[firedrake] Interpolate function only on the boundary

[Ham, David A]

Hi Andrew,

Why do you need to interpolate at all? Just set g to be the expression and put g straight into the linear form. The expression will be directly evaluated at the surface quadrature points when the form is assembled. Interpolation is just extra work and, possibly, extra rounding error.

David

From: Andrew Hicks <ahick17 at lsu.edu>
Date: Sunday, 14 March 2021 at 20:50
To: Ham, David A <david.ham at imperial.ac.uk>, firedrake <firedrake at imperial.ac.uk>
Subject: Re: Interpolate function only on the boundary
Hi David,

That isn’t actually what I’m attempting to do, it was an example (and now that you mention it, a pretty bad example) to show you more or less what I’m doing.

I have attached a PDF with a PDE as a better example to illustrate what I need to do (though the problem is still a bit contrived). If you go down to where “g” is defined, you will see my conundrum, because I need to use the interpolater to handle the trigonometric functions, and I don’t want to needlessly separate everything into several expressions, but have it all just be “g”, which I can then easily insert into my linear form (the main reason for this is because the actual problem I’m working on has a lot of automation in the code, and I don’t want to needlessly complicate things).

Andrew

________________________________
From: Ham, David A <david.ham at imperial.ac.uk>
Sent: Sunday, March 14, 2021 4:15:38 AM
To: Andrew Hicks <ahick17 at lsu.edu>; firedrake <firedrake at imperial.ac.uk>
Subject: Re: Interpolate function only on the boundary


Hi Andrew,



Interpolating facet expressions doesn’t work as the interpolation code works cell-wise.



However, can I ask more generally what you are attempting to do? I think dot(nu,nu)=1 on the boundary so I don’t quite understand what you are trying to achieve.



It is possible to project expressions defined only on the boundary, or to use them directly in boundary conditions, but I think we’d need to see what maths you are attempting to achieve in order to be able to say how to do it.



Cheers,



David



From: firedrake-bounces at imperial.ac.uk <firedrake-bounces at imperial.ac.uk> on behalf of Andrew Hicks <ahick17 at lsu.edu>
Date: Sunday, 14 March 2021 at 04:59
To: firedrake <firedrake at imperial.ac.uk>
Subject: [firedrake] Interpolate function only on the boundary

Dear all,



I am wanting to interpolate an expression involving the FacetNormal, but when I execute the following code:



V = FunctionSpace(mesh,’CG’,1)

nu = FacetNormal(mesh)

g = interpolate(dot(nu,nu),V)



Of course I get an AssertionError because the FacetNormal is only defined on the exterior facets of the mesh, and not the interior. My question is, is there perhaps a way to make “g” to be defined as “dot(nu,nu)” on the boundary, and 0 everywhere else? I bet this would work well. Or maybe there is a way to define “g” only on the boundary?



Andrew Hicks
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