Discretisation

class pybamm.Discretisation(mesh=None, spatial_methods=None)

The discretisation class, with methods to process a model and replace Spatial Operators with Matrices and Variables with StateVectors

Parameters:

• mesh (pybamm.Mesh) – contains all submeshes to be used on each domain
• spatial_methods (dict) – a dictionary of the spatial method to be used on each domain. The keys correspond to the keys in a pybamm.Model

check_initial_conditions(model)

Check initial conditions are a numpy array

check_initial_conditions_rhs(model)

Check initial conditions and rhs have the same shape

check_model(model)

Perform some basic checks to make sure the discretised model makes sense.

check_tab_conditions(symbol, bcs)

Check any boundary conditions applied on “negative tab”, “positive tab” and “no tab”. For 1D current collector meshes, these conditions are converted into boundary conditions on “left” (tab at z=0) or “right” (tab at z=l_z) depending on the tab location stored in the mesh. For 2D current collector meshes, the boundary conditions can be applied on the tabs directly.

Parameters:

• symbol (pybamm.expression_tree.symbol.Symbol) – The symbol on which the boundary conditions are applied.
• bcs (dict) – The dictionary of boundary conditions (a dict of {side: equation}).

Returns:

The dictionary of boundary conditions, with the keys changed to “left” and “right” where necessary.

Return type:

dict

check_variables(model)

Check variables in variable list against rhs Be lenient with size check if the variable in model.variables is broadcasted, or a concatenation, or an outer product (if broadcasted, variable is a multiplication with a vector of ones)

create_mass_matrix(model)

Creates mass matrix of the discretised model. Note that the model is assumed to be of the form M*y_dot = f(t,y), where M is the (possibly singular) mass matrix.

Parameters:model (pybamm.BaseModel) – Discretised model. Must have attributes rhs, initial_conditions and boundary_conditions (all dicts of {variable: equation}) Returns:The mass matrix Return type:pybamm.Matrix

process_boundary_conditions(model)

Discretise model boundary_conditions, also converting keys to ids

Parameters:model (pybamm.BaseModel) – Model to dicretise. Must have attributes rhs, initial_conditions and boundary_conditions (all dicts of {variable: equation}) Returns:Dictionary of processed boundary conditions Return type:dict

process_dict(var_eqn_dict)

Discretise a dictionary of {variable: equation}, broadcasting if necessary (can be model.rhs, model.initial_conditions or model.variables).

Parameters:var_eqn_dict (dict) – Equations ({variable: equation} dict) to dicretise (can be model.rhs, model.initial_conditions or model.variables) Returns:new_var_eqn_dict – Discretised equations Return type:dict

process_initial_conditions(model)

Discretise model initial_conditions.

Parameters:model (pybamm.BaseModel) – Model to dicretise. Must have attributes rhs, initial_conditions and boundary_conditions (all dicts of {variable: equation}) Returns:Tuple of processed_initial_conditions (dict of initial conditions) and concatenated_initial_conditions (numpy array of concatenated initial conditions) Return type:tuple

process_model(model, inplace=True)

Discretise a model. Currently inplace, could be changed to return a new model.

Parameters:

• model (pybamm.BaseModel) – Model to dicretise. Must have attributes rhs, initial_conditions and boundary_conditions (all dicts of {variable: equation})
• inplace (bool, optional) – If True, discretise the model in place. Otherwise, return a new discretised model. Default is True.

Returns:

model_disc – The discretised model. Note that if inplace is True, model will have also been discretised in place so model == model_disc. If inplace is False, model != model_disc

Return type:

pybamm.BaseModel

Raises:

pybamm.ModelError – If an empty model is passed (model.rhs = {} and model.algebraic={})

process_rhs_and_algebraic(model)

Discretise model equations - differential (‘rhs’) and algebraic.

Parameters:model (pybamm.BaseModel) – Model to dicretise. Must have attributes rhs, initial_conditions and boundary_conditions (all dicts of {variable: equation}) Returns:Tuple of processed_rhs (dict of processed differential equations), processed_concatenated_rhs, processed_algebraic (dict of processed algebraic equations) and processed_concatenated_algebraic Return type:tuple

process_symbol(symbol)

Discretise operators in model equations. If a symbol has already been discretised, the stored value is returned.

Parameters:symbol (pybamm.expression_tree.symbol.Symbol) – Symbol to discretise Returns:Discretised symbol Return type:pybamm.expression_tree.symbol.Symbol

set_internal_boundary_conditions(model)

A method to set the internal boundary conditions for the submodel. These are required to properly calculate the gradient. Note: this method modifies the state of self.boundary_conditions.

set_variable_slices(variables)

Sets the slicing for variables.

Parameters:variables (iterable of pybamm.Variables) – The variables for which to set slices