Solving Wigner time evolution as in xmds2

1

Hi everybody!

I am quite new in fenics with a background in physics. I am trying to solve the time evolution of Wigner function as in the worked-out example of xmds2 (http://www.xmds.org/worked_examples.html#wignerarguments) - Wigner Function.

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am facing two issues in doing it in fenics:

  1. Converting to weak form: e.g., how to work with terms like x*d^3W/dx^2dy

  2. Writing the expression: unlike the examples given in fenics website and the books, the equation has x and y terms (and maybe terms like x^2 and xy, to be generalized) and mixed derivatives. How to write such terms?

Any help will be appreciated.

Thanks in advance!
Akira Kaneda
Tohoku University
Japan

2

Concerning your second question, partial derivatives can be written as Dx(u, 0), Dx(u, 1).
A good source for these things is the ufl manual:
https://readthedocs.org/projects/fenics-ufl/downloads/pdf/latest/