Question about "MeshCoordinates()" in legacy FEniCS

Legacy DOLFIN
1

Hello :wave:
It’s been a while since I’ve posted a question

Recently, while exploring the legacy DOLFIN code, I came across the MeshCoordinates() function.
From posts ref1 and ref2, I thought it was a way to express the coordinate position of a declared mesh.
I ran a simple code with my Jupyter notebook,

from dolfin import * # version: 2019.1.0

lx, ly = 1.0, 1.0
elx, ely = 5, 5
msh = RectangleMesh(Point(0, 0), Point(lx, ly), elx, ely, diagonal="crossed")

x0, x1 = MeshCoordinates(msh)
print("x[0]: ", x0)
print("x[1]: ", x1)

the output was

x0:  f_3[0]
x1:  f_3[1]

The properties for the variables x0, x1 were as follows,

x0: Indexed(Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 0), VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2)), 3), MultiIndex((FixedIndex(0),)))
x1: Indexed(Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 0), VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2)), 3), MultiIndex((FixedIndex(1),)))

but it was hard to visually figure out what values they represented, hence the posting question.

My questions are:
a) What should I understand about the output of this function?
(MeshCoordinate(msh) seems to hold a lot of information.)

b) And in dolfinx, what is the function that does the same thing as MeshCoordinates()?
(Does this do the same thing as the tabulate_dof_coordinates() function? :thinking:)

2

MeshCoordinates gives you a symbolic expression for getting the vertices of the current cell, as stated in Bitbucket

It is unclear to me what the use-case of it is, as there are very few use-cases of it.

What do you want to use it for?

To me it feels like something created before ufl.SpatialCoordinate came around.

1 Like
3

Thanks for the quick reply :smiley:, @dokken:+1:!
The purpose of my exploration of the MeshCoordinates() was to convert the legacy DOLFIN code to dolfinx, which does the formula calculation for subdomains for a given mesh.

The code I was working on was similar to the code(conditional equation form) mentioned below,

and I wanted to convert this type of code to dolfinx.

You mentioned that MeshCoordinates() was a function that used before SpatialCoordinate(), and after reading that post, I googled clue1(Form compilation) and clue2(conditional.py github), and based on that,

# In dolfinx env. Assuming imported the ufl library beforehand
x0, x1 = SpatialCoordinate(mesh)
p_Ex = conditional(ge(0, x0-x1), -2*(exp(x0-x1)-1)/(exp(x0-x1)-1), -(x0-x1))

I was able to get the desired result when I ran the code in the form below.

An additional question I have is,
are MeshCoordinates() and SpatialCoordinate() the same function?
If SpatialCoordinate() came later, it seems like there would be some differences, then what differences have be…?

4

SpatialCoordinate gives you the physical coordinates of the quadrature points, which I assume is what you are after in your assembly routines.

Like this is giving you the expression

u(x0,x1)=\begin{cases} -2(e^{x0-x1}-1)/(e^{x0-x1}-1)=-2 \text{ if } 0>=x0-x1\\ -(x0-x1) \text{ otherwise } \end{cases}

Is that what you wanted?

5

Yep! @dokken, it’s similar to the form of equation my working with.
(I’m not sure about =2, though… :sweat_smile:)

By any chance, is it possible to make a declaration with additional conditions? In dolfinx environment.
(If possible, it would be helpful to have some code to compare to legacy DOLFIN to better understand.)
For example,

u(x0, x1)=\begin{cases} \frac{-2(e^{x0-x1}-1)}{e^{x0-x1}-1} & \text{if 0 $\gt$ $(x0-x1)$} \\ 0 & \text{if 0 $=$ $(x0-x1)$} \\ -(x0-x1) & \text{otherwise} \end{cases}

(I tweaked the equation a bit to add the term.)

As writing replies, I’m sure there are more questions I could ask. I apologize if I’ve bothered you :pray:

6

You can nest conditionals. There are several examples on the forum of this.

7

Thanks for the answer, it helped a lot! :raised_hands: