by (x,v)). In the same vein, I assume I can't do a line integral (e.g. along a vertical line in a 2D domain) without meshing the line and identifying it as a domain. So OK, I think I can't do the above problem in FD without using fudges or being capable enough to add new features (which I'm not). Cheers, Ed. — Reply to this email directly, view it on GitHub<#3365 (reply in thread)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4VOEAKUBWE2UEFXTW3YQ5JHVAVCNFSM6AAAAABCON7L32VHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4DENZYGEZTI>. You are receiving this because you commented.Message ID: ***@***.***>

[ethrelfall]

Many thanks, maybe we can talk after meeting later this week.

[dham]

Just to add, using cross-mesh interpolation you can actually mesh the line independently of the domain and then interpolate the expression onto the line and integrate. This is hot-off-the press Firedrake functionality that has been fully merged in the last month.

[ethrelfall]

Thanks David, that sounds like just what's needed for this sort of thing.

[colinjcotter]

I actually realised after our chat today that this less complicated than I was saying. If you have an extruded mesh, then make Phi in a function space that is independent of the depth (extruded direction) using vfamily = "R". Then the Phi equation (with test function from the same space) will restrict to depth independent functions.

The equation becomes

$$ \int p_x \Phi_x ,d x = \int p \omega_P^2 (H\frac{f}{v_N} - 1) ,dx, \quad \forall p \in \bar{V},$$

where $\bar{V}$ is the depth independent space, and $H$ is the height of your domain (that you are approximating for an infinite height), and
where here the $dx$ integral means integration over space and velocity coordinates (so integrating over your whole x-v mesh as usual).

This works because everything except for $f$ is independent of depth, so you can take the vertical part of the double integral and put it around $f$ only.

[colinjcotter]

This only works for a 1D velocity coordinate though.

[ethrelfall]

Thanks Colin - I've implemented and it looks right ...