Reference documentation for deal.II version GIT relicensing-1412-g1ee3010991 2024-08-12 04:50:02+00:00
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ScalarLagrangePolynomialWedge< dim > Class Template Reference

#include <deal.II/base/polynomials_wedge.h>

Inheritance diagram for ScalarLagrangePolynomialWedge< dim >:
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## Public Member Functions

ScalarLagrangePolynomialWedge (const unsigned int degree)

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

Tensor< 1, dim > compute_1st_derivative (const unsigned int i, const Point< dim > &p) const override

Tensor< 2, dim > compute_2nd_derivative (const unsigned int i, const Point< dim > &p) const override

Tensor< 3, dim > compute_3rd_derivative (const unsigned int i, const Point< dim > &p) const override

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

std::string name () const override

virtual std::unique_ptr< ScalarPolynomialsBase< dim > > clone () const override

unsigned int n () const

virtual unsigned int degree () const

virtual std::size_t memory_consumption () const

## Static Public Attributes

static constexpr unsigned int dimension = dim

## Private Attributes

const BarycentricPolynomials< 2 > poly_tri

const BarycentricPolynomials< 1 > poly_line

const unsigned int polynomial_degree

const unsigned int n_pols

## Detailed Description

template<int dim>
class ScalarLagrangePolynomialWedge< dim >

Polynomials defined on wedge entities. This class is basis of FE_WedgeP.

The polynomials are created via a tensor product of a BarycentricPolynomials<2>::get_fe_p_basis(degree) and a BarycentricPolynomials<1>::get_fe_p_basis(degree), however, are re-numerated to better match the definition of FiniteElement.

Definition at line 75 of file polynomials_wedge.h.

## ◆ ScalarLagrangePolynomialWedge()

template<int dim>
 ScalarLagrangePolynomialWedge< dim >::ScalarLagrangePolynomialWedge ( const unsigned int degree )

Definition at line 43 of file polynomials_wedge.cc.

## ◆ evaluate()

template<int dim>
 void ScalarLagrangePolynomialWedge< dim >::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
overridevirtual

Compute the value and the derivatives of the polynomials 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 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.

Note
Currently, only the vectors values and grads are filled.

Implements ScalarPolynomialsBase< dim >.

Definition at line 113 of file polynomials_wedge.cc.

## ◆ compute_value()

template<int dim>
 double ScalarLagrangePolynomialWedge< dim >::compute_value ( const unsigned int i, const Point< dim > & p ) const
overridevirtual

Compute the value of the ith polynomial at unit point p.

Implements ScalarPolynomialsBase< dim >.

Definition at line 54 of file polynomials_wedge.cc.

## ◆ compute_derivative()

template<int dim>
template<int order>
 Tensor< order, dim > ScalarLagrangePolynomialWedge< dim >::compute_derivative ( const unsigned int i, const Point< dim > & p ) const

Compute the orderth derivative of the ith polynomial at unit point p.

Template Parameters
 order The order of the derivative.
Note
Currently, only implemented for first derivative.

Definition at line 186 of file polynomials_wedge.h.

## ◆ compute_1st_derivative()

template<int dim>
 Tensor< 1, dim > ScalarLagrangePolynomialWedge< dim >::compute_1st_derivative ( const unsigned int i, const Point< dim > & p ) const
overridevirtual

Compute the first derivative of the ith polynomial at unit point p.

Implements ScalarPolynomialsBase< dim >.

Definition at line 139 of file polynomials_wedge.cc.

## ◆ compute_2nd_derivative()

template<int dim>
 Tensor< 2, dim > ScalarLagrangePolynomialWedge< dim >::compute_2nd_derivative ( const unsigned int i, const Point< dim > & p ) const
overridevirtual

Compute the second derivative of the ith polynomial at unit point p.

Note
Not implemented yet.

Implements ScalarPolynomialsBase< dim >.

Definition at line 150 of file polynomials_wedge.cc.

## ◆ compute_3rd_derivative()

template<int dim>
 Tensor< 3, dim > ScalarLagrangePolynomialWedge< dim >::compute_3rd_derivative ( const unsigned int i, const Point< dim > & p ) const
overridevirtual

Compute the third derivative of the ith polynomial at unit point p.

