Dot vs inner and complex suport

1

I’m sorry for creating a topic for such a short question but I don’t seem to find its answer in any place in the documentation (am I not searching in the right way?)

The question is: Is there any difference between dot and inner ? because I’ve seen codes with one or the other.

And talking about that, If dolfin-x has complex support. Does it means that every funcional space that I create is already complex valued? do real values are considered just a subset of complex values? Is there any keyword to specify a space to be complex/real?

Thank you very much, I’m sorry if this is already clear in the documentation.

2

See the comment in: Implementation — FEniCSx tutorial
and Form language — Unified Form Language (UFL) 2021.1.0 documentation

In DOLFINx you can create a function if any type by specifying the dtype, see: dolfinx.fem — DOLFINx 0.8.0.0 documentation

However, to be able to solve problems, you would need to use PETSc with appropriate floating type.
In the docker images dolfinx/dolfinx, pre-installed versions of the real-32 (default) and (complex-32)
version of PETSc (linked with DOLFINx) is installed, and can be accessed by calling source dolfinx-complex-mode or source dolfinx-real-mode (as explained in: GitHub - FEniCS/dolfinx: Next generation FEniCS problem solving environment)

3

Thank you very much for pointing me to the documentation.

By the way, in the documentation says:

For variational formulations with complex numbers, one cannot use ufl.dot to compute inner products. One has to use ufl.inner, with the test-function as the second input argument for ufl.inner

I understood that the problem was that dot was not an inner product, as it was not conjugating the second argument. However, the docstring of doc (in version 0.3.0) is:

Docstring: UFL operator: Take the dot product of a and b. The complex conjugate of the second argument is taken.

Is still necessary to use the inner function?

4

The docstring in the documentation is wrong, as illustrated by this minimal example:

import ufl
import dolfinx
from mpi4py import MPI
mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)
V = dolfinx.fem.FunctionSpace(mesh, ufl.VectorElement("Lagrange", mesh.ufl_cell(), 1))
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(u, v) * ufl.dx
print(str(a))
A = dolfinx.fem.form(a)
a2 = ufl.dot(u, v) * ufl.dx
print(str(a2))
A2 = dolfinx.fem.form(a2)

but also the actual source code

5

Can you paste the output of your minimal example? I have version 0.3.0 and it does not have dolfinx.mesh.create_unit_square

6

You can do this with pure ufl as well:

import ufl
cell = ufl.triangle
c_el = ufl.VectorElement("Lagrange", cell, 1)
mesh = ufl.Mesh(c_el)
V = ufl.FunctionSpace(mesh, c_el)
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(u, v) * ufl.dx
print(str(a))
a2 = ufl.dot(u, v) * ufl.dx
print(str(a2))

returning

{ conj(((v_0) : (v_1))) } * dx(<Mesh #0>[everywhere], {})
{ (v_1) . (v_0) } * dx(<Mesh #0>[everywhere], {})

I’ve created an issue at Error in online documentation · Issue #106 · FEniCS/ufl · GitHub

7

Thank you very much, I’m very new to all of this and I have problems creating the MWE that help me see the differences. I hope I improve with time