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Use Finite Differences Poisson equation system solver to guide cell labels. More...

Inheritance diagram for exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells:

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Collaboration diagram for exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells:

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Public Member Functions
	__init__ (self, name, relaxation_coefficient=0.6, right_hand_side=-25.0, min_value=0.0, max_value=1.0, min_threshold=0.4, max_threshold=0.6, plot=False)
	name: string A unique name for the solver.

	__str__ (self)

	create_readme_descriptor (self, domain_offset, domain_size)

	create_data_structures (self)
	Create cell and face data structures required.

	create_action_sets (self)
	Overwrite in subclasses if you wanna create different action sets.

	get_name_of_global_instance (self)

	add_to_Peano4_datamodel (self, datamodel, verbose)
	Add all required data to the Peano4 project's datamodel so it is properly built up.

	add_use_data_statements_to_Peano4_solver_step (self, step)
	Tell Peano what data to move around.

	add_actions_to_init_grid (self, step)

	add_actions_to_create_grid (self, step, evaluate_refinement_criterion)
	It is important to plug into the creation, as this is the place where we get the creational events.

	add_actions_to_plot_solution (self, step, output_path)
	We plot if and only if we are asked to do so.

	add_actions_to_perform_time_step (self, step)
	AMR.

	add_entries_to_text_replacement_dictionary (self, d)

	add_implementation_files_to_project (self, namespace, output, subdirectory="")
	The ExaHyPE2 project will call this operation when it sets up the overall environment.

	name (self)

	postprocess_updated_cell (self)

	postprocess_updated_cell (self, kernel)
	Define a postprocessing routine over the data.

Protected Member Functions
	_unknown_identifier (self)

	_get_default_includes (self)

Protected Attributes
	_name

	_relaxation_coefficient

	_right_hand_side

	_min_value

	_max_value

	_min_threshold

	_max_threshold

	_plot

	_postprocess_updated_cell

	_cell_data_model

	_face_data_model

	_action_set_smoother

Static Private Attributes
	__repr__ = __str__

Detailed Description

Use Finite Differences Poisson equation system solver to guide cell labels.

The most popular application of this solver is to guide limiters: Some codes need to know where to solve their PDE with an alternative more robust (though likely less effective) solver. For this, they solve

$ - \Delta u = f $

for a fixed right-hand side f with a Jacobi solver. The solution is subject to the constraints

$ u_{\text{min}} \leq u \leq u_{\text{max}} $

and Dirichlet boundary conditions.

Typically, the solvers than set the value of $u=1$ in regions where they need the limiter. The $u$ value will fade away from these regions, and we can implement the following heuristics with $ u_{\text{min}} < U_{\text{min}} < U_{\text{max}} < u_{\text{max}}$:

$ u<U_{\text{min}} $: Solver A is active. Solver B is not active.
$ U_{\text{min}} \leq u < \frac{1}{2} ( U_{\text{min}} + U_{\text{max}} )$: Solver A is active and sets the value of solver B which is not active but its solution exists here.
$ \frac{1}{2} ( U_{\text{min}} + U_{\text{max}} ) \leq u \leq U_{\text{max}} $: Solver B is active and sets the value of solver A which is not active but its solution exists here.
$ U_{\text{max}} < u $: Solver B is active. Solver A is not active.

As we use a Jacobi iterative solver, using this marker within ExaHyPE is equivalent to a heat equation solver which becomes stationary eventually if the areas where $ u=u_{\text{max}} $ is manually set/enforced do not change.

The solver works with a constant right-hand side and is defined over two attributes per cell: There's the actual value (u in the example above) and a marker which switches the Jacobi smoothing on and off per cell. In cells where we fix the value, we toggle the marker so Jacobi updates are disabled.

Usage

To use the marker within your project, add a new solver to your project:

 marker_solver = exahype2.solvers.elliptic.ConstrainedPoissonEquationOnCells( name="ConstrainedPoissonEquationOnCells" )
 project.add_solver( marker_solver )

Definition at line 24 of file ConstrainedPoissonEquationForMarkerOnCells.py.

Constructor & Destructor Documentation

◆ init()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.__init__	(	self,
		name,
		relaxation_coefficient = 0.6,
		right_hand_side = -25.0,
		min_value = 0.0,
		max_value = 1.0,
		min_threshold = 0.4,
		max_threshold = 0.6,
		plot = False )

name: string A unique name for the solver.

