def test_reaction_diffusion(resolution, alpha):
grid_x = field.UniformPeriodicGrid(resolution, 20)
grid_y = field.UniformPeriodicGrid(resolution, 20)
domain = field.Domain((grid_x, grid_y))
x, y = domain.values()
IC = np.exp(-(x+(y-10)**2-14)**2/8)*np.exp(-((x-10)**2+(y-10)**2)/10)
c = field.Field(domain)
X = field.FieldSystem([c])
c.data[:] = IC
D = 1e-2
dcdx2 = spatial.FiniteDifferenceUniformGrid(2, 8, c, 0)
dcdy2 = spatial.FiniteDifferenceUniformGrid(2, 8, c, 1)
rd_problem = equations.ReactionDiffusion2D(X, D, dcdx2, dcdy2)
dt = alpha*grid_x.dx
while rd_problem.t < 1-1e-5:
rd_problem.step(dt)
try:
solution = np.loadtxt('c_%i.dat' % resolution)
except:
solution = np.loadtxt('answers2/c_%i.dat' % resolution)
error = np.max(np.abs(solution - c.data))
error_est = error_RD[(resolution,alpha)]
assert error < error_est
def test_RK_3_2(resolution):
grid = field.UniformPeriodicGrid(resolution, 2 * np.pi)
x = grid.values
IC = np.exp(-(x - np.pi)**2 * 8)
u = field.Field(grid, IC)
target = np.exp(-(x - np.pi - 2 * np.pi * 0.2)**2 * 8)
d = spatial.FiniteDifferenceUniformGrid(1,
2,
grid,
stencil_type='centered')
stages = 3
a = np.array([[0, 0, 0], [1 / 2, 0, 0], [-1, 2, 0]])
b = np.array([1, 4, 1]) / 6
ts = timesteppers.Multistage(u, d, stages, a, b)
alpha = 0.5
num_periods = 1.8
ts.evolve(2 * np.pi * num_periods, alpha * grid.dx)
error = np.max(np.abs(u.data - target))
error_est = error_RK_3_2[resolution]
assert error < error_est
def test_AB_4_4(resolution):
grid = field.UniformPeriodicGrid(resolution, 2 * np.pi)
x = grid.values
IC = np.exp(-(x - np.pi)**2 * 8)
u = field.Field(grid, IC)
target = np.exp(-(x - np.pi + 2 * np.pi * 0.2)**2 * 8)
d = spatial.FiniteDifferenceUniformGrid(1,
4,
grid,
stencil_type='centered')
steps = 4
alpha = 0.25
num_periods = 1.2
ts = timesteppers.AdamsBashforth(u, d, steps, alpha * grid.dx)
ts.evolve(2 * np.pi * num_periods, alpha * grid.dx)
error = np.max(np.abs(u.data - target))
error_est = error_AB_4_4[resolution]
print(error)
assert error < error_est
def test_nu_BDF5_wave(resolution, spatial_order):
grid = field.UniformPeriodicGrid(resolution, 2 * np.pi)
x = grid.values
IC = np.exp(-(x - np.pi)**2 * 8)
u = field.Field(grid, IC)
target = np.exp(-(x - np.pi + 2 * np.pi * 0.2)**2 * 8)
d = spatial.FiniteDifferenceUniformGrid(1,
spatial_order,
grid,
stencil_type='centered')
ts = timesteppers.BackwardDifferentiationFormula(u, d, 5)
alpha = 0.5
num_periods = 1.2
ts.evolve(0.5 * np.pi * num_periods, alpha * grid.dx)
ts.evolve(1.25 * np.pi * num_periods, alpha * grid.dx / 3)
ts.evolve(2 * np.pi * num_periods, alpha * grid.dx / 2)
error = np.max(np.abs(u.data - target))
error_est = error_nu_BDF5_wave[(resolution, spatial_order)]
assert error < error_est
def test_nu_BDF4_diff(resolution, spatial_order):
grid = field.UniformPeriodicGrid(resolution, 50)
x = grid.values
IC = np.exp(-(x - 30)**2 / 4)
u = field.Field(grid, IC)
target = 1 / np.sqrt(5) * np.exp(-(x - 30)**2 / 20)
d = spatial.FiniteDifferenceUniformGrid(2,
spatial_order,
grid,
stencil_type='centered')
ts = timesteppers.BackwardDifferentiationFormula(u, d, 4)
alpha = 0.2
ts.evolve(1, alpha * grid.dx / 2)
ts.evolve(3, alpha * grid.dx / 3)
ts.evolve(4, alpha * grid.dx)
error = np.max(np.abs(u.data - target))
error_est = error_nu_BDF4_diff[(resolution, spatial_order)]
assert error < error_est
def test_derivative_1(resolution, convergence_order):
grid = field.UniformNonPeriodicGrid(resolution, (0, 5))
domain = field.Domain([grid])
x = grid.values
u = field.Field(domain, np.sin(x))
du_op = spatial.FiniteDifferenceUniformGrid(1, convergence_order, u)
du = du_op.evaluate()
error = np.max(np.abs(du.data - np.cos(x)))
error_est = error_derivative_1[(resolution, convergence_order)]
assert error < error_est
def test_BDF6_wave(resolution):
grid = field.UniformPeriodicGrid(resolution, 2 * np.pi)
x = grid.values
IC = np.exp(-(x - np.pi)**2 * 8)
u = field.Field(grid, IC)
target = np.exp(-(x - np.pi - 2 * np.pi * 0.2)**2 * 8)
d = spatial.FiniteDifferenceUniformGrid(1,
6,
grid,
stencil_type='centered')
ts = timesteppers.BackwardDifferentiationFormula(u, d, 6)
alpha = 0.5
num_periods = 1.8
ts.evolve(2 * np.pi * num_periods, alpha * grid.dx)
error = np.max(np.abs(u.data - target))
error_est = error_BDF6_wave[resolution]
assert error < error_est