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Reference documentation for deal.II version 8.5.1
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#include <deal.II/base/polynomials_p.h>
Public Member Functions | |
PolynomialsP (const unsigned int p) | |
unsigned int | degree () const |
void | directional_degrees (unsigned int n, unsigned int(°rees)[dim]) const |
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template<class Pol > | |
PolynomialSpace (const std::vector< Pol > &pols) | |
template<class StreamType > | |
void | output_indices (StreamType &out) const |
void | set_numbering (const std::vector< unsigned int > &renumber) |
void | compute (const Point< dim > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, dim > > &grads, std::vector< Tensor< 2, dim > > &grad_grads, std::vector< Tensor< 3, dim > > &third_derivatives, std::vector< Tensor< 4, dim > > &fourth_derivatives) const |
double | compute_value (const unsigned int i, const Point< dim > &p) const |
template<int order> | |
Tensor< order, dim > | compute_derivative (const unsigned int i, const Point< dim > &p) const |
Tensor< 1, dim > | compute_grad (const unsigned int i, const Point< dim > &p) const |
Tensor< 2, dim > | compute_grad_grad (const unsigned int i, const Point< dim > &p) const |
unsigned int | n () const |
unsigned int | degree () const |
Static Public Attributes | |
static const unsigned int | dimension = dim |
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static const unsigned int | dimension = dim |
Private Member Functions | |
void | create_polynomial_ordering (std::vector< unsigned int > &index_map) const |
Private Attributes | |
const unsigned int | p |
Additional Inherited Members | |
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static unsigned int | compute_n_pols (const unsigned int n) |
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void | compute_index (const unsigned int n, unsigned int(&index)[dim >0?dim:1]) const |
This class implements the polynomial space of degree p
based on the monomials . I.e. in
d
dimensions it constructs all polynomials of the form , where
. The base polynomials are given a specific ordering, e.g. in 2 dimensions:
. The ordering of the monomials in
matches the ordering of the monomials in
for
.
Definition at line 48 of file polynomials_p.h.
PolynomialsP< dim >::PolynomialsP | ( | const unsigned int | p | ) |
Constructor. Creates all basis functions of .
Definition at line 23 of file polynomials_p.cc.
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inline |
Return the degree p
of the polynomial space P_p
.
Note, that this number is PolynomialSpace::degree()-1
, compare definition in PolynomialSpace.
Definition at line 96 of file polynomials_p.h.
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inline |
For the n
th polynomial this function gives the degrees i,j,k in the x,y,z directions.
Definition at line 104 of file polynomials_p.h.
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private |
Fills the index_map
.
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static |
Access to the dimension of this object, for checking and automatic setting of dimension in other classes.
Definition at line 55 of file polynomials_p.h.
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private |
Degree p
of the polynomial space , i.e. the number
p
which was given to the constructor.
Definition at line 89 of file polynomials_p.h.