Reference documentation for deal.II version 9.2.0
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#include <deal.II/base/polynomials_p.h>
Public Member Functions | |
PolynomialsP (const unsigned int p) | |
unsigned int | degree () const |
std::array< unsigned int, dim > | directional_degrees (unsigned int n) const |
Static Public Attributes | |
static const unsigned int | dimension = dim |
Private Member Functions | |
void | create_polynomial_ordering (std::vector< unsigned int > &index_map) const |
void | create_polynomial_ordering (std::vector< unsigned int > &index_map) const |
void | create_polynomial_ordering (std::vector< unsigned int > &index_map) const |
void | create_polynomial_ordering (std::vector< unsigned int > &index_map) const |
Private Attributes | |
const unsigned int | p |
This class implements the polynomial space of degree p
based on the monomials \({1,x,x^2,...}\). I.e. in d
dimensions it constructs all polynomials of the form \(\prod_{i=1}^d x_i^{n_i}\), where \(\sum_i n_i\leq p\). The base polynomials are given a specific ordering, e.g. in 2 dimensions: \({1,x,y,xy,x^2,y^2,x^2y,xy^2,x^3,y^3,...}\). The ordering of the monomials in \(P_k1\) matches the ordering of the monomials in \(P_k2\) for \(k2>k1\).
Definition at line 48 of file polynomials_p.h.
PolynomialsP< dim >::PolynomialsP | ( | const unsigned int | p | ) |
Constructor. Creates all basis functions of \(P_p\).
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 99 of file polynomials_p.h.
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inline |
For the n
th polynomial \(p_n(x,y,z)=x^i y^j z^k\) this function gives the degrees i,j,k in the x,y,z directions.
In 1d and 2d, obviously only i and i,j are returned.
Definition at line 107 of file polynomials_p.h.
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private |
Fills the index_map
.
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private |
Definition at line 36 of file polynomials_p.cc.
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private |
Definition at line 61 of file polynomials_p.cc.
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private |
Definition at line 90 of file polynomials_p.cc.
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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 \(P_p\), i.e. the number p
which was given to the constructor.
Definition at line 92 of file polynomials_p.h.