Public Member Functions | |
PolynomialsABF (const unsigned int k) | |
~PolynomialsABF () | |
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 |
Static Public Member Functions | |
static unsigned int | compute_n_pols (unsigned int degree) |
Private Attributes | |
const unsigned int | my_degree |
AnisotropicPolynomials< dim > * | polynomial_space |
unsigned int | n_pols |
std::vector< double > | p_values |
std::vector< Tensor< 1, dim > > | p_grads |
std::vector< Tensor< 2, dim > > | p_grad_grads |
This class implements the Hdiv-conforming, vector-valued Arnold-Boffi-Falk polynomials as described in the article by Arnold-Boffi-Falk: Quadrilateral H(div) finite elements, SIAM J. Numer. Anal. Vol.42, No.6, pp.2429-2451
The ABF polynomials are constructed such that the divergence is in the tensor product polynomial space Qk. Therefore, the polynomial order of each component must be two orders higher in the corresponding direction, yielding the polynomial spaces (Qk+2,k, Qk,k+2) and (Qk+2,k,k, Qk,k+2,k, Qk,k,k+2) in 2D and 3D, resp.
PolynomialsABF< dim >::PolynomialsABF | ( | const unsigned int | k | ) |
Constructor. Creates all basis functions for Raviart-Thomas polynomials of given degree.
PolynomialsABF< dim >::~PolynomialsABF | ( | ) |
Destructor deleting the polynomials.
void PolynomialsABF< 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 Raviart-Thomas 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 PolynomialsABF< dim >::n | ( | ) | const [inline] |
Returns the number of ABF polynomials.
References PolynomialsABF< dim >::n_pols.
unsigned int PolynomialsABF< dim >::degree | ( | ) | const [inline] |
Returns the degree of the ABF space, which is two less than the highest polynomial degree.
References PolynomialsABF< dim >::my_degree.
static unsigned int PolynomialsABF< dim >::compute_n_pols | ( | unsigned int | degree | ) | [static] |
Return the number of polynomials in the space RT(degree)
without requiring to build an object of PolynomialsABF. This is required by the FiniteElement classes.
const unsigned int PolynomialsABF< dim >::my_degree [private] |
The degree of this object as given to the constructor.
Referenced by PolynomialsABF< dim >::degree().
AnisotropicPolynomials<dim>* PolynomialsABF< 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.
unsigned int PolynomialsABF< dim >::n_pols [private] |
Number of Raviart-Thomas polynomials.
Referenced by PolynomialsABF< dim >::n().
std::vector<double> PolynomialsABF< dim >::p_values [mutable, private] |
Auxiliary memory.
std::vector<Tensor<1,dim> > PolynomialsABF< dim >::p_grads [mutable, private] |
Auxiliary memory.
std::vector<Tensor<2,dim> > PolynomialsABF< dim >::p_grad_grads [mutable, private] |
Auxiliary memory.