Reference documentation for deal.II version Git d9b14c2d54 2019-09-14 18:13:29 -0600
TensorProductPolynomialsConst< dim > Class Template Reference

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

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

template<class Pol >
TensorProductPolynomialsConst (const std::vector< Pol > &pols)

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

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

Public Member Functions inherited from TensorProductPolynomials< dim >
TensorProductPolynomials (const std::vector< Pol > &pols)

void output_indices (std::ostream &out) const

void set_numbering (const std::vector< unsigned int > &renumber)

const std::vector< unsigned int > & get_numbering () const

const std::vector< unsigned int > & get_numbering_inverse () const

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

double compute_value (const unsigned int i, const Point< dim > &p) const

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

## Static Public Attributes

static const unsigned int dimension = dim

Static Public Attributes inherited from TensorProductPolynomials< dim >
static const unsigned int dimension

Protected Member Functions inherited from TensorProductPolynomials< dim >
void compute_index (const unsigned int i, unsigned int(&indices)[(dim > 0 ? dim :1)]) const

Protected Attributes inherited from TensorProductPolynomials< dim >
std::vector< Polynomials::Polynomial< double > > polynomials

unsigned int n_tensor_pols

std::vector< unsigned int > index_map

std::vector< unsigned int > index_map_inverse

## Detailed Description

### template<int dim> class TensorProductPolynomialsConst< dim >

Tensor product of given polynomials and a locally constant function. This class inherits most of its functionality from TensorProductPolynomials. It works similarly to that class but adds a constant function for the last index.

Definition at line 48 of file tensor_product_polynomials_const.h.

## ◆ TensorProductPolynomialsConst()

template<int dim>
template<class Pol >
 TensorProductPolynomialsConst< dim >::TensorProductPolynomialsConst ( const std::vector< Pol > & pols )

Constructor. pols is a vector of objects that should be derived or otherwise convertible to one-dimensional polynomial objects. It will be copied element by element into a private variable.

## ◆ evaluate()

template<int dim>
 void TensorProductPolynomialsConst< 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

Compute the value and the first and second derivatives of each tensor product 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.

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.

Definition at line 89 of file tensor_product_polynomials_const.cc.

## ◆ compute_value()

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

Compute the value of the ith tensor product polynomial at unit_point. Here i is given in tensor product numbering.

Note, that using this function within a loop over all tensor product polynomials is not efficient, because then each point value of the underlying (one-dimensional) polynomials is (unnecessarily) computed several times. Instead use the compute() function with values.size()==n() to get the point values of all tensor polynomials all at once and in a much more efficient way.

Definition at line 29 of file tensor_product_polynomials_const.cc.

## ◆ compute_derivative()

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

Compute the orderth derivative of the ith tensor product polynomial at unit_point. Here i is given in tensor product numbering.

Note, that using this function within a loop over all tensor product polynomials is not efficient, because then each derivative value of the underlying (one-dimensional) polynomials is (unnecessarily) computed several times. Instead use the compute() function, see above, with the size of the appropriate parameter set to n() to get the point value of all tensor polynomials all at once and in a much more efficient way.

Template Parameters
 order The derivative order.

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

Compute the grad of the ith tensor product polynomial at unit_point. Here i is given in tensor product numbering.

Note, that using this function within a loop over all tensor product polynomials is not efficient, because then each derivative value of the underlying (one-dimensional) polynomials is (unnecessarily) computed several times. Instead use the compute() function, see above, with grads.size()==n() to get the point value of all tensor polynomials all at once and in a much more efficient way.

Definition at line 57 of file tensor_product_polynomials_const.cc.

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

Compute the second derivative (grad_grad) of the ith tensor product polynomial at unit_point. Here i is given in tensor product numbering.

Note, that using this function within a loop over all tensor product polynomials is not efficient, because then each derivative value of the underlying (one-dimensional) polynomials is (unnecessarily) computed several times. Instead use the compute() function, see above, with grad_grads.size()==n() to get the point value of all tensor polynomials all at once and in a much more efficient way.

Definition at line 73 of file tensor_product_polynomials_const.cc.

## ◆ n()

template<int dim>
 unsigned int TensorProductPolynomialsConst< dim >::n ( ) const

Return the number of tensor product polynomials plus the constant function. For n 1d polynomials this is ndim+1.

## ◆ dimension

template<int dim>
 const unsigned int TensorProductPolynomialsConst< dim >::dimension = dim
static

Access to the dimension of this object, for checking and automatic setting of dimension in other classes.

Definition at line 55 of file tensor_product_polynomials_const.h.

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