Combining test and trial function from different spaces

1

Hello everybody,

i have a problem where i want to combine test and trial functions from different spaces at the end. Is this somehow possible in fenics?

Thanks!

2

This is common in mixed problems, and can be done. However, if you mix the trial and test functions for your global system, you end up with a non-square (rectangular) matrix, that will not be invertible.

3

Thank you dokken.
Does this mean that i have to use a semi-implicit method to solve the discrete equation or should i use the pseudoinvers? What are you suggesting please?

4

I am sorry dokken. How is it possible please?
I am just getting the error

Did you combine test or trial functions from different spaces?
The Arguments found are:
  v_1
  v_1
  v_0
  v_0
5

You can for instance do:

from dolfin import *
mesh = UnitSquareMesh(10, 10)
V1 = FiniteElement("Lagrange", triangle, 1)
V2 = FiniteElement("Lagrange", triangle, 1)
el = MixedElement([V1, V2])

V = FunctionSpace(mesh, el)
u1,u2 = TrialFunctions(V)
v1,v2 = TestFunctions(V)

a = inner(u1, v2) * dx
assemble(a)

However, this is assembled into a rectangular matrix.

The following minimal example shows how to assemble with different test and trial functions:

from dolfin import *
mesh = UnitSquareMesh(10, 10)
V1 = FunctionSpace(mesh, "CG", 1)
V2 = FunctionSpace(mesh, "CG", 2)

u = TrialFunction(V1)
v = TestFunction(V2)
A = assemble(inner(u,v)*dx)
A_petsc = as_backend_type(A)                                                                                                                                             

A_dense =  A_petsc.mat()[:,:]  
print(A_dense.shape)
6

Thank you very much again dokken!
You are so great!

7

Hi @dokken ,

Could you please post this minimal example using dolfinX?

Thank you very much in advance!

8 
import dolfinx
import ufl
from mpi4py import MPI
mesh = dolfinx.UnitSquareMesh(MPI.COMM_WORLD, 10, 10)
V1 = dolfinx.FunctionSpace(mesh, ("CG", 1))
V2 = dolfinx.FunctionSpace(mesh, ("CG", 2))

u = ufl.TrialFunction(V1)
v = ufl.TestFunction(V2)
A = dolfinx.fem.assemble_matrix(ufl.inner(u, v) * ufl.dx)
A.assemble()

A_dense = A[:, :]
print(A_dense.shape)
print(A_dense)
1 Like
9

Thank you very much @dokken !