This one will be used for all generated classes.

plot: Boolean Clarifies whether a dump of the data should be enriched with grid info (such as enclave status flags), too.

relaxation_coefficient: Double (0< value <1) How quickly should the solution be relaxed against real solution. This is the damping parameter in the Jacobi update scheme and thus has to be bigger than 0 and smaller than 1. If the coefficient approaches 1, you might see oscillations.

right_hand_side: Double (negative) Basically describes how fast the solution is pulled down to 0 once we go away from the AMR transition area.

Definition at line 82 of file ConstrainedPoissonEquationForMarkerOnCells.py.

Member Function Documentation

◆ str()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.__str__ ( self )

Definition at line 132 of file ConstrainedPoissonEquationForMarkerOnCells.py.

Referenced by peano4.toolbox.particles.postprocessing.ParticleVTUReader.VTUParticleSet.__repr__().

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◆ _get_default_includes()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells._get_default_includes ( self )

protected

Definition at line 262 of file ConstrainedPoissonEquationForMarkerOnCells.py.

Referenced by exahype2.solvers.fv.FV.FV.create_action_sets().

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◆ _unknown_identifier()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells._unknown_identifier ( self )

protected

Definition at line 226 of file ConstrainedPoissonEquationForMarkerOnCells.py.

Referenced by exahype2.solvers.aderdg.ADERDG.ADERDG._init_dictionary_with_default_parameters(), exahype2.solvers.fv.FV.FV._init_dictionary_with_default_parameters(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG._init_dictionary_with_default_parameters(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences._init_dictionary_with_default_parameters(), exahype2.solvers.aderdg.ADERDG.ADERDG.add_actions_to_plot_solution(), exahype2.solvers.fv.FV.FV.add_actions_to_plot_solution(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.add_actions_to_plot_solution(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.add_actions_to_plot_solution(), and exahype2.solvers.elliptic.AMRMarker.AMRMarker.couple_with_FV_solver().

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◆ add_actions_to_create_grid()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.add_actions_to_create_grid	(	self,
		step,
		evaluate_refinement_criterion )

It is important to plug into the creation, as this is the place where we get the creational events.

Definition at line 284 of file ConstrainedPoissonEquationForMarkerOnCells.py.

References exahype2.solvers.elliptic.AMRMarker.AMRMarker._action_set_smoother, and exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells._action_set_smoother.

◆ add_actions_to_init_grid()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.add_actions_to_init_grid	(		self,
			step )

Definition at line 275 of file ConstrainedPoissonEquationForMarkerOnCells.py.

◆ add_actions_to_perform_time_step()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.add_actions_to_perform_time_step	(		self,
			step )

AMR.

It is important that we do the inter-grid transfer operators before we apply the boundary conditions.

Definition at line 332 of file ConstrainedPoissonEquationForMarkerOnCells.py.

◆ add_actions_to_plot_solution()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.add_actions_to_plot_solution	(	self,
		step,
		output_path )

We plot if and only if we are asked to do so.

Definition at line 295 of file ConstrainedPoissonEquationForMarkerOnCells.py.

◆ add_entries_to_text_replacement_dictionary()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.add_entries_to_text_replacement_dictionary	(		self,
			d )

Definition at line 346 of file ConstrainedPoissonEquationForMarkerOnCells.py.

Referenced by exahype2.solvers.aderdg.ADERDG.ADERDG._generate_kernels(), exahype2.solvers.fv.FV.FV.add_actions_to_perform_time_step(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.add_actions_to_perform_time_step(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.add_actions_to_perform_time_step(), exahype2.solvers.aderdg.ADERDG.ADERDG.add_actions_to_plot_solution(), exahype2.solvers.fv.FV.FV.add_actions_to_plot_solution(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.add_actions_to_plot_solution(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.add_actions_to_plot_solution(), exahype2.solvers.aderdg.ADERDG.ADERDG.add_implementation_files_to_project(), exahype2.solvers.fv.EnclaveTasking.EnclaveTasking.add_implementation_files_to_project(), exahype2.solvers.rkdg.SeparateSweepsWithEnclaveTasking.SeparateSweepsWithEnclaveTasking.add_implementation_files_to_project(), and exahype2.solvers.rkfd.SeparateSweepsWithEnclaveTasking.SeparateSweepsWithEnclaveTasking.add_implementation_files_to_project().

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◆ add_implementation_files_to_project()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.add_implementation_files_to_project	(	self,
		namespace,
		output,
		subdirectory = "" )

The ExaHyPE2 project will call this operation when it sets up the overall environment.

