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Base class for generating matrices that we pipe into the C++ code. More...

Inheritance diagram for mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator:

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Public Member Functions
	__init__ (self, dimensions, poly_degree, unknowns_per_node=1)

	get_polynomial1d (self)
	Method to create a list of 1D polynomials.

	get_points1d (self)
	Method to set the quadrature points, used for integration.

	get_integration_points_over_unit_interval (self)
	Most schemes define the integration point over the interval [-1,1] whereas MGHyPE often needs it on the unit interval.

	get_weights1d (self)
	Method to set the quadrature weights, used for integration.

	get_points_for_dimension (self, dim=-1)
	We promote the 1D quadrature points in into the dimensions of our problem by taking cartesian product.

	get_weights_for_dimension (self, dim=-1)
	We promote the 1D quadrature weights in into the dimensions of our problem by taking cartesian product.

	convert_index_to_dim (self, index, dim=-1)
	This method helps with indexing.

	get_polynomial (self, index, dim=-1)
	Promote 1d polynomials to many dimensions by taking products.

	get_deriv (self, index, dimForDeriv, dim=-1)
	dimForDeriv is the singular dimension that we wanna take a polyderiv in

	eval_integral (self, functions, dim=-1, factor=1)

	get_cell_system_matrix_for_laplacian (self)
	Construct the Laplacian.

	get_cell_mass_matrix (self)
	Factory for cell mass matrix.

	get_cell_identity_matrix (self)
	Construct identity for this particular equation system.

Data Fields
	dimensions

	poly_degree

	unknowns_per_node

	polynomials1d

	derivatives1d

	points1d

	weights1d

Detailed Description

Base class for generating matrices that we pipe into the C++ code.

Every method marked abstract is intended to be overwritten in child classes, but some will come with default behaviour.

Definition at line 12 of file MatrixGenerator.py.

Constructor & Destructor Documentation

◆ init()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.__init__	(	self,
		dimensions,
		poly_degree,
		unknowns_per_node = 1 )

Reimplemented in mghype.api.matrixgenerators.GaussLobatto.GaussLobattoMatrixFree, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity, and mghype.api.matrixgenerators.DLinear.DLinear.

Definition at line 21 of file MatrixGenerator.py.

Member Function Documentation

◆ convert_index_to_dim()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.convert_index_to_dim	(	self,
		index,
		dim = -1 )

This method helps with indexing.

Typically, for polynomial degree p, we have (p+1) nodal points per coordinate axis, for a total of \( p^d \). This method converts an index in the range \( (0, ..., p^d) \) into a tuple of (x,y,z) coordinates.

Definition at line 175 of file MatrixGenerator.py.

References exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.dimensions, exahype2.symhype.PDE.PDE.dimensions, peano4.visualisation.input.PatchFileParser.UnknownAttributes.dimensions, peano4.visualisation.input.PatchFileParser.PatchFileParser.dimensions, convert::data::PatchData.dimensions, convert::data::Variable.dimensions, mghype.api.matrixgenerators.DLinear.DLinear.dimensions, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobattoMatrixFree.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.dimensions, api.solvers.DiscontinuousGalerkinDiscretisation.DiscontinuousGalerkinDiscretisation.dimensions, equations.acoustic.Acoustic.dimensions, equations.advection.Advection.dimensions, equations.elastic.Elastic.dimensions, equations.equation.Equation.dimensions, equations.euler.Euler.dimensions, equations.swe.SWE_W_Bathymetry.dimensions, equations.swe.SWE_WO_Bathymetry.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.poly_degree, and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.poly_degree.

Referenced by mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_deriv(), and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_polynomial().

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◆ eval_integral()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.eval_integral	(	self,
		functions,
		dim = -1,
		factor = 1 )

Reimplemented in mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.

Definition at line 273 of file MatrixGenerator.py.

References exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.dimensions, exahype2.symhype.PDE.PDE.dimensions, peano4.visualisation.input.PatchFileParser.UnknownAttributes.dimensions, peano4.visualisation.input.PatchFileParser.PatchFileParser.dimensions, convert::data::PatchData.dimensions, convert::data::Variable.dimensions, mghype.api.matrixgenerators.DLinear.DLinear.dimensions, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobattoMatrixFree.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.dimensions, api.solvers.DiscontinuousGalerkinDiscretisation.DiscontinuousGalerkinDiscretisation.dimensions, equations.acoustic.Acoustic.dimensions, equations.advection.Advection.dimensions, equations.elastic.Elastic.dimensions, equations.equation.Equation.dimensions, equations.euler.Euler.dimensions, equations.swe.SWE_W_Bathymetry.dimensions, equations.swe.SWE_WO_Bathymetry.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_points_for_dimension(), and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_weights_for_dimension().

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◆ get_cell_identity_matrix()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_cell_identity_matrix ( self )

Construct identity for this particular equation system.

Not that this is identity construction has to take the number of unknowns into account as well as the number of degrees of freedom hosted within a cell.

Reimplemented in mghype.api.matrixgenerators.DLinear.DLinear, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto, and mghype.api.matrixgenerators.GaussLobatto.GaussLobattoMatrixFree.

Definition at line 337 of file MatrixGenerator.py.

Referenced by mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.get_cell_mass_matrix().

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◆ get_cell_mass_matrix()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_cell_mass_matrix ( self )

Factory for cell mass matrix.

Consult get_cell_system_matrix_for_laplacian() for an overview of the result types. As the mass matrix is typically fairly simple (it does not host any derivative), and as we work within a finite element mindset, this routine returns a list with one matrix as first argument, and then a list with the integer self.dimensions.

Definition at line 322 of file MatrixGenerator.py.

Referenced by mghype.api.matrixgenerators.DLinear.DLinear.get_lumped_mass_matrix(), and mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.get_lumped_mass_matrix().

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◆ get_cell_system_matrix_for_laplacian()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_cell_system_matrix_for_laplacian ( self )

Construct the Laplacian.

Create the Laplacian. This routine represents the fact that the Laplacian is kind of the evergreen of many PDEs, and we therefore provide a factory method for this one always.

These factory methods all return two lists. The first one is a list of matrices \( A_1, A_2, ... \) defined relative to the unit cube or square, respectively. The second list has the same length as the first list, and stores integer indices \( k_1, k_2, k_3, ... \). Throughout the assemly, you should then apply the local matrix \( A = h^{k_1} A_1 + h^{k_2} A_2 + ... \). The mass matrix typically is only one matrix scaled with d, i.e. we return a list hosting only one matrix as first argument and the second list only hosts the integer self.dimensions.

Implement this in child class.

Returns: [Matrix] x [Int] The two lists have to have the same number of entries.

Definition at line 292 of file MatrixGenerator.py.

Referenced by mghype.api.matrixgenerators.GaussLobatto.GaussLobattoMatrixFree.get_A_tilde().

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◆ get_deriv()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_deriv	(	self,
		index,
		dimForDeriv,
		dim = -1 )

dimForDeriv is the singular dimension that we wanna take a polyderiv in

Behaves the same as get_polynomial, except in that in the specified dimension, we take a derivative rather than the poly itself

Definition at line 238 of file MatrixGenerator.py.

References assert, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.convert_index_to_dim(), mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.derivatives1d, exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.dimensions, exahype2.symhype.PDE.PDE.dimensions, peano4.visualisation.input.PatchFileParser.UnknownAttributes.dimensions, peano4.visualisation.input.PatchFileParser.PatchFileParser.dimensions, convert::data::PatchData.dimensions, convert::data::Variable.dimensions, mghype.api.matrixgenerators.DLinear.DLinear.dimensions, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobattoMatrixFree.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.dimensions, api.solvers.DiscontinuousGalerkinDiscretisation.DiscontinuousGalerkinDiscretisation.dimensions, equations.acoustic.Acoustic.dimensions, equations.advection.Advection.dimensions, equations.elastic.Elastic.dimensions, equations.equation.Equation.dimensions, equations.euler.Euler.dimensions, equations.swe.SWE_W_Bathymetry.dimensions, equations.swe.SWE_WO_Bathymetry.dimensions, and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.polynomials1d.

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◆ get_integration_points_over_unit_interval()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_integration_points_over_unit_interval ( self )

Most schemes define the integration point over the interval [-1,1] whereas MGHyPE often needs it on the unit interval.

