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lfa-lab's Issues

Restriction and Interpolation for Systems of Equations

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?

gallery_test.py broken

This particular test seems to be broken:

======================================================================
ERROR: test_fw_restriction_2 (gallery_test.GalleryTest)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "lfa-lab/test/gallery_test.py", line 62, in test_fw_restriction_2
    s = fw_restriction_stencil(grid)
TypeError: fw_restriction_stencil() takes exactly 2 arguments (1 given)

======================================================================
ERROR: test_fw_restriction_3 (gallery_test.GalleryTest)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "lfa-lab/test/gallery_test.py", line 74, in test_fw_restriction_3
    s = fw_restriction_stencil(grid)
TypeError: fw_restriction_stencil() takes exactly 2 arguments (1 given)

======================================================================
ERROR: test_ml_interpolation_2 (gallery_test.GalleryTest)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "lfa-lab/test/gallery_test.py", line 29, in test_ml_interpolation_2
    s = ml_interpolation_stencil(grid)
TypeError: ml_interpolation_stencil() takes exactly 2 arguments (1 given)

======================================================================
ERROR: test_ml_interpolation_3 (gallery_test.GalleryTest)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "lfa-lab/test/gallery_test.py", line 40, in test_ml_interpolation_3
    s = ml_interpolation_stencil(grid)
TypeError: ml_interpolation_stencil() takes exactly 2 arguments (1 given)

----------------------------------------------------------------------

Best way to compute h-ellipticity?

(This is a support question not a bug or other real issue.)

Suppose I define an operator but not a smoother (splitting):

from lfa_lab import *                                                              
fine = Grid(2, [1.0/32, 1.0/32])                                                   
L = gallery.poisson_2d(fine)

I want the h-ellipticity as defined by Trottenberg et al seciton 4.7, i.e. E_h(L) = min(|lshigh|) / max(|ls|) where ls is the symbol of L and lshigh is the symbol over the high-frequency modes.

I can imagine various awkward methods for computing E_h(L) but I wonder what you would suggest?

PS Just found your nice library!

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