exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis Class Reference

The Gauss-Lobatto quadrature points do not yield a diagonal mass matrix. More...

Inheritance diagram for exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis:

Collaboration diagram for exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis:

Public Member Functions
	__init__ (self, polynomial_order)
	quadrature_points (self)
Public Member Functions inherited from exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix
	__str__ (self)
	init_dictionary_with_default_parameters (self, dictionary, use_multidimensional_arrays)
	To be implemented by subclass.
	quadrature_weights (self)
	value1d (self, x, number)
	Return the numberth shape function's value at x.
	derivative1d (self, x, number)
	Return the numberth shape function's derivative at x.
Public Member Functions inherited from exahype2.solvers.LagrangeBasis.LagrangeBasis
	order (self)
	dofs_per_axis (self)

Additional Inherited Members
Data Fields inherited from exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix
	dofs_per_axis
Static Public Attributes inherited from exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix
str	QuadraturePoints1dDocumentation
str	QuadratureWeights1dDocumentation
str	MassMatrix1dDocumentation
str	StiffnessOperator1dDocumentation
str	BasisFunctionValuesLeft1dDocumentation
str	DerivativeOperator1dDocumentation
str	InterpolationMatrix1dDocumentation
str	RestrictionMatrix1dDocumentation
Protected Attributes inherited from exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix
	_polynomial_order
Protected Attributes inherited from exahype2.solvers.LagrangeBasis.LagrangeBasis
	_polynomial_order
	_render_digits

Detailed Description

The Gauss-Lobatto quadrature points do not yield a diagonal mass matrix.

They yield a full matrix. However, there are codes which ignore this fact and lump the basis. Mathematically, this is equivalent to the Gauss-Lobatto quadrature because this leads to a diagonal matrix that is easy to invert

Definition at line 684 of file LagrangeBasisWithDiagonalMassMatrix.py.

Constructor & Destructor Documentation

__init__()

exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis.__init__	(		self,
			polynomial_order )

Reimplemented from exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix.

Definition at line 694 of file LagrangeBasisWithDiagonalMassMatrix.py.

References exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis.__init__().

Referenced by exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis.__init__().

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Member Function Documentation

quadrature_points()

exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis.quadrature_points

(

self

)

Reimplemented from exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix.

Definition at line 699 of file LagrangeBasisWithDiagonalMassMatrix.py.

References exahype2.solvers.aderdg.LagrangeBasis.LagrangeBasis._transform_and_sort_points_and_weights(), exahype2.solvers.LagrangeBasis.LagrangeBasis.dofs_per_axis(), exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix.dofs_per_axis, and peano4.toolbox.blockstructured.ReconstructPatchAndApplyFunctor.ReconstructPatchAndApplyFunctor.dofs_per_axis.

Referenced by exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix.__compute_derivative_operator(), exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix.__compute_restriction_matrix(), exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix.derivative1d(), exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix.init_dictionary_with_default_parameters(), and exahype2.solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix.value1d().

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

• python/exahype2/solvers/LagrangeBasisWithDiagonalMassMatrix.py