4.5.2 pde.solvers.base module

Package that contains base classes for solvers.

Beside the abstract base class SolverBase defining the interfaces, we also provide AdaptiveSolverBase, which contains methods for adaptive solvers.

`SolverBase`	Base class for PDE solvers.
`AdaptiveSolverBase`	Base class for adaptive time steppers.
`ConvergenceError`	Indicates that an implicit step did not converge.

class AdaptiveSolverBase(pde, *, backend='auto', adaptive=False, tolerance=0.0001)[source]

Bases: SolverBase

Base class for adaptive time steppers.

Parameters:

pde (PDEBase) – The partial differential equation that should be solved
backend (str) – The backend used for numerical operations
adaptive (bool) – Whether to use adaptive time stepping
tolerance (float) – Error tolerance for adaptive time stepping

dt_max: float = 10000000000.0

maximal time step that the adaptive solver will use

Type:: float

dt_min: float = 1e-10

minimal time step that the adaptive solver will use

Type:: float

make_stepper(state, dt=None)[source]

Return a stepper function using an explicit scheme.

Parameters:

state (FieldBase) – An example for the state from which the grid and other information can be extracted
dt (float) – Time step used (Uses SolverBase.dt_default if None). This sets the initial time step for adaptive solvers.

Returns:

Function that can be called to advance the state from time t_start to time t_end. The function call signature is (state: numpy.ndarray, t_start: float, t_end: float)

Return type:

StepperType

exception ConvergenceError[source]

Bases: RuntimeError

Indicates that an implicit step did not converge.

class SolverBase(pde, *, backend='auto')[source]

Bases: object

Base class for PDE solvers.

Parameters:

pde (PDEBase) – The partial differential equation that should be solved
backend (str or BackendBase) – The backend used for numerical operations

property backend: BackendBase

The backend for this solver.

Type:: BackendBase

property backend_name: str

The name of the backend used for this solver.

Type:: str

dt_default: float = 0.001

default time step used if no time step was specified

Type:: float

classmethod from_name(name, pde, **kwargs)[source]

Create solver class based on its name.

Solver classes are automatically registered when they inherit from SolverBase. Note that this also requires that the respective python module containing the solver has been loaded before it is attempted to be used.

Parameters:

name (str) – The name of the solver to construct
pde (PDEBase) – The partial differential equation that should be solved
**kwargs – Additional arguments for the constructor of the solver

Returns:

An instance of a subclass of SolverBase

Return type:

SolverBase

info: dict[str, Any]

make_stepper(state, dt=None)[source]

Return a stepper function using an explicit scheme.

Parameters:

state (FieldBase) – An example for the state from which the grid and other information can be extracted
dt (float) – Time step used (Uses SolverBase.dt_default if None)

Returns:

Function that can be called to advance the state from time t_start to time t_end. The function call signature is (state: numpy.ndarray, t_start: float, t_end: float)

Return type:

StepperType

registered_solvers()[source]

Returns all solvers that are currently registered.

Returns:: a dictionary with the names of the solvers and the associated class
Return type:: dict