How to add values of outer product to function in TensorFunctionSpace in parallel

Question

Hi!

A small code chunk as this:

TFS = TensorFunctionSpace(mesh, "CG", 1)
L = Function(TFS)
u_outer = outer(u, u)

Where u is some valued Function in a VectorFunctionSpace. How can u_outer be added to L in a smart way such that L becomes a function filled with the values in u_outer? Is it even possible?

I ask because the normal way of doing this applying project(u_outer, TFS) does not work in parallel (yields allow_extrapolation error, I can't allow extrapolation since it destroys my whole solver), in addition I want to apply the LagrangeInterpolator function, hence both arguments then needs to be functions..

Thanks!

Answer 1

Something like this could perhaps do the trick?

from dolfin import *

mesh = UnitSquareMesh(4, 4)
Q = FunctionSpace(mesh, "CG", 1)
V = VectorFunctionSpace(mesh, "CG", 1)
T = TensorFunctionSpace(mesh, "CG", 1)
u = interpolate(Constant((1,2)), V)
uiuj = Function(T)
dummy = Function(Q)
u0 = Function(Q)
u1 = Function(Q)
assign(u0, u.sub(0))
assign(u1, u.sub(1))
dummy.vector()[:] = u0.vector()*u0.vector() 
assign(uiuj.sub(0), dummy)
dummy.vector()[:] = u0.vector()*u1.vector() 
assign(uiuj.sub(1), dummy)
assign(uiuj.sub(2), dummy) # symmetric
dummy.vector()[:] = u1.vector()*u1.vector() 
assign(uiuj.sub(3), dummy)

Comments

Thanks Mikael for your excellent answer!

Answer 2

You can try

L = project(u_outer, TFS)

It's a bit expensive as it inverts a mass matrix, but it should work for general expressions.

Comments

Thanks for your answer martinal!

I forgot to provide critical information regarding my question: the problem occurrs when I'm trying to run this in parallel. On one processor project works fine, however on several processors project yields allow_extrapolation-error...

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Is u on a different mesh?