Matrix-free Collocated Solver for d-linear shape functions. More...

Inheritance diagram for solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi:

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Collaboration diagram for solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi:

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Public Member Functions
	__init__ (self, name, unknowns_per_vertex, dimensions, min_h, max_h, local_assembly_matrix, local_assembly_matrix_scaling, mass_matrix, mass_matrix_scaling, solver_tolerance, smoother_relaxation=0.6, custom_init_actionset=None, custom_plot_actionset=None, custom_init_vertex="", custom_boundary_conditions="", enable_plotting=True, plot_predicate="true")
	Collocated low-order (d-linear) Finite Elements.

	add_to_Peano4_datamodel (self, datamodel, verbose)

	add_use_statements (self, observer)
	This routine should still be called even if overwritten in child class.

	add_to_plot (self, observer)
	Tell the project's observer how to plot the data.

	add_to_create_grid (self, observer)

	add_to_init_solution (self, observer)
	Solution initialisation.

	add_to_solve (self, observer)

	add_implementation_files_to_project (self, namespace, output, subdirectory="", abstract_overwrite=True)
	The solver creates two classes: An abstract base class and its implementations.

	get_vertex_merge_method (self)

Public Member Functions inherited from solvers.api.Solver.Solver
	typename (self)

	instance_name (self)
	Return the name of the object that will be created for this solver.

	create_readme_descriptor (self)

	add_to_abstract_solver (self, header, implementation)

	add_to_vertex_data (self, name, size)
	Add in extra attributes on the fly.

	add_to_cell_data (self, name, size)
	Add in extra attributes on the fly.

	add_to_face_data (self, name, size)
	Add in extra attributes on the fly.

	name (self)

	__str__ (self)

Data Fields
	max_h

	min_h

Data Fields inherited from solvers.api.Solver.Solver
	min_h

	max_h

Detailed Description

Matrix-free Collocated Solver for d-linear shape functions.

Mathematical and algorithmic descriptions are to follow later. For now, we describe how to use this solver and a little about how it works under the hood.

Each vertex stores a certain number of values, given by the parameter unknowns_per_vertex. In essence, if this parameter is more than one, we are solving multiple different equations simultaneously, or we can equivalently think of our PDE being vector-valued.

The user needs to provide an assembly matrix, and a mass matrix. If our vector-valued PDE has \( K \) components, then each of these matrices should be square, with \( K * 2^D \) rows.

In particular, they should be structured as block diagonals. Let \( A_i \) be square with \( 2^D \) rows. Then the mass/assembly matrices should be structured as follows:

\( diag( A_1, A_2, \dots A_K ) \).

During the actual solver step, we run through each equation one after another, fetching the appropriate mass and assembly matrices for the equation in hand.

At present, it hasn't been decided how to plot the output of multiple equations, since only 1 is supported.

Data held on the vertices

Solution (formerly named Value)

This array holds the actual solution which we later plot. This is updated when we touch a vertex for the last time.

Rhs

This array holds the right-hand side of the equation. We assign this in experiment-specific implementation files.

Diagonal

This array holds the sum of the diagonals of the local assembly matrix. This is set to 0 at the start of every solver step

Residual

This is used to store \( Mb - Ax \), i.e. the RHS multiplied by the matrix, and subtract the solution multiplied by the assembly matrix.

Solver Steps

Initialisation

After the grid is created, we run around the mesh and assign types to the vertices and cells.

Vertices:

"Coarse" if the vertex is due to be refined
"Interior" if it's not on the boundary
"Boundary" if it is on the boundary

Cells:

"Coarse" if it's due to be refined
Otherwise marked as "Interior"

Solve

There is only one action set in this solver. We do something non-trivial during touchCellFirstTime, touchVertexFirstTime and touchVertexLastTime.

touchVertexFirstTime

We check that the Vertex is not a coarse grid vertex, then we set the residuals and the diagonals to 0.

touchCellFirstTime

All four vertices are in scope here. We create three vectors, each of length \( 2^D \) to hold one value per vertex. For each vertex in the cell (regardless of whether it is on the boundary), we :

Update the residual to be \( Mb - Ax \)
Increment the diagonal

touchVertexLastTime

We update the solution value (on all vertices) to be equal to the solution at the previous sweep, and we add on \( \omega \times r / d \) where \( r \) and \( d \) stand for the residual and diagonal respectively.

