Runs nice with linear elements CG1 but fails with quadratic elements CG2

Question

Dear Fenics community,

I would like to share the following problem with you. In a nutshell: Everything works fine with CG(1) Elements, but as soon as I try higher degree elements, the computation takes a lot of time, even with very small problems, for example

Here are the details. I have a strain gradient elasticity implemented (4th order PDE) via two coupled 2nd order PDE. A cube is fixed on the bottom face, on the top face an indentation test is performed. Here is the derivation from the PDE to the weak form:

The last integral equation has been implemented in the following py file:

minimum_example_strain_gradient_elasticity_3d
It runs nicely and gives reasonable results for linear CG elements. However, changing

FunctionSpace(mesh, "CG", 1) 

to

FunctionSpace(mesh, "CG", 2) 

with only 48 Elements practically kills the computer. I get results for pretty small problems after waiting a long time. Sometimes i have to increase the recursion limit,

sys.setrecursionlimit(10000)

sometimes I need to use the MUMPS solver

solve(a == L, w, bc, solver_parameters={'linear_solver':'mumps'})

Can somebody suggest something?

Answer 1

Try still experimental UFLACS compiler

from dolfin import *
parameters['form_compiler']['representation'] = 'uflacs'

# The rest of the program

It is known to scale much better than FFC quadrature backend with the increasing complexity of forms.

Comments

When I do this I get

ImportError: No module named uflacs.backends.ffc.representation

when

FunctionSpace(mesh, "CG", 1)

is called.

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