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deal.II version GIT relicensing-3696-g88d7b26363 2025-07-08 15:10:00+00:00
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#include <deal.II/base/polynomials_raviart_thomas.h>
This class implements the Hdiv-conforming, Raviart-Thomas polynomials as described in the book by Brezzi and Fortin. Most of the functionality comes from the vector-valued anisotropic polynomials class PolynomialsVectorAnisotropic.
The Raviart-Thomas polynomials are constructed such that the divergence is in the tensor product polynomial space Qk. Therefore, the polynomial order of each component must be one order higher in the corresponding direction, yielding the polynomial spaces (Qk+1,k, Qk,k+1) and (Qk+1,k,k, Qk,k+1,k, Qk,k,k+1) in 2d and 3d, resp.
Definition at line 51 of file polynomials_raviart_thomas.h.
Public Member Functions | |
PolynomialsRaviartThomas (const unsigned int k) | |
virtual std::unique_ptr< TensorPolynomialsBase< dim > > | clone () const override |
void | evaluate (const Point< dim > &unit_point, std::vector< Tensor< 1, dim > > &values, std::vector< Tensor< 2, dim > > &grads, std::vector< Tensor< 3, dim > > &grad_grads, std::vector< Tensor< 4, dim > > &third_derivatives, std::vector< Tensor< 5, dim > > &fourth_derivatives) const override |
std::string | name () const override |
unsigned int | get_tangential_degree () const |
unsigned int | get_normal_degree () const |
std::vector< Point< dim > > | get_polynomial_support_points () const |
unsigned int | n () const |
unsigned int | degree () const |
Static Public Member Functions | |
static unsigned int | n_polynomials (const unsigned int degree) |
static std::vector< unsigned int > | get_lexicographic_numbering (const unsigned int degree) |
static unsigned int | n_polynomials (const unsigned int normal_degree, const unsigned int tangential_degree) |
Private Attributes | |
const unsigned int | normal_degree |
const unsigned int | tangential_degree |
const AnisotropicPolynomials< dim > | polynomial_space |
std::vector< unsigned int > | lexicographic_to_hierarchic |
std::vector< unsigned int > | hierarchic_to_lexicographic |
std::array< std::vector< unsigned int >, dim > | renumber_aniso |
const unsigned int | polynomial_degree |
const unsigned int | n_pols |
PolynomialsRaviartThomas< dim >::PolynomialsRaviartThomas | ( | const unsigned int | k | ) |
Constructor, using the common Raviart-Thomas space of degree k + 1
in normal direction and k
in the tangential directions.
Definition at line 30 of file polynomials_raviart_thomas.cc.
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static |
Variant of the n_polynomials() function taking only a single argument degree
, assuming degree + 1
in the normal direction and degree
in the tangential directions.
Definition at line 38 of file polynomials_raviart_thomas.cc.
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static |
Compute the lexicographic to hierarchic numbering underlying this class, computed as a free function.
Definition at line 47 of file polynomials_raviart_thomas.cc.
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overridevirtual |
A sort of virtual copy constructor, this function returns a copy of the polynomial space object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.
Some places in the library, for example the constructors of FE_PolyTensor, need to make copies of polynomial spaces without knowing their exact type. They do so through this function.
Reimplemented from PolynomialsVectorAnisotropic< dim >.
Definition at line 102 of file polynomials_raviart_thomas.cc.
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overridevirtualinherited |
Compute the value and certain derivatives of each anisotropic polynomial at unit_point
.
The size of the vectors must either be zero or equal n()
. In the first case, the function will not compute these values.
Implements TensorPolynomialsBase< dim >.
Definition at line 144 of file polynomials_vector_anisotropic.cc.
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overridevirtualinherited |
Return the name of the space, which is PolynomialsVectorAnisotropic
.
Implements TensorPolynomialsBase< dim >.
Definition at line 237 of file polynomials_vector_anisotropic.cc.
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staticinherited |
Return the number of polynomials in the space without requiring to build an object of PolynomialsVectorAnisotropic. This is required by the FiniteElement classes.
Definition at line 246 of file polynomials_vector_anisotropic.cc.
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inherited |
Return degree of polynomials in tangential direction.
Definition at line 258 of file polynomials_vector_anisotropic.cc.
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inherited |
Return degree of polynomials in normal direction.
Definition at line 267 of file polynomials_vector_anisotropic.cc.
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inherited |
Compute the generalized support points in the ordering used by the polynomial shape functions. Note that these points are not support points in the classical sense as the Lagrange polynomials of the different components have different points, which need to be combined in terms of Piola transformations.
Definition at line 285 of file polynomials_vector_anisotropic.cc.
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inlineinherited |
Return the number of polynomials.
Definition at line 151 of file tensor_polynomials_base.h.
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inlineinherited |
Return the highest polynomial degree of polynomials represented by this class. A derived class may override this if its value is different from my_degree
.
Definition at line 160 of file tensor_polynomials_base.h.
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privateinherited |
The given degree in the normal direction.
Definition at line 130 of file polynomials_vector_anisotropic.h.
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privateinherited |
The given degree in the tangential direction.
Definition at line 135 of file polynomials_vector_anisotropic.h.
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privateinherited |
An object representing the polynomial space for a single component. We can re-use it for all components by rotating the coordinates of the evaluation point.
Definition at line 142 of file polynomials_vector_anisotropic.h.
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privateinherited |
Renumbering from lexicographic order that is used in the underlying scalar anisotropic tensor-product polynomial space to the numbering used by the finite element.
Definition at line 149 of file polynomials_vector_anisotropic.h.
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privateinherited |
Renumbering from hierarchic to lexicographic order. Inverse of lexicographic_to_hierarchic.
Definition at line 155 of file polynomials_vector_anisotropic.h.
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privateinherited |
Renumbering from shifted polynomial spaces to lexicographic one.
Definition at line 160 of file polynomials_vector_anisotropic.h.
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privateinherited |
The highest polynomial degree of this functions represented by this object.
Definition at line 139 of file tensor_polynomials_base.h.
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privateinherited |
The number of polynomials represented by this object.
Definition at line 144 of file tensor_polynomials_base.h.