Note
Not implemented yet.

Implements ScalarPolynomialsBase< dim >.

Definition at line 166 of file polynomials_wedge.cc.

## ◆ compute_4th_derivative()

template<int dim>
 Tensor< 4, dim > ScalarLagrangePolynomialWedge< dim >::compute_4th_derivative ( const unsigned int i, const Point< dim > & p ) const
overridevirtual

Compute the fourth derivative of the ith polynomial at unit point p.

Note
Not implemented yet.

Implements ScalarPolynomialsBase< dim >.

Definition at line 182 of file polynomials_wedge.cc.

template<int dim>
 Tensor< 1, dim > ScalarLagrangePolynomialWedge< dim >::compute_grad ( const unsigned int i, const Point< dim > & p ) const
overridevirtual

Compute the gradient of the ith polynomial at unit point p.

Note
Not implemented yet.

Implements ScalarPolynomialsBase< dim >.

Definition at line 73 of file polynomials_wedge.cc.

template<int dim>
 Tensor< 2, dim > ScalarLagrangePolynomialWedge< dim >::compute_grad_grad ( const unsigned int i, const Point< dim > & p ) const
overridevirtual

Compute the second derivative (grad_grad) of the ith polynomial at unit point p.

Note
Not implemented yet.

Implements ScalarPolynomialsBase< dim >.

Definition at line 99 of file polynomials_wedge.cc.

## ◆ name()

template<int dim>
 std::string ScalarLagrangePolynomialWedge< dim >::name ( ) const
overridevirtual

Return the name of the space.

Implements ScalarPolynomialsBase< dim >.

Definition at line 198 of file polynomials_wedge.cc.

## ◆ clone()

template<int dim>
 std::unique_ptr< ScalarPolynomialsBase< dim > > ScalarLagrangePolynomialWedge< dim >::clone ( ) const
overridevirtual

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.

Implements ScalarPolynomialsBase< dim >.

Definition at line 207 of file polynomials_wedge.cc.

## ◆ n()

template<int dim>
 unsigned int ScalarPolynomialsBase< dim >::n ( ) const
inlineinherited

Return the number of polynomials.

Definition at line 239 of file scalar_polynomials_base.h.

## ◆ degree()

template<int dim>
 unsigned int ScalarPolynomialsBase< dim >::degree ( ) const
inlinevirtualinherited

Return the highest polynomial degree of polynomials represented by this class. A derived class may override this if its value is different from my_degree.

Reimplemented in PolynomialsP< dim >.

Definition at line 248 of file scalar_polynomials_base.h.

## ◆ memory_consumption()

template<int dim>
 std::size_t ScalarPolynomialsBase< dim >::memory_consumption ( ) const
virtualinherited

Return an estimate (in bytes) for the memory consumption of this object.

Definition at line 38 of file scalar_polynomials_base.cc.

## ◆ dimension

template<int dim>
 constexpr unsigned int ScalarLagrangePolynomialWedge< dim >::dimension = dim
staticconstexpr

Make the dimension available to the outside.

Definition at line 81 of file polynomials_wedge.h.

## ◆ poly_tri

template<int dim>
 const BarycentricPolynomials<2> ScalarLagrangePolynomialWedge< dim >::poly_tri
private

Scalar polynomials defined on a triangle.

Definition at line 173 of file polynomials_wedge.h.

## ◆ poly_line

template<int dim>
 const BarycentricPolynomials<1> ScalarLagrangePolynomialWedge< dim >::poly_line
private

Scalar polynomials defined on a line.

Definition at line 178 of file polynomials_wedge.h.

## ◆ polynomial_degree

template<int dim>
 const unsigned int ScalarPolynomialsBase< dim >::polynomial_degree
privateinherited

The highest polynomial degree of this functions represented by this object.

Definition at line 227 of file scalar_polynomials_base.h.

## ◆ n_pols

template<int dim>
 const unsigned int ScalarPolynomialsBase< dim >::n_pols
privateinherited

The number of polynomials represented by this object.

Definition at line 232 of file scalar_polynomials_base.h.

The documentation for this class was generated from the following files: