How the point source value assigned to the nodal points

variational formulation
1

Hi all,

I was wondering in the source code, how is FEnics “transferring” the point source value to the mesh points? It seems in 1D it is based on the distance between the mesh points and the source point, but how about higher dimensions? Thank you very much.

Kind regards,
Alice

2

What do you mean by transferring it? A point source is an evaluation of the basis functions at the given point in the element, i.e. if you put a point source in the middle of an element, you will get evaluations of basis functions in the middle of the element.

1 Like
3

Hi @dokken,

Thanks for the reply. I mean, indeed if you have a point source inside the mesh element but not at the mesh points, how do you compute the evaluations of the mesh points of this element that is caused by this point source?

4

As I said, a point source boils down to an addition to your integral of the form (given a mass matrix)
\int_\Omega uv \delta(x_p)~\mathrm{d}x= u(x_p)v(x_p)=\phi_i(x_p)\phi_j(x_p) where \delta is the point source at x_p, \phi_k the basis functions (defined in global coordinates).