def test_three_grids(nx=11, ny=11, ratio=3, offset=0):
"""Computes the observed order of convergence using the solution on three
consecutive grids with constant refinement ratio.
The solution on the finest grid is random.
The solution of the medium grid is the finest solution restricted
and incremented by 1.
The solution of the coarsest grid is the finest solution restricted
and incremented by 1+ratio.
Therefore, no matter the norm used, we expect an order of convergence of 1.
Parameters
----------
nx, ny: integers, optional
Number of grid-points along each direction on the grid used a mask
to project the three solutions;
default: 11, 11.
ratio: integer, optional
Grid refinement ratio;
default: 3.
offset: integer, optional
Position of the coarsest grid relatively to the mask grid;
default: 0 (the coarsest solution is defined on the mask grid)
"""
# grid used as mask
grid = [numpy.random.random(nx), numpy.random.random(ny)]
# create fields
fine = Field(values=numpy.random.rand(ny * ratio**(offset + 2),
nx * ratio**(offset + 2)),
label='fine')
medium = Field(values=fine.values[::ratio, ::ratio] + 1.0, label='medium')
coarse = Field(values=fine.values[::ratio**2, ::ratio**2] + (1.0 + ratio),
label='coarse')
# fill nodal stations
coarse.x, coarse.y = numpy.ones(nx * ratio**offset), numpy.ones(
ny * ratio**offset)
coarse.x[::ratio**offset], coarse.y[::ratio**offset] = grid[0][:], grid[
1][:]
medium.x, medium.y = numpy.ones(nx * ratio**(offset + 1)), numpy.ones(
ny * ratio**(offset + 1))
medium.x[::ratio**(offset +
1)], medium.y[::ratio**(offset +
1)] = grid[0][:], grid[1][:]
fine.x, fine.y = numpy.ones(nx * ratio**(offset + 2)), numpy.ones(
ny * ratio**(offset + 2))
fine.x[::ratio**(offset +
2)], fine.y[::ratio**(offset +
2)] = grid[0][:], grid[1][:]
# compute observed order of convergence
p = convergence.get_observed_order(coarse, medium, fine, ratio, grid)
assert p == 1.0
p = convergence.get_observed_order(coarse,
medium,
fine,
ratio,
grid,
order=numpy.inf)
assert p == 1.0
def test_three_grids(nx=11, ny=11, ratio=3, offset=0):
"""Computes the observed order of convergence using the solution on three
consecutive grids with constant refinement ratio.
The solution on the finest grid is random.
The solution of the medium grid is the finest solution restricted
and incremented by 1.
The solution of the coarsest grid is the finest solution restricted
and incremented by 1+ratio.
Therefore, no matter the norm used, we expect an order of convergence of 1.
Parameters
----------
nx, ny: integers, optional
Number of grid-points along each direction on the grid used a mask
to project the three solutions;
default: 11, 11.
ratio: integer, optional
Grid refinement ratio;
default: 3.
offset: integer, optional
Position of the coarsest grid relatively to the mask grid;
default: 0 (the coarsest solution is defined on the mask grid)
"""
# grid used as mask
grid = [numpy.random.random(nx), numpy.random.random(ny)]
# create fields
fine = Field(values=numpy.random.rand(ny*ratio**(offset+2), nx*ratio**(offset+2)),
label='fine')
medium = Field(values=fine.values[::ratio, ::ratio]+1.0,
label='medium')
coarse = Field(values=fine.values[::ratio**2, ::ratio**2]+(1.0+ratio),
label='coarse')
# fill nodal stations
coarse.x, coarse.y = numpy.ones(nx*ratio**offset), numpy.ones(ny*ratio**offset)
coarse.x[::ratio**offset], coarse.y[::ratio**offset] = grid[0][:], grid[1][:]
medium.x, medium.y = numpy.ones(nx*ratio**(offset+1)), numpy.ones(ny*ratio**(offset+1))
medium.x[::ratio**(offset+1)], medium.y[::ratio**(offset+1)] = grid[0][:], grid[1][:]
fine.x, fine.y = numpy.ones(nx*ratio**(offset+2)), numpy.ones(ny*ratio**(offset+2))
fine.x[::ratio**(offset+2)], fine.y[::ratio**(offset+2)] = grid[0][:], grid[1][:]
# compute observed order of convergence
p = convergence.get_observed_order(coarse, medium, fine, ratio, grid)
assert p == 1.0
p = convergence.get_observed_order(coarse, medium, fine, ratio, grid,
order=numpy.inf)
assert p == 1.0
