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Discretisation and spatial methods

Spatial Method

# Discretisation¶

class pybamm.Discretisation(mesh=None, spatial_methods=None)[source]

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)[source]

Check initial conditions are a numpy array

check_initial_conditions_rhs(model)[source]

Check initial conditions and rhs have the same shape

check_model(model)[source]

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

check_tab_conditions(symbol, bcs)[source]

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}). The dictionary of boundary conditions, with the keys changed to “left” and “right” where necessary. dict
check_variables(model)[source]

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)[source]

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}) The mass matrix pybamm.Matrix
process_boundary_conditions(model)[source]

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}) Dictionary of processed boundary conditions dict
process_dict(var_eqn_dict)[source]

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) new_var_eqn_dict – Discretised equations dict
process_initial_conditions(model)[source]

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}) Tuple of processed_initial_conditions (dict of initial conditions) and concatenated_initial_conditions (numpy array of concatenated initial conditions) tuple
process_model(model, inplace=True)[source]

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. 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 pybamm.BaseModel pybamm.ModelError – If an empty model is passed (model.rhs = {} and model.algebraic={})
process_rhs_and_algebraic(model)[source]

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}) Tuple of processed_rhs (dict of processed differential equations), processed_concatenated_rhs, processed_algebraic (dict of processed algebraic equations) and processed_concatenated_algebraic tuple
process_symbol(symbol)[source]

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 Discretised symbol pybamm.expression_tree.symbol.Symbol
set_internal_boundary_conditions(model)[source]

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)[source]

Sets the slicing for variables.

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