Public Member Functions | |
PolynomialsRaviartThomas (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 |
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 |
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.
PolynomialsRaviartThomas< dim >::PolynomialsRaviartThomas | ( | const unsigned int | k | ) |
Constructor. Creates all basis functions for Raviart-Thomas polynomials of given degree.
void PolynomialsRaviartThomas< 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 PolynomialsRaviartThomas< dim >::n | ( | ) | const [inline] |
Returns the number of Raviart-Thomas polynomials.
References PolynomialsRaviartThomas< dim >::n_pols.
unsigned int PolynomialsRaviartThomas< dim >::degree | ( | ) | const [inline] |
Returns the degree of the Raviart-Thomas space, which is one less than the highest polynomial degree.
References PolynomialsRaviartThomas< dim >::my_degree.
static unsigned int PolynomialsRaviartThomas< 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 PolynomialsRaviartThomas. This is required by the FiniteElement classes.
static std::vector<std::vector< Polynomials::Polynomial< double > > > PolynomialsRaviartThomas< 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 PolynomialsRaviartThomas< dim >::my_degree [private] |
The degree of this object as given to the constructor.
Referenced by PolynomialsRaviartThomas< dim >::degree().
const AnisotropicPolynomials<dim> PolynomialsRaviartThomas< 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.
const unsigned int PolynomialsRaviartThomas< dim >::n_pols [private] |
Number of Raviart-Thomas polynomials.
Referenced by PolynomialsRaviartThomas< dim >::n().