IDAKLU Solver

class pybamm.IDAKLUSolver(rtol=1e-06, atol=1e-06, root_method='casadi', root_tol=1e-06, extrap_tol=None, options=None)

Solve a discretised model, using sundials with the KLU sparse linear solver.

Parameters:

• 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).

• extrap_tol (float, optional) – The tolerance to assert whether extrapolation occurs or not (default is 0).

• options (dict, optional) –

  Addititional options to pass to the solver, by default:

  options = {
      # print statistics of the solver after every solve
      "print_stats": False,
  
      # jacobian form, can be "none", "dense", "sparse", "matrix-free"
      "jacobian": "sparse",
  
      # name of sundials linear solver to use options are: "SUNLinSol_KLU",
      # "SUNLinSol_Dense", "SUNLinSol_SPBCGS",
      # "SUNLinSol_SPFGMR", "SUNLinSol_SPGMR", "SUNLinSol_SPTFQMR",
      "linear_solver": "SUNLinSol_KLU",
  
      # preconditioner for iterative solvers, can be "none", "BBDP"
      "preconditioner": "BBDP",
  
      # for iterative linear solvers, max number of iterations
      "linsol_max_iterations": 5,
  
      # for iterative linear solver preconditioner, bandwidth of
      # approximate jacobian
      "precon_half_bandwidth": 5,
  
      # for iterative linear solver preconditioner, bandwidth of
      # approximate jacobian that is kept
      "precon_half_bandwidth_keep": 5
  }
  

  Note: These options only have an effect if model.convert_to_format == ‘casadi’

set_atol_by_variable(variables_with_tols, model)

A method to set the absolute tolerances in the solver by state variable. This method attaches a vector of tolerance to the model. (i.e. model.atol)

Parameters:

• variables_with_tols (dict) – A dictionary with keys that are strings indicating the variable you wish to set the tolerance of and values that are the tolerances.

• model (pybamm.BaseModel) – The model that is going to be solved.

set_state_vec_tol(atol, state_vec, tol)

A method to set the tolerances in the atol vector of a specific state variable. This method modifies self.atol

Parameters:

• state_vec (pybamm.StateVector) – The state vector to apply to the tolerance to

• tol (float) – The tolerance value

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

Unpack model, perform checks, 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