Base Solver

class pybamm.BaseSolver(method=None, rtol=1e-06, atol=1e-06, root_method=None, root_tol=1e-06, max_steps='deprecated')

Solve a discretised model.

Parameters:

• method (str, optional) – The method to use for integration, specific to each solver
• rtol (float, optional) – The relative tolerance for the solver (default is 1e-6).
• atol (float, optional) – The absolute tolerance for the solver (default is 1e-6).
• root_method (str or pybamm algebraic solver class, optional) – The method to use to find initial conditions (for DAE solvers). If a solver class, must be an algebraic solver class. If “casadi”, the solver uses casadi’s Newton rootfinding algorithm to find initial conditions. Otherwise, the solver uses ‘scipy.optimize.root’ with method specified by ‘root_method’ (e.g. “lm”, “hybr”, …)
• root_tol (float, optional) – The tolerance for the initial-condition solver (default is 1e-6).

calculate_consistent_state(model, time=0, inputs=None)

Calculate consistent state for the algebraic equations through root-finding. model.y0 is used as the initial guess for rootfinding

Parameters:

• model (pybamm.BaseModel) – The model for which to calculate initial conditions.
• time (float) – The time at which to calculate the states
• inputs (dict, optional) – Any input parameters to pass to the model when solving

Returns:

y0_consistent – Initial conditions that are consistent with the algebraic equations (roots of the algebraic equations). If self.root_method == None then returns model.y0.

Return type:

array-like, same shape as y0_guess

copy()

Returns a copy of the solver

get_termination_reason(solution, events)

Identify the cause for termination. In particular, if the solver terminated due to an event, (try to) pinpoint which event was responsible. Note that the current approach (evaluating all the events and then finding which one is smallest at the final timestep) is pretty crude, but is the easiest one that works for all the different solvers.

Parameters:

• solution (pybamm.Solution) – The solution object
• events (dict) – Dictionary of events

set_up(model, inputs=None, t_eval=None)

Unpack model, perform checks, simplify and calculate jacobian.

Parameters:

• model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions
• inputs (dict, optional) – Any input parameters to pass to the model when solving
• t_eval (numeric type, optional) – The times (in seconds) at which to compute the solution

solve(model, t_eval=None, external_variables=None, inputs=None)

Execute the solver setup and calculate the solution of the model at specified times.

Parameters:

• model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions
• t_eval (numeric type) – The times (in seconds) at which to compute the solution
• external_variables (dict) – A dictionary of external variables and their corresponding values at the current time
• inputs (dict, optional) – Any input parameters to pass to the model when solving

Raises:

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

step(old_solution, model, dt, npts=2, external_variables=None, inputs=None, save=True)

Step the solution of the model forward by a given time increment. The first time this method is called it executes the necessary setup by calling self.set_up(model).

Parameters:

• old_solution (pybamm.Solution or None) – The previous solution to be added to. If None, a new solution is created.
• model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions
• dt (numeric type) – The timestep (in seconds) over which to step the solution
• npts (int, optional) – The number of points at which the solution will be returned during the step dt. default is 2 (returns the solution at t0 and t0 + dt).
• external_variables (dict) – A dictionary of external variables and their corresponding values at the current time
• inputs (dict, optional) – Any input parameters to pass to the model when solving
• save (bool) – Turn on to store the solution of all previous timesteps

Raises:

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