deal.II version GIT relicensing-2206-gaa53ff9447 2024-12-02 09:10:00+00:00
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#include <deal.II/base/polynomials_p.h>
Public Member Functions | |
PolynomialsP (const unsigned int p) | |
virtual unsigned int | degree () const override |
std::array< unsigned int, dim > | directional_degrees (unsigned int n) const |
std::unique_ptr< ScalarPolynomialsBase< dim > > | clone () const override |
template<typename StreamType > | |
void | output_indices (StreamType &out) const |
void | set_numbering (const std::vector< unsigned int > &renumber) |
void | evaluate (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 override |
double | compute_value (const unsigned int i, const Point< dim > &p) const override |
template<int order> | |
Tensor< order, dim > | compute_derivative (const unsigned int i, const Point< dim > &p) const |
virtual Tensor< 1, dim > | compute_1st_derivative (const unsigned int i, const Point< dim > &p) const override |
virtual Tensor< 2, dim > | compute_2nd_derivative (const unsigned int i, const Point< dim > &p) const override |
virtual Tensor< 3, dim > | compute_3rd_derivative (const unsigned int i, const Point< dim > &p) const override |
virtual Tensor< 4, dim > | compute_4th_derivative (const unsigned int i, const Point< dim > &p) const override |
Tensor< 1, dim > | compute_grad (const unsigned int i, const Point< dim > &p) const override |
Tensor< 2, dim > | compute_grad_grad (const unsigned int i, const Point< dim > &p) const override |
unsigned int | n_polynomials (const unsigned int) |
std::string | name () const override |
unsigned int | n () const |
virtual std::size_t | memory_consumption () const |
Static Public Member Functions | |
static unsigned int | n_polynomials (const unsigned int n) |
Static Public Attributes | |
static constexpr unsigned int | dimension = dim |
Protected Member Functions | |
std::array< unsigned int, dim > | compute_index (const unsigned int n) const |
std::array< unsigned int, 1 > | compute_index (const unsigned int n) const |
std::array< unsigned int, 2 > | compute_index (const unsigned int n) const |
std::array< unsigned int, 3 > | compute_index (const unsigned int n) const |
std::array< unsigned int, 1 > | compute_index (const unsigned int i) const |
std::array< unsigned int, 2 > | compute_index (const unsigned int i) const |
std::array< unsigned int, 3 > | compute_index (const unsigned int i) const |
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 |
const std::vector< Polynomials::Polynomial< double > > | polynomials |
std::vector< unsigned int > | index_map |
std::vector< unsigned int > | index_map_inverse |
const unsigned int | polynomial_degree |
const unsigned int | n_pols |
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 46 of file polynomials_p.h.
PolynomialsP< dim >::PolynomialsP | ( | const unsigned int | p | ) |
Constructor. Creates all basis functions of \(P_p\).
Definition at line 22 of file polynomials_p.cc.
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inlineoverridevirtual |
Return the degree p
of the polynomial space P_p
.
Note, that this number is PolynomialSpace::degree()-1
, compare definition in PolynomialSpace.
Reimplemented from ScalarPolynomialsBase< dim >.
Definition at line 103 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 111 of file polynomials_p.h.
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inlineoverridevirtual |
A sort of virtual copy constructor, this function returns a copy of the polynomial space object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.
Some places in the library, for example the constructors of FE_Poly, need to make copies of polynomial spaces without knowing their exact type. They do so through this function.
Reimplemented from PolynomialSpace< dim >.
Definition at line 80 of file polynomials_p.h.
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private |
Fills the index_map
.
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private |
Definition at line 35 of file polynomials_p.cc.
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private |
Definition at line 60 of file polynomials_p.cc.
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private |
Definition at line 89 of file polynomials_p.cc.
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inherited |
Prints the list of the indices to out
.
Definition at line 317 of file polynomial_space.h.
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inherited |
Set the ordering of the polynomials. Requires renumber.size()==n()
. Stores a copy of renumber
.
Definition at line 113 of file polynomial_space.cc.
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overridevirtualinherited |
Compute the value and the first and second derivatives of each polynomial at unit_point
.
The size of the vectors must either be equal 0 or equal n(). In the first case, the function will not compute these values, i.e. you indicate what you want to have computed by resizing those vectors which you want filled.
If you need values or derivatives of all 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 polynomials.
Implements ScalarPolynomialsBase< dim >.
Definition at line 204 of file polynomial_space.cc.
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overridevirtualinherited |
Compute the value of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 127 of file polynomial_space.cc.
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inherited |
Compute the order
th derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
order | The order of the derivative. |
Definition at line 332 of file polynomial_space.h.
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inlineoverridevirtualinherited |
Compute the first derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 449 of file polynomial_space.h.
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inlineoverridevirtualinherited |
Compute the second derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 459 of file polynomial_space.h.
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inlineoverridevirtualinherited |
Compute the third derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 469 of file polynomial_space.h.
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inlineoverridevirtualinherited |
Compute the fourth derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 479 of file polynomial_space.h.
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overridevirtualinherited |
Compute the gradient of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 144 of file polynomial_space.cc.
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overridevirtualinherited |
Compute the second derivative (grad_grad) of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 169 of file polynomial_space.cc.
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staticinherited |
Return the number of polynomials spanning the space represented by this class. Here, if N
is the number of one-dimensional polynomials given, then the result of this function is N in 1d, N(N+1)/2 in 2d, and N(N+1)(N+2)/6 in 3d.
Definition at line 26 of file polynomial_space.cc.
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inherited |
Definition at line 40 of file polynomial_space.cc.
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inlineoverridevirtualinherited |
Return the name of the space, which is PolynomialSpace
.
Implements ScalarPolynomialsBase< dim >.
Definition at line 308 of file polynomial_space.h.
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protectedinherited |
Compute numbers in x, y and z direction. Given an index n
in the d-dimensional polynomial space, return the indices i,j,k such that pn(x,y,z) = pi(x)pj(y)pk(z).
In 1d and 2d, obviously only i and i,j are returned.
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protectedinherited |
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protectedinherited |
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protectedinherited |
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protectedinherited |
Definition at line 48 of file polynomial_space.cc.
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protectedinherited |
Definition at line 58 of file polynomial_space.cc.
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protectedinherited |
Definition at line 84 of file polynomial_space.cc.
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inlineinherited |
Return the number of polynomials.
Definition at line 239 of file scalar_polynomials_base.h.
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virtualinherited |
Return an estimate (in bytes) for the memory consumption of this object.
Reimplemented in BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, TensorProductPolynomials< dim, PolynomialType >, and TensorProductPolynomials< dim - 1 >.
Definition at line 38 of file scalar_polynomials_base.cc.
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staticconstexpr |
Access to the dimension of this object, for checking and automatic setting of dimension in other classes.
Definition at line 53 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 96 of file polynomials_p.h.
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privateinherited |
Copy of the vector pols
of polynomials given to the constructor.
Definition at line 255 of file polynomial_space.h.
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privateinherited |
Index map for reordering the polynomials.
Definition at line 260 of file polynomial_space.h.
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privateinherited |
Index map for reordering the polynomials.
Definition at line 265 of file polynomial_space.h.
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privateinherited |
The highest polynomial degree of this functions represented by this object.
Definition at line 227 of file scalar_polynomials_base.h.
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privateinherited |
The number of polynomials represented by this object.
Definition at line 232 of file scalar_polynomials_base.h.