Public Member Functions | |
| PolynomialsNedelec (const unsigned int k) | |
| void | compute (const Point< dim > &unit_point, std::vector< Tensor< 1, dim > > &values, std::vector< Tensor< 2, dim > > &grads, std::vector< Tensor< 3, dim > > &grad_grads) const |
| unsigned int | n () const |
| unsigned int | degree () const |
| std::string | name () const |
Static Public Member Functions | |
| static unsigned int | compute_n_pols (unsigned int degree) |
Static Private Member Functions | |
| static std::vector < std::vector < Polynomials::Polynomial < double > > > | create_polynomials (const unsigned int k) |
Private Attributes | |
| const unsigned int | my_degree |
| const AnisotropicPolynomials< dim > | polynomial_space |
| const unsigned int | n_pols |
This class implements the first family Hcurl-conforming, vector-valued polynomials, proposed by J.-C. Nédélec in 1980 (Numer. Math. 35).
The Nédélec polynomials are constructed such that the curl is in the tensor product polynomial space Qk. Therefore, the polynomial order of each component must be one order higher in the corresponding two directions, yielding the polynomial spaces (Qk,k+1, Qk+1,k) and (Qk,k+1,k+1, Qk+1,k,k+1, Qk+1,k+1,k) in 2D and 3D, resp.
Definition at line 48 of file polynomials_nedelec.h.
| PolynomialsNedelec< dim >::PolynomialsNedelec | ( | const unsigned int | k | ) |
Constructor. Creates all basis functions for Nédélec polynomials of given degree.
| void PolynomialsNedelec< dim >::compute | ( | const Point< dim > & | unit_point, |
| std::vector< Tensor< 1, dim > > & | values, | ||
| std::vector< Tensor< 2, dim > > & | grads, | ||
| std::vector< Tensor< 3, dim > > & | grad_grads | ||
| ) | const |
Computes the value and the first and second derivatives of each Nédélec 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.
If you need values or derivatives of all tensor product polynomials then use this function, rather than using any of the compute_value, compute_grad or compute_grad_grad functions, see below, in a loop over all tensor product polynomials.
| unsigned int PolynomialsNedelec< dim >::n | ( | ) | const [inline] |
Returns the number of Nédélec polynomials.
Definition at line 153 of file polynomials_nedelec.h.
| unsigned int PolynomialsNedelec< dim >::degree | ( | ) | const [inline] |
Returns the degree of the Nédélec space, which is one less than the highest polynomial degree.
Definition at line 160 of file polynomials_nedelec.h.
| std::string PolynomialsNedelec< dim >::name | ( | ) | const [inline] |
Return the name of the space , which is Nedelec.
Definition at line 168 of file polynomials_nedelec.h.
| static unsigned int PolynomialsNedelec< dim >::compute_n_pols | ( | unsigned int | degree | ) | [static] |
Return the number of polynomials in the space N(degree) without requiring to build an object of PolynomialsNedelec. This is required by the FiniteElement classes.
| static std::vector<std::vector< Polynomials::Polynomial< double > > > PolynomialsNedelec< dim >::create_polynomials | ( | const unsigned int | k | ) | [static, private] |
A static member function that creates the polynomial space we use to initialize the polynomial_space member variable.
const unsigned int PolynomialsNedelec< dim >::my_degree [private] |
The degree of this object as given to the constructor.
Definition at line 125 of file polynomials_nedelec.h.
const AnisotropicPolynomials<dim> PolynomialsNedelec< dim >::polynomial_space [private] |
An object representing the polynomial space for a single component. We can re-use it by rotating the coordinates of the evaluation point.
Definition at line 134 of file polynomials_nedelec.h.
const unsigned int PolynomialsNedelec< dim >::n_pols [private] |
Number of Nédélec polynomials.
Definition at line 139 of file polynomials_nedelec.h.
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