Enforcement of boundary conditions

Todos

We currently overcount the residual on vertices that are shared across boundaries. This isn't an issue at present, since we only check for the max, which is unaffected by this bug. But something to fix at later date.

Definition at line 19 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Constructor & Destructor Documentation

◆ init()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.__init__	(	self,
		name,
		unknowns_per_vertex,
		dimensions,
		min_h,
		max_h,
		local_assembly_matrix,
		local_assembly_matrix_scaling,
		mass_matrix,
		mass_matrix_scaling,
		solver_tolerance,
		smoother_relaxation = `0.6`,
		custom_init_actionset = `None`,
		custom_plot_actionset = `None`,
		custom_init_vertex = `""`,
		custom_boundary_conditions = `""`,
		enable_plotting = `True`,
		plot_predicate = `"true"`
	)

Collocated low-order (d-linear) Finite Elements.

Reimplemented from solvers.api.Solver.Solver.

Definition at line 115 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

References solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.__init__(), solvers.api.Solver.Solver._vertex_data, solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.get_vertex_merge_method(), solvers.api.CollocatedMG.CollocatedMG.get_vertex_merge_method(), and solvers.api.CollocatedMGSingleThreaded.CollocatedMGSingleThreaded.get_vertex_merge_method().

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.__init__().

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Member Function Documentation

◆ add_implementation_files_to_project()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_implementation_files_to_project	(	self,
		namespace,
		output,
		subdirectory = `""`,
		abstract_overwrite = `True`
	)

The solver creates two classes: An abstract base class and its implementations.

The abstract base class will be overwritten if there is one in the directory. I pipe all the Python constants into this base class, so they are available in the C++ code.

Definition at line 258 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

References peano4.api.output.ActionSet.ActionSet.__class__, peano4.api.output.Jinja2TemplatedHeaderImplementationFilePair.Jinja2TemplatedHeaderImplementationFilePair.__class__, and peano4.api.output.TemplatedHeaderFile.TemplatedHeaderFile.__class__.

◆ add_to_create_grid()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_create_grid	(	self,
		observer
	)

Definition at line 227 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ add_to_init_solution()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_init_solution	(	self,
		observer
	)

Solution initialisation.

We can either use the standard initialisation procedure or pass in another one when we instantiate this solver class.

Definition at line 231 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

References solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._custom_init_actionset, solvers.api.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi._custom_init_actionset, and solvers.api.DiscontinuousGalerkinDiscretisationPointWiseRiemannSolver.DiscontinuousGalerkinDiscretisationPointWiseRiemannSolver._custom_init_actionset.

◆ add_to_Peano4_datamodel()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_Peano4_datamodel	(	self,
		datamodel,
		verbose
	)

Reimplemented from solvers.api.Solver.Solver.

Definition at line 186 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

References solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_Peano4_datamodel().

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_Peano4_datamodel().

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◆ add_to_plot()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_plot	(	self,
		observer
	)

Tell the project's observer how to plot the data.

Nothing fancy here. We add plotters from Peano's toolbox to visualise solution and right-hand side.

Definition at line 196 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ add_to_solve()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_solve	(	self,
		observer
	)

Definition at line 246 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

References solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._basic_descend_order, solvers.api.CollocatedMG.CollocatedMG._basic_descend_order, and solvers.api.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi._basic_descend_order.

◆ add_use_statements()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_use_statements	(	self,
		observer
	)

This routine should still be called even if overwritten in child class.

Reimplemented from solvers.api.Solver.Solver.

Definition at line 191 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

References solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_use_statements().

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_use_statements().

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◆ get_vertex_merge_method()

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.get_vertex_merge_method ( self )

Definition at line 331 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

References solvers.api.Solver.Solver.typename(), and api.solvers.Solver.Solver.typename().

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.__init__().

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Field Documentation

◆ _abstract_solver_header_extras

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._abstract_solver_header_extras

protected

Definition at line 289 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.Solver.Solver.add_to_abstract_solver().

◆ _abstract_solver_implementation_extras

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._abstract_solver_implementation_extras

protected

Definition at line 290 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.Solver.Solver.add_to_abstract_solver().

◆ _basic_descend_order

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._basic_descend_order

protected

Definition at line 174 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_solve(), solvers.api.CollocatedMG.CollocatedMG.add_to_solve(), solvers.api.CollocatedMGSingleThreaded.CollocatedMGSingleThreaded.add_to_solve(), and solvers.api.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.add_to_solve().

