def source(left, right, boundary=False):
"""A convinience function for creating (part of) an expression tree representing
a source term. This is necessary for spatial methods where the mass matrix
is not the identity (e.g. finite element formulation with piecwise linear
basis functions). The left child is the symbol representing the source term
and the right child is the symbol of the equation variable (currently, the
finite element formulation in PyBaMM assumes all functions are constructed
using the same basis, and the matrix here is constructed accoutning for the
boundary conditions of the right child). The method returns the matrix-vector
product of the mass matrix (adjusted to account for any Dirichlet boundary
conditions imposed the the right symbol) and the discretised left symbol.
Parameters
----------
left : :class:`Symbol`
The left child node, which represents the expression for the source term.
right : :class:`Symbol`
The right child node. This is the symbol whose boundary conditions are
accounted for in the construction of the mass matrix.
boundary : bool, optional
If True, then the mass matrix should is assembled over the boundary,
corresponding to a source term which only acts on the boundary of the
domain. If False (default), the matrix is assembled over the entire domain,
corresponding to a source term in the bulk.
"""
# Broadcast if left is number
if isinstance(left, numbers.Number):
left = pybamm.PrimaryBroadcast(left, "current collector")
if left.domain != ["current collector"] or right.domain != ["current collector"]:
raise pybamm.DomainError(
"""'source' only implemented in the 'current collector' domain,
but symbols have domains {} and {}""".format(
left.domain, right.domain
)
)
if boundary:
return pybamm.BoundaryMass(right) @ left
else:
return pybamm.Mass(right) @ left
def test_manufactured_solution_exponential_grid(self):
param = pybamm.ParameterValues(
values={
"Electrode width [m]": 1,
"Electrode height [m]": 1,
"Negative tab width [m]": 1,
"Negative tab centre y-coordinate [m]": 0.5,
"Negative tab centre z-coordinate [m]": 0,
"Positive tab width [m]": 1,
"Positive tab centre y-coordinate [m]": 0.5,
"Positive tab centre z-coordinate [m]": 1,
"Negative electrode thickness [m]": 0.3,
"Separator thickness [m]": 0.3,
"Positive electrode thickness [m]": 0.3,
}
)
geometry = pybamm.battery_geometry(
include_particles=False, current_collector_dimension=2
)
param.process_geometry(geometry)
var = pybamm.standard_spatial_vars
var_pts = {var.x_n: 3, var.x_s: 3, var.x_p: 3, var.y: 32, var.z: 32}
submesh_types = {
"negative electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"separator": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"current collector": pybamm.MeshGenerator(
pybamm.ScikitExponential2DSubMesh
),
}
mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"current collector": pybamm.ScikitFiniteElement(),
}
disc = pybamm.Discretisation(mesh, spatial_methods)
# laplace of u = cos(pi*y)*sin(pi*z)
var = pybamm.Variable("var", domain="current collector")
laplace_eqn = pybamm.laplacian(var)
# set boundary conditions ("negative tab" = bottom of unit square,
# "positive tab" = top of unit square, elsewhere normal derivative is zero)
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Dirichlet"),
"positive tab": (pybamm.Scalar(0), "Dirichlet"),
}
}
disc.set_variable_slices([var])
laplace_eqn_disc = disc.process_symbol(laplace_eqn)
y_vertices = mesh["current collector"].coordinates[0, :][:, np.newaxis]
z_vertices = mesh["current collector"].coordinates[1, :][:, np.newaxis]
u = np.cos(np.pi * y_vertices) * np.sin(np.pi * z_vertices)
mass = pybamm.Mass(var)
mass_disc = disc.process_symbol(mass)
soln = -np.pi ** 2 * u
np.testing.assert_array_almost_equal(
laplace_eqn_disc.evaluate(None, u), mass_disc.entries @ soln, decimal=1
)
def test_manufactured_solution(self):
mesh = get_unit_2p1D_mesh_for_testing(ypts=32, zpts=32, include_particles=False)
spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"current collector": pybamm.ScikitFiniteElement(),
}
disc = pybamm.Discretisation(mesh, spatial_methods)
# linear u = z (to test coordinates to degree of freedom mapping)
var = pybamm.Variable("var", domain="current collector")
disc.set_variable_slices([var])
var_disc = disc.process_symbol(var)
z_vertices = mesh["current collector"].coordinates[1, :]
np.testing.assert_array_almost_equal(
var_disc.evaluate(None, z_vertices), z_vertices[:, np.newaxis]
)
# linear u = 6*y (to test coordinates to degree of freedom mapping)
y_vertices = mesh["current collector"].coordinates[0, :]
np.testing.assert_array_almost_equal(
var_disc.evaluate(None, 6 * y_vertices), 6 * y_vertices[:, np.newaxis]
)
# mixed u = y*z (to test coordinates to degree of freedom mapping)
np.testing.assert_array_almost_equal(
var_disc.evaluate(None, y_vertices * z_vertices),
y_vertices[:, np.newaxis] * z_vertices[:, np.newaxis],
)
# laplace of u = sin(pi*z)
var = pybamm.Variable("var", domain="current collector")
eqn_zz = pybamm.laplacian(var)
# set boundary conditions ("negative tab" = bottom of unit square,
# "positive tab" = top of unit square, elsewhere normal derivative is zero)
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Dirichlet"),
"positive tab": (pybamm.Scalar(0), "Dirichlet"),
}
}
disc.set_variable_slices([var])
eqn_zz_disc = disc.process_symbol(eqn_zz)
z_vertices = mesh["current collector"].coordinates[1, :][:, np.newaxis]
u = np.sin(np.pi * z_vertices)
mass = pybamm.Mass(var)
mass_disc = disc.process_symbol(mass)
soln = -np.pi ** 2 * u
np.testing.assert_array_almost_equal(
eqn_zz_disc.evaluate(None, u), mass_disc.entries @ soln, decimal=3
)
# laplace of u = cos(pi*y)*sin(pi*z)
var = pybamm.Variable("var", domain="current collector")
laplace_eqn = pybamm.laplacian(var)
# set boundary conditions ("negative tab" = bottom of unit square,
# "positive tab" = top of unit square, elsewhere normal derivative is zero)
disc.bcs = {
var.id: {
"negative tab": (pybamm.Scalar(0), "Dirichlet"),
"positive tab": (pybamm.Scalar(0), "Dirichlet"),
}
}
disc.set_variable_slices([var])
laplace_eqn_disc = disc.process_symbol(laplace_eqn)
y_vertices = mesh["current collector"].coordinates[0, :][:, np.newaxis]
z_vertices = mesh["current collector"].coordinates[1, :][:, np.newaxis]
u = np.cos(np.pi * y_vertices) * np.sin(np.pi * z_vertices)
mass = pybamm.Mass(var)
mass_disc = disc.process_symbol(mass)
soln = -np.pi ** 2 * u
np.testing.assert_array_almost_equal(
laplace_eqn_disc.evaluate(None, u), mass_disc.entries @ soln, decimal=2
)