mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre Class Reference

Concrete implementation for Gauss Legendre nodes. More...

Inheritance diagram for mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre:

Collaboration diagram for mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre:

Public Member Functions
	get_Gauss_Lobatto_nodes (self, poly_degree)
	Return coordinates of Gauss-Lobatto nodes in [-1, 1] for given polynomial degree.
	nodal_points (self, degree)
	Set nodal points xi_0, xi_1, ..., xi_p.
	node1d (self, degree, j)
	Return the j-th nodal point of a Lagrange polynomial of given degree :arg degree: polynomial degree :arg j: index of node.
	lagrange_polynomial (self, degree, k)
	Returns k-th basis function L^{(m)}_k(xi) of degree m as a numpy polynomial object :arg degree: polynomial degree :arg k: index of basis function (= index of node)
	evaluate (self, degree, k, xi)
	Evaluate the k-th basis function L^{(m)}_k(xi) of degree m at point xi in [-1,+1], return L^{(m)}_k(xi) :arg degree: polynomial degree :arg k: index of basis function :arg xi: position xi.
	evaluate_derivative (self, degree, k, xi)
	Evaluate the derivative of the k-basis function L^{(m)}_k(xi) of degree m at point xi in [-1,+1] return dL^{(m)}_k(xi)/dxi :arg degree: polynomial degree :arg k: index of basis function :arg xi: position xi.
	plot_basis_functions (self)
	Implement the below code in a method.
Public Member Functions inherited from mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasis
	__init__ (self, dim)
	Initialise a new instance :arg dim: dimension.

Additional Inherited Members
Data Fields inherited from mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasis
	dim
	Initialise a new instance :arg dim: dimension.

Detailed Description

Concrete implementation for Gauss Legendre nodes.

Definition at line 26 of file nodal_basis.py.

Member Function Documentation

evaluate()

mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.evaluate	(		self,
			degree,
			k,
			xi )

Evaluate the k-th basis function L^{(m)}_k(xi) of degree m at point xi in [-1,+1], return L^{(m)}_k(xi) :arg degree: polynomial degree :arg k: index of basis function :arg xi: position xi.

Definition at line 102 of file nodal_basis.py.

References mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.lagrange_polynomial().

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evaluate_derivative()

mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.evaluate_derivative	(		self,
			degree,
			k,
			xi )

Evaluate the derivative of the k-basis function L^{(m)}_k(xi) of degree m at point xi in [-1,+1] return dL^{(m)}_k(xi)/dxi :arg degree: polynomial degree :arg k: index of basis function :arg xi: position xi.

Definition at line 114 of file nodal_basis.py.

References mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.lagrange_polynomial().

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get_Gauss_Lobatto_nodes()

mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.get_Gauss_Lobatto_nodes	(		self,
			poly_degree )

Return coordinates of Gauss-Lobatto nodes in [-1, 1] for given polynomial degree.

Roots of deriv(P_{n-1}), where P_{n-1} is the Legendre polynomial and n is the number of nodal points; plus endpoints of the interval.

Definition at line 29 of file nodal_basis.py.

Referenced by mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.nodal_points().

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lagrange_polynomial()

mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.lagrange_polynomial	(		self,
			degree,
			k )

Returns k-th basis function L^{(m)}_k(xi) of degree m as a numpy polynomial object :arg degree: polynomial degree :arg k: index of basis function (= index of node)

Definition at line 88 of file nodal_basis.py.

References mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.nodal_points().

Referenced by mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.evaluate(), and mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.evaluate_derivative().

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nodal_points()

mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.nodal_points	(		self,
			degree )

Set nodal points xi_0, xi_1, ..., xi_p.

Definition at line 65 of file nodal_basis.py.

References mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.get_Gauss_Lobatto_nodes().

Referenced by mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.lagrange_polynomial(), and mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.node1d().

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node1d()

mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.node1d	(		self,
			degree,
			j )

Return the j-th nodal point of a Lagrange polynomial of given degree :arg degree: polynomial degree :arg j: index of node.

Reimplemented from mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasis.

Definition at line 79 of file nodal_basis.py.

References mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.nodal_points().

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plot_basis_functions()

mghype.api.matrixgenerators.blockmatrix.nodal_basis.NodalBasisGaussLegendre.plot_basis_functions

(

self

)

Implement the below code in a method.

Definition at line 127 of file nodal_basis.py.

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

• src/mghype/api/matrixgenerators/blockmatrix/nodal_basis.py