def test_boundary_integral(self):
mesh = get_2p1d_mesh_for_testing(include_particles=False)
spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"current collector": pybamm.ScikitFiniteElement(),
}
disc = pybamm.Discretisation(mesh, spatial_methods)
var = pybamm.Variable("var", domain="current collector")
disc.set_variable_slices([var])
full = pybamm.BoundaryIntegral(var)
neg = pybamm.BoundaryIntegral(var, region="negative tab")
pos = pybamm.BoundaryIntegral(var, region="positive tab")
full_disc = disc.process_symbol(full)
neg_disc = disc.process_symbol(neg)
pos_disc = disc.process_symbol(pos)
# check integrating 1 gives correct *dimensionless* region lengths
perimeter = 2 * (1 + 0.8)
l_tab_n = 0.1 / 0.5
l_tab_p = 0.1 / 0.5
constant_y = np.ones(mesh["current collector"].npts)
# Integral around boundary is exact
np.testing.assert_array_almost_equal(
full_disc.evaluate(None, constant_y), perimeter
)
# Ideally mesh edges should line up with tab edges.... then we would get
# better agreement between actual and numerical tab width
np.testing.assert_array_almost_equal(
neg_disc.evaluate(None, constant_y), l_tab_n, decimal=1
)
np.testing.assert_array_almost_equal(
pos_disc.evaluate(None, constant_y), l_tab_p, decimal=1
)
def test_mass_matrix_inverse(self):
# get mesh
mesh = get_2p1d_mesh_for_testing(ypts=5, zpts=5)
spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"current collector": pybamm.ScikitFiniteElement(),
}
# create model
a = pybamm.Variable("a", domain="negative electrode")
b = pybamm.Variable("b", domain="current collector")
model = pybamm.BaseModel()
model.rhs = {a: pybamm.Laplacian(a), b: 4 * pybamm.Laplacian(b)}
model.initial_conditions = {a: pybamm.Scalar(3), b: pybamm.Scalar(10)}
model.boundary_conditions = {
a: {"left": (0, "Neumann"), "right": (0, "Neumann")},
b: {"negative tab": (0, "Neumann"), "positive tab": (0, "Neumann")},
}
model.variables = {"a": a, "b": b}
# create discretisation
disc = pybamm.Discretisation(mesh, spatial_methods)
disc.process_model(model)
# test that computing mass matrix block-by-block (as is done during
# discretisation) gives the correct result
# Note: inverse is more efficient in csc format
mass_inv = inv(csc_matrix(model.mass_matrix.entries))
np.testing.assert_equal(
model.mass_matrix_inv.entries.toarray(), mass_inv.toarray()
)
def test_not_implemented(self):
mesh = get_2p1d_mesh_for_testing(include_particles=False)
spatial_method = pybamm.ScikitFiniteElement()
spatial_method.build(mesh)
self.assertEqual(spatial_method.mesh, mesh)
with self.assertRaises(NotImplementedError):
spatial_method.divergence(None, None, None)
with self.assertRaises(NotImplementedError):
spatial_method.indefinite_integral(None, None)
def test_definite_integral(self):
mesh = get_2p1d_mesh_for_testing()
spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"current collector": pybamm.ScikitFiniteElement(),
}
disc = pybamm.Discretisation(mesh, spatial_methods)
var = pybamm.Variable("var", domain="current collector")
y = pybamm.SpatialVariable("y", ["current collector"])
z = pybamm.SpatialVariable("z", ["current collector"])
integral_eqn = pybamm.Integral(var, [y, z])
disc.set_variable_slices([var])
integral_eqn_disc = disc.process_symbol(integral_eqn)
y_test = 6 * np.ones(mesh["current collector"][0].npts)
fem_mesh = mesh["current collector"][0]
ly = fem_mesh.coordinates[0, -1]
lz = fem_mesh.coordinates[1, -1]
np.testing.assert_array_almost_equal(
integral_eqn_disc.evaluate(None, y_test), 6 * ly * lz)
def test_neg_pos(self):
mesh = get_2p1d_mesh_for_testing()
spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"current collector": pybamm.ScikitFiniteElement(),
}
disc = pybamm.Discretisation(mesh, spatial_methods)
var = pybamm.Variable("var", domain="current collector")
disc.set_variable_slices([var])
extrap_neg = pybamm.BoundaryValue(var, "negative tab")
extrap_pos = pybamm.BoundaryValue(var, "positive tab")
extrap_neg_disc = disc.process_symbol(extrap_neg)
extrap_pos_disc = disc.process_symbol(extrap_pos)