This routine is typically not invoked by a user.

output: peano4.output.Output

Definition at line 350 of file ConstrainedPoissonEquationForMarkerOnCells.py.

◆ add_to_Peano4_datamodel()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.add_to_Peano4_datamodel	(	self,
		datamodel,
		verbose )

Add all required data to the Peano4 project's datamodel so it is properly built up.

Definition at line 234 of file ConstrainedPoissonEquationForMarkerOnCells.py.

◆ add_use_data_statements_to_Peano4_solver_step()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.add_use_data_statements_to_Peano4_solver_step	(		self,
			step )

Tell Peano what data to move around.

Inform Peano4 step which data are to be moved around via the use_cell and use_face commands. This operation is generic from ExaHyPE's point of view, i.e. I use it for all grid sweep types.

Definition at line 249 of file ConstrainedPoissonEquationForMarkerOnCells.py.

References exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells._cell_data_model, and exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells._face_data_model.

◆ create_action_sets()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.create_action_sets ( self )

Overwrite in subclasses if you wanna create different action sets.

Call order and ownership

This operation can be called multiple times. However, only the very last call matters. All previous calls are wiped out.

If you have a hierarchy of solvers, every create_data_structure() should first(!) call its parent version. This way, you always ensure that all data are in place before you continue to alter the more specialised versions. So it is (logically) a top-down (general to specialised) run through all create_data_structure() variants within the inheritance tree.

Postprocessing algorithm

After we have updated the cell, i.e. computed the Poisson equation update, we launch a series of postprocessing steps:

We impose the value constraints, i.e. ensure the solution is within min and max.

Definition at line 172 of file ConstrainedPoissonEquationForMarkerOnCells.py.

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◆ create_data_structures()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.create_data_structures ( self )

Create cell and face data structures required.

For the face data, we rely on the multigrid toolbox routines.

Definition at line 154 of file ConstrainedPoissonEquationForMarkerOnCells.py.

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◆ create_readme_descriptor()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.create_readme_descriptor	(	self,
		domain_offset,
		domain_size )

Definition at line 147 of file ConstrainedPoissonEquationForMarkerOnCells.py.

◆ get_name_of_global_instance()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.get_name_of_global_instance ( self )

Definition at line 230 of file ConstrainedPoissonEquationForMarkerOnCells.py.

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◆ name()

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.name ( self )

Definition at line 393 of file ConstrainedPoissonEquationForMarkerOnCells.py.

Referenced by exahype2.solvers.aderdg.kernels.Gemms.Gemms.__repr__(), swift2.particle.ExplicitEulerFixedSearchRadius.ExplicitEulerFixedSearchRadius.__setup_algorithm_steps(), swift2.particle.LeapfrogFixedSearchRadius.LeapfrogFixedSearchRadius.__setup_algorithm_steps(), swift2.particle.AlgorithmStep.AlgorithmStep.__str__(), peano4.datamodel.DoF.DoF.additional_load_and_store_arguments_for_other_dof(), swift2.particle.ExplicitEulerDynamicSearchRadius.ExplicitEulerDynamicSearchRadius.algorithm_steps(), swift2.particle.tests.DastgenTestDummyParticle.DastgenTestDummyParticle.algorithm_steps(), peano4.solversteps.UserActionSet.UserActionSet.get_action_set_name(), peano4.datamodel.DoF.DoF.get_full_qualified_type(), peano4.datamodel.DoF.DoF.get_logical_type_name(), dastgen2.attributes.Enumeration.Enumeration.get_to_string(), and swift2.particle.Particle.Particle.readme_descriptor().

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◆ postprocess_updated_cell() [1/2]

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.postprocess_updated_cell ( self )

Definition at line 398 of file ConstrainedPoissonEquationForMarkerOnCells.py.

References exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells._postprocess_updated_cell.

◆ postprocess_updated_cell() [2/2]

exahype2.solvers.elliptic.ConstrainedPoissonEquationForMarkerOnCells.ConstrainedPoissonEquationForMarkerOnCells.postprocess_updated_cell	(		self,
			kernel )

Define a postprocessing routine over the data.

Typically, you do something similar to

if ( not repositories::{{SOLVER_INSTANCE}}.patchCanUseStatelessPDETerms(marker.x(), marker.h(), timeStamp, timeStepSize) ) { fineGridCell{{CELL_NAME}}.setValue(1.0); }

We evaluate some criterion (here, we only look at a global function, but we also have access to all the other solver data in the kernel) and then set the cell value to the maximum if the criterion holds.