simplex_basis.Basis Class Reference

Inheritance diagram for simplex_basis.Basis:

Public Member Functions
def	__init__ (self, order, orthogonal_polynomials, monomials, collocation_nodes, exact_quadrature_rule, face_quadrature_rule, positivity_preserving_extra_quad_nodes)
def	num_nodes (self)
def	cfl_limit (self)
def	ortho_collocation_vandermonde (self, sym='p')
def	ortho_vandermonde (self, points, sym='p')
def	V_inv (self)
def	ortho_optimal_gq_vandermonde (self, sym='p')
def	ortho_exact_quad_node_vandermonde (self, sym='p')
def	lagrange_optimal_gq_vandermonde (self)
def	monomial_collocation_vandermonde (self)
def	lagrange_mass_matrix (self)
def	M_inv (self)
def	lagrange_advection_matrix (self, sym)
	Computes the "advection" matrix for the Lagrange polynomials: \int p_i(x) d/dr p_j(x) \, dx, where the integral is taken over the simplex element.
def	lift_matrices (self)
def	element_average (self)
def	element_center (self)
def	evalute_at_positivity_preserving_extra_quad_nodes (self)
def	optimal_gq_source_mass_matrix (self)
def	lagrange_interpolating_polynomials (self)
	Return a list of polynomial objects which can be used to evaluate the Lagrange interpolating polynomials.
def	plot_positivity_nodes (self, ax)
def	save_figures (self, file, figs)

Public Attributes
	order
	max_degree
	orthogonal_polynomials
	collocation_nodes
	monomials
	exact_quadrature_rule
	face_quadrature_rule
	positivity_preserving_extra_quad_nodes

Constructor & Destructor Documentation

__init__()

def simplex_basis.Basis.__init__	(		self,
			order,
			orthogonal_polynomials,
			monomials,
			collocation_nodes,
			exact_quadrature_rule,
			face_quadrature_rule,
			positivity_preserving_extra_quad_nodes
	)

Reimplemented in line_basis.LineBasis, and triangle_basis.TriangleBasis.

Member Function Documentation

cfl_limit()

def simplex_basis.Basis.cfl_limit

(

self

)

element_average()

def simplex_basis.Basis.element_average

(

self

)

element_center()

def simplex_basis.Basis.element_center

(

self

)

evalute_at_positivity_preserving_extra_quad_nodes()

def simplex_basis.Basis.evalute_at_positivity_preserving_extra_quad_nodes

(

self

)

lagrange_advection_matrix()

def simplex_basis.Basis.lagrange_advection_matrix	(		self,
			sym
	)

Computes the "advection" matrix for the Lagrange polynomials: \int p_i(x) d/dr p_j(x) \, dx, where the integral is taken over the simplex element.

Parameters

sym	the symbol indicating which derivative is desired, i.e. dpdr for d/dr, or dpds for d/ds.

lagrange_interpolating_polynomials()

def simplex_basis.Basis.lagrange_interpolating_polynomials

(

self

)

Return a list of polynomial objects which can be used to evaluate the Lagrange interpolating polynomials.

lagrange_mass_matrix()

def simplex_basis.Basis.lagrange_mass_matrix

(

self

)

lagrange_optimal_gq_vandermonde()

def simplex_basis.Basis.lagrange_optimal_gq_vandermonde

(

self

)

lift_matrices()

def simplex_basis.Basis.lift_matrices

(

self

)

M_inv()

def simplex_basis.Basis.M_inv

(

self

)

monomial_collocation_vandermonde()

def simplex_basis.Basis.monomial_collocation_vandermonde

(

self

)

num_nodes()

def simplex_basis.Basis.num_nodes

(

self

)

Reimplemented in triangle_basis.TriangleBasis.

optimal_gq_source_mass_matrix()

def simplex_basis.Basis.optimal_gq_source_mass_matrix

(

self

)

ortho_collocation_vandermonde()

def simplex_basis.Basis.ortho_collocation_vandermonde	(		self,
			sym = 'p'
	)

ortho_exact_quad_node_vandermonde()

def simplex_basis.Basis.ortho_exact_quad_node_vandermonde	(		self,
			sym = 'p'
	)

ortho_optimal_gq_vandermonde()

def simplex_basis.Basis.ortho_optimal_gq_vandermonde	(		self,
			sym = 'p'
	)

ortho_vandermonde()

def simplex_basis.Basis.ortho_vandermonde	(		self,
			points,
			sym = 'p'
	)

plot_positivity_nodes()

def simplex_basis.Basis.plot_positivity_nodes	(		self,
			ax
	)

Reimplemented in line_basis.LineBasis, and triangle_basis.TriangleBasis.

save_figures()

def simplex_basis.Basis.save_figures	(		self,
			file,
			figs
	)

V_inv()

def simplex_basis.Basis.V_inv

(

self

)

Member Data Documentation

collocation_nodes

simplex_basis.Basis.collocation_nodes

exact_quadrature_rule

simplex_basis.Basis.exact_quadrature_rule

face_quadrature_rule

simplex_basis.Basis.face_quadrature_rule

max_degree

simplex_basis.Basis.max_degree

monomials

simplex_basis.Basis.monomials

order

simplex_basis.Basis.order

orthogonal_polynomials

simplex_basis.Basis.orthogonal_polynomials

positivity_preserving_extra_quad_nodes

simplex_basis.Basis.positivity_preserving_extra_quad_nodes

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

• src/basis/nodal_basis/generators/simplex_basis.py