Spatial Method#
- class pybamm.SpatialMethod(options=None)[source]#
A general spatial methods class, with default (trivial) behaviour for some spatial operations. All spatial methods will follow the general form of SpatialMethod in that they contain a method for broadcasting variables onto a mesh, a gradient operator, and a divergence operator.
- Parameters:
mesh – Contains all the submeshes for discretisation
- boundary_integral(child, discretised_child, region)[source]#
Implements the boundary integral for a spatial method.
- Parameters:
child (
pybamm.Symbol
) – The symbol to which is being integrateddiscretised_child (
pybamm.Symbol
) – The discretised symbol of the correct sizeregion (str) – The region of the boundary over which to integrate. If region is None (default) the integration is carried out over the entire boundary. If region is negative tab or positive tab then the integration is only carried out over the appropriate part of the boundary corresponding to the tab.
- Returns:
Contains the result of acting the discretised boundary integral on the child discretised_symbol
- Return type:
class: pybamm.Array
- boundary_value_or_flux(symbol, discretised_child, bcs=None)[source]#
Returns the boundary value or flux using the appropriate expression for the spatial method. To do this, we create a sparse vector ‘bv_vector’ that extracts either the first (for side=”left”) or last (for side=”right”) point from ‘discretised_child’.
- Parameters:
symbol (
pybamm.Symbol
) – The boundary value or flux symboldiscretised_child (
pybamm.StateVector
) – The discretised variable from which to calculate the boundary valuebcs (dict (optional)) – The boundary conditions. If these are supplied and “use bcs” is True in the options, then these will be used to improve the accuracy of the extrapolation.
- Returns:
The variable representing the surface value.
- Return type:
- broadcast(symbol, domains, broadcast_type)[source]#
Broadcast symbol to a specified domain.
- Parameters:
symbol (
pybamm.Symbol
) – The symbol to be broadcasteddomains (dict of strings) – The domains for broadcasting
broadcast_type (str) – The type of broadcast: ‘primary to node’, ‘primary to edges’, ‘secondary to nodes’, ‘secondary to edges’, ‘tertiary to nodes’, ‘tertiary to edges’, ‘full to nodes’ or ‘full to edges’
- Returns:
broadcasted_symbol – The discretised symbol of the correct size for the spatial method
- Return type:
class: pybamm.Symbol
- concatenation(disc_children)[source]#
Discrete concatenation object.
- Parameters:
disc_children (list) – List of discretised children
- Returns:
Concatenation of the discretised children
- Return type:
- delta_function(symbol, discretised_symbol)[source]#
Implements the delta function on the approriate side for a spatial method.
- Parameters:
symbol (
pybamm.Symbol
) – The symbol to which is being integrateddiscretised_symbol (
pybamm.Symbol
) – The discretised symbol of the correct size
- divergence(symbol, discretised_symbol, boundary_conditions)[source]#
Implements the divergence for a spatial method.
- Parameters:
symbol (
pybamm.Symbol
) – The symbol that we will take the gradient of.discretised_symbol (
pybamm.Symbol
) – The discretised symbol of the correct sizeboundary_conditions (dict) – The boundary conditions of the model ({symbol: {“left”: left bc, “right”: right bc}})
- Returns:
Contains the result of acting the discretised divergence on the child discretised_symbol
- Return type:
class: pybamm.Array
- evaluate_at(symbol, discretised_child, position)[source]#
Returns the symbol evaluated at a given position in space.
- Parameters:
symbol (
pybamm.Symbol
) – The boundary value or flux symboldiscretised_child (
pybamm.StateVector
) – The discretised variable from which to calculate the boundary valueposition (
pybamm.Scalar
) – The point in one-dimensional space at which to evaluate the symbol.
- Returns:
The variable representing the value at the given point.
- Return type:
- gradient(symbol, discretised_symbol, boundary_conditions)[source]#
Implements the gradient for a spatial method.
