Restriction and Interpolation for Systems of Equations

[jonas-schmitt]

Hi,

as there is already support for systems of equations with the the SystemNode class, it should be also possible to define restriction and interpolation operators that can be applied to a system. It is although not obvious to me how to do this.

As a concrete example consider the following biharmonic system:

from lfa_lab import *

fine = Grid(2, [1.0, 1.0])
coarse = fine.coarse((2, 2))

# Create a poisson operator.
L = gallery.poisson_2d(fine)
Z = L.matching_zero()
A = system([[L, Z], [operator.from_stencil([((0, 0), -1)], fine), L]])
R = gallery.fw_restriction(fine, coarse)
P = gallery.ml_interpolation(fine, coarse)
A_c = R * A * P # does obviously not work
A_c = system([[R, R * Z], [R * Z, R]]) * A * system([[P, Z * P], [Z * P, P]]) # does not work either
A_c.symbol()

How can one for example define the Galerkin coarse grid operator for this system?

[hrittich]

There were a few bugs in the SystemSymbol class and in the Python two_grid module and a few missing functions. The commit 36b96618a6552231401412befc4e62d0bfe56d61 should fix this issues.

I have added the file biharmonic_twogrid.py in the demo directory, which should make clear, how to make a two grid system analysis.

Please check if these changes fix your problems. Be aware that I did not check thoroughly the implementation for systems. Treat the results with some skepticism.

In case you have any problems, feel free to reopen the issue.

[jonas-schmitt]

Thank you! :)