porepy.models.abstract_model module

Contains the mother class for all models, that is, standardized setups for complex problems.

Some methods may raise NotImplementedErrors instead of being abstract methods. This is because they are only needed for some model types (typically nonlinear ones).

Note on running simulations: We provide run_time_dependent_model and run_stationary_model. Both call the Model’s prepare_simulation and after_simulation methods, as well as the solve method of either a LinearSolver or NewtonSolver (the only non-linear solver available for the time being). The Solvers call methods before_newton_loop, check_convergence, after_newton_convergence/after_newton_divergence, (only NewtonSolver:) before_newton_iteration, after_newton_iteration. The name “newton” is there for legacy reasons, a more fitting and general name would be something like “equation_solve”.

class AbstractModel(params=None)

Bases: object

This is a class that specifies methods that a model must implement to be compatible with the Newton and time stepping methods.

Public attributes:

params (Dict): Simulation specific parameters. Which items are admissible

depends on the model in question.

convergence_status (bool): Whether the non-linear iteration has converged. linear_solver (str): Specification of linear solver. Only known permissible

value is ‘direct’.

dof_manager (pp.DofManager): Degree of freedom manager.

Parameters

params (Optional[Dict]) –

after_newton_convergence(solution, errors, iteration_counter)

Method to be called after every non-linear iteration.

Possible usage is to distribute information on the solution, visualization, etc.

Parameters

• np.array – The new solution state, as computed by the non-linear solver.

• solution (ndarray) –

• errors (float) –

• iteration_counter (int) –

Return type

None

after_newton_failure(solution, errors, iteration_counter)

Parameters

• solution (ndarray) –

• errors (float) –

• iteration_counter (int) –

Return type

None

after_newton_iteration(solution_vector)

Method to be called after every non-linear iteration.

Possible usage is to distribute information on the new trial state, visualize the current approximation etc.

Parameters

• np.array – The new solution state, as computed by the non-linear solver.

• solution_vector (ndarray) –

after_simulation()

Run at the end of simulation. Can be used for cleanup etc.

Return type

None

assemble_linear_system()

Assemble the linearized system.

The linear system is defined by the current state of the model.

Return type

None

linear_system is assigned.

before_newton_iteration()

Method to be called at the start of every non-linear iteration.

Possible usage is to update non-linear parameters, discretizations etc.

Return type

None

before_newton_loop()

Method to be called before entering the non-linear solver, thus at the start of a new time step.

Possible usage is to update time-dependent parameters, discretizations etc.

Return type

None

check_convergence(solution, prev_solution, init_solution, nl_params)

Implements a convergence check, to be called by a non-linear solver.

Parameters

• solution (np.array) – Newly obtained solution vector

• prev_solution (np.array) – Solution obtained in the previous non-linear iteration.

• init_solution (np.array) – Solution obtained from the previous time-step.

• nl_params (dict) – Dictionary of parameters used for the convergence check. Which items are required will depend on the convergence test to be implemented.

Returns

Error, computed to the norm in question. boolean: True if the solution is converged according to the test

implemented by this method.

boolean: True if the solution is diverged according to the test

implemented by this method.

Return type

float

Raises: NotImplementedError if the problem is nonlinear and AD is not used.

Convergence criteria are more involved in this case, so we do not risk providing a general method.

create_grid()

Create the grid bucket.

A unit square grid with no fractures is assigned by default.

The method assigns the following attributes to self:

mdg (pp.MixedDimensionalGrid): The produced grid bucket. box (dict): The bounding box of the domain, defined through minimum and

maximum values in each dimension.

Return type

None

prepare_simulation()

Method called prior to the start of time stepping, or prior to entering the non-linear solver for stationary problems.

The intended use is to define parameters, geometry and grid, discretize linear and time-independent terms, and generally prepare for the simulation.

Return type

None

solve_linear_system()

Solve linear system.

Default method is a direct solver. The linear solver is chosen in the initialize_linear_solver of this model. Implemented options are

scipy.sparse.spsolve

with and without call to umfpack

pypardiso.spsolve

Returns

Solution vector.

Return type

np.ndarray