# check constant returns constant at tab
constant_y = np.ones(mesh["current collector"][0].npts)[:, np.newaxis]
np.testing.assert_array_almost_equal(
extrap_neg_disc.evaluate(None, constant_y), 1)
np.testing.assert_array_almost_equal(
extrap_pos_disc.evaluate(None, constant_y), 1)
def test_definite_integral_vector(self):
mesh = get_2p1d_mesh_for_testing(include_particles=False)
spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"current collector": pybamm.ScikitFiniteElement(),
}
disc = pybamm.Discretisation(mesh, spatial_methods)
var = pybamm.Variable("var", domain="current collector")
disc.set_variable_slices([var])
# row (default)
vec = pybamm.DefiniteIntegralVector(var)
vec_disc = disc.process_symbol(vec)
self.assertEqual(vec_disc.shape[0], 1)
self.assertEqual(vec_disc.shape[1], mesh["current collector"].npts)
# column
vec = pybamm.DefiniteIntegralVector(var, vector_type="column")
vec_disc = disc.process_symbol(vec)
self.assertEqual(vec_disc.shape[0], mesh["current collector"].npts)
self.assertEqual(vec_disc.shape[1], 1)
def test_discretise_equations(self):
# get mesh
mesh = get_2p1d_mesh_for_testing(include_particles=False)
spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"current collector": pybamm.ScikitFiniteElement(),
}
disc = pybamm.Discretisation(mesh, spatial_methods)
# discretise some equations
var = pybamm.Variable("var", domain="current collector")
y = pybamm.SpatialVariable("y", ["current collector"])
z = pybamm.SpatialVariable("z", ["current collector"])
disc.set_variable_slices([var])
y_test = np.ones(mesh["current collector"].npts)
unit_source = pybamm.PrimaryBroadcast(1, "current collector")
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Neumann"),
"positive tab": (pybamm.Scalar(0), "Neumann"),
}
}
for eqn in [
pybamm.laplacian(var),
pybamm.source(unit_source, var),
pybamm.laplacian(var) - pybamm.source(unit_source, var),
pybamm.source(var, var),
pybamm.laplacian(var) - pybamm.source(2 * var, var),
pybamm.laplacian(var) - pybamm.source(unit_source ** 2 + 1 / var, var),
pybamm.Integral(var, [y, z]) - 1,
pybamm.source(var, var, boundary=True),
pybamm.laplacian(var) - pybamm.source(unit_source, var, boundary=True),
pybamm.laplacian(var)
- pybamm.source(unit_source ** 2 + 1 / var, var, boundary=True),
]:
# Check that equation can be evaluated in each case
# Dirichlet
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Dirichlet"),
"positive tab": (pybamm.Scalar(1), "Dirichlet"),
}
}
eqn_disc = disc.process_symbol(eqn)
eqn_disc.evaluate(None, y_test)
# Neumann
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Neumann"),
"positive tab": (pybamm.Scalar(1), "Neumann"),
}
}
eqn_disc = disc.process_symbol(eqn)
eqn_disc.evaluate(None, y_test)
# One of each
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Neumann"),
"positive tab": (pybamm.Scalar(1), "Dirichlet"),
}
}
eqn_disc = disc.process_symbol(eqn)
eqn_disc.evaluate(None, y_test)
# One of each
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Dirichlet"),
"positive tab": (pybamm.Scalar(1), "Neumann"),
}
}
eqn_disc = disc.process_symbol(eqn)
eqn_disc.evaluate(None, y_test)
# check ValueError raised for non Dirichlet or Neumann BCs
eqn = pybamm.laplacian(var) - pybamm.source(unit_source, var)
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Dirichlet"),
"positive tab": (pybamm.Scalar(1), "Other BC"),
}
}
with self.assertRaises(ValueError):
eqn_disc = disc.process_symbol(eqn)
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Other BC"),
"positive tab": (pybamm.Scalar(1), "Neumann"),
}
}
with self.assertRaises(ValueError):
eqn_disc = disc.process_symbol(eqn)
# raise ModelError if no BCs provided
new_var = pybamm.Variable("new_var", domain="current collector")
disc.set_variable_slices([new_var])
eqn = pybamm.laplacian(new_var)
with self.assertRaises(pybamm.ModelError):
eqn_disc = disc.process_symbol(eqn)
# check GeometryError if using scikit-fem not in y or z
x = pybamm.SpatialVariable("x", ["current collector"])
with self.assertRaises(pybamm.GeometryError):
disc.process_symbol(x)
