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

Inheritance diagram for solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis:

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Collaboration diagram for solvers.LagrangeBasisWithDiagonalMassMatrix.GaussLobattoBasisWithLumpedDiagonalBasis:

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Public Member Functions
	__init__ (self, polynomial_order)

	quadrature_points (self)

Public Member Functions inherited from 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 solvers.LagrangeBasis.LagrangeBasis
	order (self)

	dofs_per_axis (self)

Additional Inherited Members
Data Fields inherited from solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix
	mass_matrix

	dofs_per_axis

Static Public Attributes inherited from solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix
str	QuadraturePoints1dDocumentation

str	QuadratureWeights1dDocumentation

str	MassMatrix1dDocumentation

str	StiffnessOperator1dDocumentation

str	BasisFunctionValuesLeft1dDocumentation

str	DerivativeOperator1dDocumentation

str	InterpolationMatrix1dDocumentation

str	RestrictionMatrix1dDocumentation

	stiffness_matrix = None

Protected Attributes inherited from solvers.LagrangeBasisWithDiagonalMassMatrix.LagrangeBasisWithDiagonalMassMatrix
	_polynomial_order

Protected Attributes inherited from 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 690 of file LagrangeBasisWithDiagonalMassMatrix.py.