core.problem module

Description

Module containing the base Problem class for pySDC

class Problem(init: Any)

Bases: RegisterParams

Prototype class for problems, just defines the attributes essential to get started.

Parameters:

• init (list of args) – Argument(s) used to initialize data types.

• dtype_u (type) – Variable data type. Should generate a data variable using dtype_u(init).

• dtype_f (type) – RHS data type. Should generate a data variable using dtype_f(init).

logger

custom logger for problem-related logging.

Type:

logging.Logger

apply_mass_matrix(u: Any) → Any

Default mass matrix : identity

dtype_f: Type[Any] | None = None

dtype_u: Type[Any] | None = None

eval_f(u: Any, t: float) → Any

Abstract interface to RHS computation of the ODE

Parameters:

• u (dtype_u) – Current values.

• t (float) – Current time.

Returns:

f – The RHS values.

Return type:

dtype_f

property f_init: Any

Generate a data variable for RHS

generate_scipy_reference_solution(eval_rhs: Callable, t: float, u_init: Any | None = None, t_init: float | None = None, **kwargs: Any) → Any

Compute a reference solution using scipy.solve_ivp with very small tolerances. Keep in mind that scipy needs the solution to be a one dimensional array. If you are solving something higher dimensional, you need to make sure the function eval_rhs takes a flattened one-dimensional version as an input and output, but reshapes to whatever the problem needs for evaluation.

The keyword arguments will be passed to scipy.solve_ivp. You should consider passing method=’BDF’ for stiff problems and to accelerate that you can pass a function that evaluates the Jacobian with arguments jac(t, u) as jac=jac.

Parameters:

• eval_rhs (function) – Function evaluate the full right hand side. Must have signature eval_rhs(float: t, numpy.1darray: u)

• t (float) – current time

• u_init (pySDC.implementations.problem_classes.Lorenz.dtype_u) – initial conditions for getting the exact solution

• t_init (float) – the starting time

Returns:

Reference solution

Return type:

numpy.ndarray

getOutputFile(fileName: str) → Any

classmethod get_default_sweeper_class() → Type[Any]

get_fig() → Any

Get a figure suitable to plot the solution of this problem

Returns:

self.fig

Return type:

matplotlib.pyplot.figure.Figure

logger: Logger = <Logger problem (WARNING)>

plot(u: Any, t: float | None = None, fig: Any | None = None) → None

Plot the solution. Please supply a figure with the same structure as returned by self.get_fig.

Parameters:

• u (dtype_u) – Solution to be plotted

• t (float) – Time to display at the top of the figure

• fig (matplotlib.pyplot.figure.Figure) – Figure with the correct structure

Return type:

None

processSolutionForOutput(u: Any) → Any

setUpFieldsIO() → None

Set up FieldsIO for MPI with the space decomposition of this problem

solve_jacobian(rhs: Any, dt: float, u: Any | None = None, u0: Any | None = None, t: float = 0, **kwargs: Any) → Any

Solve the Jacobian for an Euler step, linearized around u. This defaults to an Euler step to accommodate linear problems.

Parameters:

• rhs – Right hand side for the Euler step

• dt (float) – Step size for the Euler step

• u – Solution to linearize around

• u0 – Initial guess

• t (float) – Current time

Returns:

Solution

solve_system(rhs: Any, dt: float, u0: Any, t: float) → Any

Perform an Euler step.

Parameters:

• rhs – Right hand side for the Euler step

• dt (float) – Step size for the Euler step

• u0 – Initial guess

• t (float) – Current time

Returns:

solution to the Euler step

property u_init: Any

Generate a data variable for u

class WorkCounter

Bases: object

Utility class for counting iterations.

Contains one attribute niter initialized to zero during instantiation, which can be incremented by calling object as a function, e.g

>>> count = WorkCounter()  # => niter = 0
>>> count()                # => niter = 1
>>> count()                # => niter = 2

decrement() → None

niter: int