- Parameters:
symbol (
pybamm.Symbol
) – The symbol that we will take the gradient of.discretised_symbol (
pybamm.Symbol
) – The discretised symbol of the correct sizeboundary_conditions (dict) – The boundary conditions of the model ({symbol: {“left”: left bc, “right”: right bc}})
- Returns:
Contains the result of acting the discretised gradient on the child discretised_symbol
- Return type:
class: pybamm.Array
- gradient_squared(symbol, discretised_symbol, boundary_conditions)[source]#
Implements the inner product of the gradient with itself for a spatial method.
- Parameters:
symbol (
pybamm.Symbol
) – The symbol that we will take the gradient of.discretised_symbol (
pybamm.Symbol
) – The discretised symbol of the correct sizeboundary_conditions (dict) – The boundary conditions of the model ({symbol: {“left”: left bc, “right”: right bc}})
- Returns:
Contains the result of taking the inner product of the result of acting the discretised gradient on the child discretised_symbol with itself
- Return type:
class: pybamm.Array
- indefinite_integral(child, discretised_child, direction)[source]#
Implements the indefinite integral for a spatial method.
- Parameters:
child (
pybamm.Symbol
) – The symbol to which is being integrateddiscretised_child (
pybamm.Symbol
) – The discretised symbol of the correct sizedirection (str) – The direction of integration
- Returns:
Contains the result of acting the discretised indefinite integral on the child discretised_symbol
- Return type:
class: pybamm.Array
- integral(child, discretised_child, integration_dimension)[source]#
Implements the integral for a spatial method.
- Parameters:
child (
pybamm.Symbol
) – The symbol to which is being integrateddiscretised_child (
pybamm.Symbol
) – The discretised symbol of the correct sizeintegration_dimension (str, optional) – The dimension in which to integrate (default is “primary”)
- Returns:
Contains the result of acting the discretised integral on the child discretised_symbol
- Return type:
class: pybamm.Array
- internal_neumann_condition(left_symbol_disc, right_symbol_disc, left_mesh, right_mesh)[source]#
A method to find the internal Neumann conditions between two symbols on adjacent subdomains.
- Parameters:
left_symbol_disc (
pybamm.Symbol
) – The discretised symbol on the left subdomainright_symbol_disc (
pybamm.Symbol
) – The discretised symbol on the right subdomainleft_mesh (list) – The mesh on the left subdomain
right_mesh (list) – The mesh on the right subdomain
- laplacian(symbol, discretised_symbol, boundary_conditions)[source]#
Implements the Laplacian for a spatial method.
- Parameters:
symbol (
pybamm.Symbol
) – The symbol that we will take the gradient of.discretised_symbol (
pybamm.Symbol
) – The discretised symbol of the correct sizeboundary_conditions (dict) – The boundary conditions of the model ({symbol: {“left”: left bc, “right”: right bc}})
- Returns:
Contains the result of acting the discretised Laplacian on the child discretised_symbol
- Return type:
class: pybamm.Array
- mass_matrix(symbol, boundary_conditions)[source]#
Calculates the mass matrix for a spatial method.
- Parameters:
symbol (
pybamm.Variable
) – The variable corresponding to the equation for which we are calculating the mass matrix.boundary_conditions (dict) – The boundary conditions of the model ({symbol: {“left”: left bc, “right”: right bc}})
- Returns:
The (sparse) mass matrix for the spatial method.
- Return type:
- process_binary_operators(bin_op, left, right, disc_left, disc_right)[source]#
Discretise binary operators in model equations. Default behaviour is to return a new binary operator with the discretised children.
- Parameters:
bin_op (
pybamm.BinaryOperator
) – Binary operator to discretiseleft (
pybamm.Symbol
) – The left child of bin_opright (
pybamm.Symbol
) – The right child of bin_opdisc_left (
pybamm.Symbol
) – The discretised left child of bin_opdisc_right (
pybamm.Symbol
) – The discretised right child of bin_op
- Returns:
Discretised binary operator
- Return type:
- spatial_variable(symbol)[source]#
Convert a
pybamm.SpatialVariable
node to a linear algebra object that can be evaluated (here, apybamm.Vector
on either the nodes or the edges).- Parameters:
symbol (
pybamm.SpatialVariable
) – The spatial variable to be discretised.- Returns:
Contains the discretised spatial variable
- Return type: