Why are Expressions obtained via subclassing Expression in Python interpolated but not evaluated on

Question

I have written code in Python using fenics, dolfin etc. to solve the three dimensional Schroedinger Equation. For my choice of potential and weight function I observer slow or non-existing convergence to theoretically known values. After counting the number of calls to the python class implementing the potential I realized, that this does not depend on the interpolation order chosen via parameters["form_compiler"]["quadraturedegree"] but is consistent with being called at all nodes of the interpolation. Is there a way to change a parameter such that the Expression is evaluated at all integration grid points, of course at the cost of much larger CPU time? I will not be able to use fenics for publishable results if this cannot be done/fixed

Answer 1

Expressions are interpolated in a finite element space. To control the space in which an Expression is interpolated, you can supply the finite element as an argument. Take a look at

http://fenicsproject.org/documentation/dolfin/1.2.0/python/programmers-reference/functions/expression/Expression.html#dolfin.functions.expression.Expression

for examples, especially Points 1 and 3.

If you want to evaluate an Expression at quadrature points, then define your Expression on a QuadratureElement, e.g.

element = FiniteElement("Quadrature", triangle, 3)

where 3 is the degree in the above case.

Comments

Dear Garth

Thanks a lot for your answer.
I am now quite a lot wiser.
Thus, in order to increase my accuracy I need to use a higher order function space.
However, what I really would like Is a way to force dolfin to evaluate the
factors / functipns appearing in my bilinear form at all integration grid points!
Is there any way to achieve this without rewriting ffc etc from scratch?

regards

Moritz

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I've edited my answer to also explain how to evaluate an Expression at quadrature points.