Therefore, I offer this genereric recalibration routine.

Definition at line 80 of file MatrixGenerator.py.

References mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.get_points1d(), and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_points1d().

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◆ get_points1d()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_points1d ( self )

Method to set the quadrature points, used for integration.

Provide a method here to produce Gauss-Legendre points, but this can be overwritten in child class.

Slightly redundant use of the leggauss function here, but I thought it better to separate the calculation of points and weights for ease of implementing in child class.

Reimplemented in mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.

Definition at line 63 of file MatrixGenerator.py.

References mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.poly_degree, and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.poly_degree.

Referenced by mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_integration_points_over_unit_interval(), and mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.get_weights1d().

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◆ get_points_for_dimension()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_points_for_dimension	(		self,
			dim = -1 )

We promote the 1D quadrature points in into the dimensions of our problem by taking cartesian product.

This works for any dimension and does not need to be implemented in the child class.

We may need to produce arrays of points for number of dimensions which is less

Definition at line 110 of file MatrixGenerator.py.

References exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.dimensions, exahype2.symhype.PDE.PDE.dimensions, peano4.visualisation.input.PatchFileParser.UnknownAttributes.dimensions, peano4.visualisation.input.PatchFileParser.PatchFileParser.dimensions, convert::data::PatchData.dimensions, convert::data::Variable.dimensions, mghype.api.matrixgenerators.DLinear.DLinear.dimensions, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobattoMatrixFree.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.dimensions, api.solvers.DiscontinuousGalerkinDiscretisation.DiscontinuousGalerkinDiscretisation.dimensions, equations.acoustic.Acoustic.dimensions, equations.advection.Advection.dimensions, equations.elastic.Elastic.dimensions, equations.equation.Equation.dimensions, equations.euler.Euler.dimensions, equations.swe.SWE_W_Bathymetry.dimensions, equations.swe.SWE_WO_Bathymetry.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.points1d, and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.points1d.

Referenced by mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.eval_integral().

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◆ get_polynomial()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_polynomial	(	self,
		index,
		dim = -1 )

Promote 1d polynomials to many dimensions by taking products.

We pass in an index and a dimension, which will, by default be set to the number of dimensions of the problem.

The index should be betweeen 0 and (self.poly_degree)^self.dimensions

We convert the index into a tuple (x,y,z) of indices, pull out appropriate polynomials and return a function object. This function object will expect dim arguments.

Definition at line 195 of file MatrixGenerator.py.

References assert, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.convert_index_to_dim(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.dimensions, exahype2.symhype.PDE.PDE.dimensions, peano4.visualisation.input.PatchFileParser.UnknownAttributes.dimensions, peano4.visualisation.input.PatchFileParser.PatchFileParser.dimensions, convert::data::PatchData.dimensions, convert::data::Variable.dimensions, mghype.api.matrixgenerators.DLinear.DLinear.dimensions, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobattoMatrixFree.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.dimensions, api.solvers.DiscontinuousGalerkinDiscretisation.DiscontinuousGalerkinDiscretisation.dimensions, equations.acoustic.Acoustic.dimensions, equations.advection.Advection.dimensions, equations.elastic.Elastic.dimensions, equations.equation.Equation.dimensions, equations.euler.Euler.dimensions, equations.swe.SWE_W_Bathymetry.dimensions, equations.swe.SWE_WO_Bathymetry.dimensions, and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.polynomials1d.

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◆ get_polynomial1d()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_polynomial1d ( self )

Method to create a list of 1D polynomials.

We promote these to higher dimensions by taking tensor products.

By default, we will return Lagrange polynomials, but we can overwrite this in child class

Definition at line 36 of file MatrixGenerator.py.

References mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.poly_degree, and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.poly_degree.

◆ get_weights1d()

mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.get_weights1d ( self )

Method to set the quadrature weights, used for integration.

Provide a method here to produce Gauss-Legendre weights, but this can be overwritten in child class.

Slightly redundant use of the leggauss function here, but I thought it better to separate the calculation of points and weights for ease of implementing in child class.

Reimplemented in mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.

Definition at line 93 of file MatrixGenerator.py.

References mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.poly_degree, and mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.poly_degree.