def test_same_grid():
"""Computes the observed order of convergence using three solutions
on the same grid.
The first and last fields are a zero-solution; the middle solution is random.
Therefore, no matter the norm used, we expect an order of convergence of 0.
"""
# create grid
x, y = numpy.linspace(0.0, 1.0, 11), numpy.linspace(0.0, 10.0, 51)
# create three fields on the same grid
field1 = Field(x=x, y=y, time_step=0, label='field1',
values=numpy.zeros((y.size, x.size)))
field2 = Field(x=x, y=y, time_step=0, label='field2',
values=numpy.random.rand(y.size, x.size))
field3 = Field(x=x, y=y, time_step=0, label='field3',
values=numpy.zeros((y.size, x.size)))
# compute observed order of convergence in L2-norm
p = convergence.get_observed_order(field1, field2, field3,
3, [field1.x, field1.y])
assert p == 0.0
# compute observed order of convergence in Linf-norm
p = convergence.get_observed_order(field1, field2, field3,
3, [field1.x, field1.y],
order=numpy.inf)
assert p == 0.0
def test_get_observed_order(self):
p = convergence.get_observed_order(self.coarse,
self.coarse2,
self.coarse,
self.ratio,
self.grid,
order=None)
assert abs(p - 0.0) <= atol
p = convergence.get_observed_order(self.coarse,
self.coarse2,
self.coarse,
self.ratio,
self.grid,
order=numpy.inf)
assert abs(p - 0.0) <= atol
p = convergence.get_observed_order(self.coarse,
self.medium,
self.fine,
self.ratio,
self.grid,
order=None)
assert abs(p - 1.0) <= atol
p = convergence.get_observed_order(self.coarse,
self.medium,
self.fine,
self.ratio,
self.grid,
order=numpy.inf)
assert abs(p - 1.0) <= atol
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_get_observed_order(self):
p = convergence.get_observed_order(self.coarse, self.coarse2, self.coarse,
self.ratio, self.grid, order=None)
assert abs(p - 0.0) <= atol
p = convergence.get_observed_order(self.coarse, self.coarse2, self.coarse,
self.ratio, self.grid, order=numpy.inf)
assert abs(p - 0.0) <= atol
p = convergence.get_observed_order(self.coarse, self.medium, self.fine,
self.ratio, self.grid, order=None)
assert abs(p - 1.0) <= atol
p = convergence.get_observed_order(self.coarse, self.medium, self.fine,
self.ratio, self.grid, order=numpy.inf)
assert abs(p - 1.0) <= atol
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_same_grid():
"""Computes the observed order of convergence using three solutions
on the same grid.
The first and last fields are a zero-solution; the middle solution is random.
Therefore, no matter the norm used, we expect an order of convergence of 0.
"""
# create grid
x, y = numpy.linspace(0.0, 1.0, 11), numpy.linspace(0.0, 10.0, 51)
# create three fields on the same grid
field1 = Field(x=x,
y=y,
time_step=0,
label='field1',
values=numpy.zeros((y.size, x.size)))
field2 = Field(x=x,
y=y,
time_step=0,
label='field2',
values=numpy.random.rand(y.size, x.size))
field3 = Field(x=x,
y=y,
time_step=0,
label='field3',
values=numpy.zeros((y.size, x.size)))
# compute observed order of convergence in L2-norm
p = convergence.get_observed_order(field1, field2, field3, 3,
[field1.x, field1.y])
assert p == 0.0
# compute observed order of convergence in Linf-norm
p = convergence.get_observed_order(field1,
field2,
field3,
3, [field1.x, field1.y],
order=numpy.inf)
assert p == 0.0
