Interpolate on MixedFunctionSpace

Question

Hi all,

This question is somehow related to
http://fenicsproject.org/qa/8556/interpolation-on-mixef-function-space-failled,
but the above Q/A is too problem specific and I can not understand how to use it to solve my problem.

I would like to understand better why the following piece of code does not behave as expected
(I have tried using both FEniCS 1.5 and FEniCS 1.6).

mesh = dl.UnitSquareMesh(10,10)
V1 = dl.VectorFunctionSpace(mesh, "CG", 2)
V2 = dl.FunctionSpace(mesh, "CG", 1)
V3 = dl.FunctionSpace(mesh, "CG", 1)
V = dl.MixedFunctionSpace([V1,V2,V3])

f1 = dl.Expression( ("A + B*x[1]*(1-x[1])", "0."), A=1., B=1.)
f2 = dl.Expression( "A*x[0]", A=1.)
f3 = dl.Expression( "A", A = -3.)

state = dl.Function(V)
state.sub(0,deepcopy=False).assign( dl.interpolate(f1, V1))
state.sub(1,deepcopy=False).assign( dl.interpolate(f2, V2))
state.sub(2,deepcopy=False).assign( dl.interpolate(f3, V3))

print "|| state ||^2_L^(2) = ", dl.assemble( dl.inner(state, state)*dl.dx)

dl.plot(state.sub(0))
dl.plot(state.sub(1)) 
dl.plot(state.sub(2))

I would expect this code to initialize each component of the state to the functions f1,f2,f3.
However the output of the code is

|| state ||^2_L^(2) = 0.0

and the three plots are identically 0.

What I am missing? This seems that sub() command creates a copy instead of a view of the underlying data.

Could you please suggest some workaround? Please note that the expressions for f1,f2,f3 are actually more complicated, and they MUST use the additional parameters A and B.

Thank you in advance!

Umbe

Comments

I have also tried out a similar technique, but I am getting the same result:

state = dl.Function(V)
s1, s2, s3 = state.split(deepcopy=False)
s1.assign(dl.interpolate(f1,V1))
s2.assign(dl.interpolate(f2,V2))
s3.assign(dl.interpolate(f3,V3))

print "|| (s1,s2,s3) ||^2_L^(2)  = ", dl.assemble( (dl.inner(s1,s1) + s2*s2 + s3*s3)*dl.dx)
print "|| state ||^2_L^(2) = ", dl.assemble( dl.inner(state, state)*dl.dx)

Output:

|| (s1,s2,s3) ||^2_L^(2) = 10.7
|| state ||^2_L^(2) = 0.0

Answer 1

Hi, consider using FunctionAssigner

import dolfin as dl

mesh = dl.UnitSquareMesh(10,10)
V1 = dl.VectorFunctionSpace(mesh, "CG", 2)
V2 = dl.FunctionSpace(mesh, "CG", 1)
V3 = dl.FunctionSpace(mesh, "CG", 1)
V = dl.MixedFunctionSpace([V1,V2,V3])

f1 = dl.Expression( ("A + B*x[1]*(1-x[1])", "0."), A=1., B=1.)
f2 = dl.Expression( "A*x[0]", A=1.)
f3 = dl.Expression( "A", A = -3.)

F1, F2, F3 = [dl.interpolate(fi, Vi) for fi, Vi in zip((f1, f2, f3), (V1, V2, V3))]

assigner = dl.FunctionAssigner(V, [V1, V2, V3])
state = dl.Function(V)
assigner.assign(state, [F1, F2, F3])

print "|| state ||^2_L^(2) = ", dl.assemble( dl.inner(state, state)*dl.dx)

dl.plot(state.sub(0))
dl.plot(state.sub(1)) 
dl.plot(state.sub(2))

dl.interactive()

Comments

Hi MiroK,

Thank you very much for pointing out the FunctionAssigner class.
It worked perfectly and it is also extremely clean.

However could you explain why does

state.sub(0,deepcopy=False).assign( dl.interpolate(f1, V1))

modify a temporary data, instead of the data in the state function?

Thanks,

Umberto