◆ _custom_boundary_conditions

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._custom_boundary_conditions

protected

Definition at line 181 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ _custom_init_actionset

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._custom_init_actionset

protected

Definition at line 177 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_init_solution(), and solvers.api.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.add_to_init_solution().

◆ _custom_init_vertex

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._custom_init_vertex

protected

Definition at line 180 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ _custom_plot_actionset

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._custom_plot_actionset

protected

Definition at line 178 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_plot(), and solvers.api.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.add_to_plot().

◆ _enable_plotting

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._enable_plotting

protected

Definition at line 183 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_plot(), and solvers.api.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.add_to_plot().

◆ _local_assembly_matrix

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._local_assembly_matrix

protected

Definition at line 167 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ _local_assembly_matrix_scaling

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._local_assembly_matrix_scaling

protected

Definition at line 168 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ _mass_matrix

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._mass_matrix

protected

Definition at line 170 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ _mass_matrix_scaling

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._mass_matrix_scaling

protected

Definition at line 171 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ _plot_predicate

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._plot_predicate

protected

Definition at line 184 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.add_to_plot(), solvers.api.CollocatedMG.CollocatedMG.add_to_plot(), and solvers.api.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.ContinuousGalerkinDiscretisationGaussLobattoWithBlockJacobi.add_to_plot().

◆ _smoother_relaxation

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._smoother_relaxation

protected

Definition at line 175 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ _solver_tolerance

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._solver_tolerance

protected

Definition at line 172 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ _unknowns_per_vertex_node

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi._unknowns_per_vertex_node

protected

Definition at line 165 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

◆ max_h

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.max_h

Definition at line 228 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.Solver.Solver.__str__(), exaparty.api.particle.Particle.Particle.readme_descriptor(), and tarch.plotter.api.filters.ExtractMeshResolution.ExtractMeshResolution.render().

◆ min_h

solvers.api.CollocatedDLinearDiscretisationWithPointJacobi.CollocatedDLinearDiscretisationWithPointJacobi.min_h

Definition at line 279 of file CollocatedDLinearDiscretisationWithPointJacobi.py.

Referenced by solvers.api.Solver.Solver.__str__(), exaparty.api.particle.Particle.Particle.readme_descriptor(), and tarch.plotter.api.filters.ExtractMeshResolution.ExtractMeshResolution.render().

The documentation for this class was generated from the following file:

src/mghype/matrixfree/solvers/api/CollocatedDLinearDiscretisationWithPointJacobi.py

Protected Attributes
	_unknowns_per_vertex_node

	_local_assembly_matrix

	_local_assembly_matrix_scaling

	_mass_matrix

	_mass_matrix_scaling

	_solver_tolerance

	_basic_descend_order

	_smoother_relaxation

	_custom_init_actionset

	_custom_plot_actionset

	_custom_init_vertex

	_custom_boundary_conditions

	_enable_plotting

	_plot_predicate

	_abstract_solver_header_extras

	_abstract_solver_implementation_extras

Protected Attributes inherited from solvers.api.Solver.Solver
	_name

	_vertex_data

	_face_data

	_cell_data

	_abstract_solver_header_extras

	_abstract_solver_implementation_extras

Public Member Functions

Data Fields

Protected Attributes

Detailed Description

Data held on the vertices

Solution (formerly named Value)

Rhs

Diagonal

Residual

Solver Steps

Initialisation

Solve

touchVertexFirstTime

touchCellFirstTime

touchVertexLastTime

Enforcement of boundary conditions

Todos

Constructor & Destructor Documentation

◆ __init__()

Member Function Documentation

◆ add_implementation_files_to_project()

◆ add_to_create_grid()

◆ add_to_init_solution()

◆ add_to_Peano4_datamodel()

◆ add_to_plot()

◆ add_to_solve()

◆ add_use_statements()

◆ get_vertex_merge_method()

Field Documentation

◆ _abstract_solver_header_extras

◆ _abstract_solver_implementation_extras

◆ _basic_descend_order

◆ _custom_boundary_conditions

◆ _custom_init_actionset

◆ _custom_init_vertex

◆ _custom_plot_actionset

◆ _enable_plotting

◆ _local_assembly_matrix

◆ _local_assembly_matrix_scaling

◆ _mass_matrix

◆ _mass_matrix_scaling

◆ _plot_predicate

◆ _smoother_relaxation

◆ _solver_tolerance

◆ _unknowns_per_vertex_node

◆ max_h

◆ min_h

◆ init()