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Reference documentation for deal.II version 9.6.0
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#include <deal.II/base/tensor_product_polynomials.h>
Public Member Functions | |
template<class Pol > | |
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 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 |
std::string | name () const override |
virtual std::unique_ptr< ScalarPolynomialsBase< dim > > | clone () const override |
virtual std::size_t | memory_consumption () const override |
std::vector< PolynomialType > | get_underlying_polynomials () const |
void | output_indices (std::ostream &) const |
void | set_numbering (const std::vector< unsigned int > &) |
double | compute_value (const unsigned int, const Point< 0 > &) const |
Tensor< 1, 0 > | compute_grad (const unsigned int, const Point< 0 > &) const |
Tensor< 2, 0 > | compute_grad_grad (const unsigned int, const Point< 0 > &) const |
void | evaluate (const Point< 0 > &, std::vector< double > &, std::vector< Tensor< 1, 0 > > &, std::vector< Tensor< 2, 0 > > &, std::vector< Tensor< 3, 0 > > &, std::vector< Tensor< 4, 0 > > &) const |
unsigned int | n () const |
virtual unsigned int | degree () const |
Static Public Attributes | |
static constexpr unsigned int | dimension = dim |
Protected Member Functions | |
void | compute_index (const unsigned int i, std::array< unsigned int, dim > &indices) const |
void | compute_index (const unsigned int, std::array< unsigned int, 0 > &) const |
Protected Attributes | |
std::vector< PolynomialType > | polynomials |
std::vector< unsigned int > | index_map |
std::vector< unsigned int > | index_map_inverse |
Private Attributes | |
const unsigned int | polynomial_degree |
const unsigned int | n_pols |
Friends | |
class | TensorProductPolynomialsBubbles< dim > |
class | TensorProductPolynomialsConst< dim > |
Tensor product of given polynomials.
Given a vector of n one-dimensional polynomials P1 to Pn, this class generates ndim polynomials of the form Qijk(x,y,z) = Pi(x)Pj(y)Pk(z). If the base polynomials are mutually orthogonal on the interval [-1,1] or [0,1], then the tensor product polynomials are orthogonal on [-1,1]dim or [0,1]dim, respectively.
Indexing is as follows: the order of dim-dimensional polynomials is x-coordinates running fastest, then y-coordinate, etc. The first few polynomials are thus P1(x)P1(y), P2(x)P1(y), P3(x)P1(y), ..., P1(x)P2(y), P2(x)P2(y), P3(x)P2(y), ... and likewise in 3d.
The output_indices() function prints the ordering of the dim-dimensional polynomials, i.e. for each polynomial in the polynomial space it gives the indices i,j,k of the one-dimensional polynomials in x,y and z direction. The ordering of the dim-dimensional polynomials can be changed by using the set_numbering() function.
PolynomialType | A class that satisfies the required interface for computing tensor products. Typical choices for this template argument are Polynomials::Polynomial and Polynomials::PiecewisePolynomial. |
Definition at line 75 of file tensor_product_polynomials.h.
TensorProductPolynomials< dim, PolynomialType >::TensorProductPolynomials | ( | const std::vector< Pol > & | pols | ) |
Constructor. pols
is a vector of objects that should be derived or otherwise convertible to one-dimensional polynomial objects of type PolynomialType
(template argument of class). It will be copied element by element into a protected member variable.
void TensorProductPolynomials< dim, PolynomialType >::output_indices | ( | std::ostream & | out | ) | const |
Print the list of the indices to out
.
Definition at line 110 of file tensor_product_polynomials.cc.
void TensorProductPolynomials< dim, PolynomialType >::set_numbering | ( | const std::vector< unsigned int > & | renumber | ) |
Set the ordering of the polynomials. Requires renumber.size()==n()
. Stores a copy of renumber
.
Definition at line 180 of file tensor_product_polynomials.cc.
const std::vector< unsigned int > & TensorProductPolynomials< dim, PolynomialType >::get_numbering | ( | ) | const |
Give read access to the renumber vector.
const std::vector< unsigned int > & TensorProductPolynomials< dim, PolynomialType >::get_numbering_inverse | ( | ) | const |
Give read access to the inverse renumber vector.
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overridevirtual |
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.
Implements ScalarPolynomialsBase< dim >.
Definition at line 542 of file tensor_product_polynomials.cc.
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overridevirtual |
Compute the value of the i
th 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 evaluate() function with values.size()==
n() to get the point values of all tensor polynomials all at once and in a much more efficient way.
Implements ScalarPolynomialsBase< dim >.
Definition at line 205 of file tensor_product_polynomials.cc.
Tensor< order, dim > TensorProductPolynomials< dim, PolynomialType >::compute_derivative | ( | const unsigned int | i, |
const Point< dim > & | p ) const |
Compute the order
th derivative of the i
th 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 evaluate() 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.
order | The derivative order. |
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overridevirtual |
Compute the first derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
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overridevirtual |
Compute the second derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
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overridevirtual |
Compute the third derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
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overridevirtual |
Compute the fourth derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
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overridevirtual |
Compute the grad of the i
th 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 evaluate() 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.
Implements ScalarPolynomialsBase< dim >.
Definition at line 238 of file tensor_product_polynomials.cc.
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overridevirtual |
Compute the second derivative (grad_grad) of the i
th 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 evaluate() 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.
Implements ScalarPolynomialsBase< dim >.
Definition at line 288 of file tensor_product_polynomials.cc.
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overridevirtual |
Return the name of the space, which is TensorProductPolynomials
.
Implements ScalarPolynomialsBase< dim >.
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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 652 of file tensor_product_polynomials.cc.
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overridevirtual |
Return an estimate (in bytes) for the memory consumption of this object.
Reimplemented from ScalarPolynomialsBase< dim >.
Definition at line 661 of file tensor_product_polynomials.cc.
std::vector< PolynomialType > TensorProductPolynomials< dim, PolynomialType >::get_underlying_polynomials | ( | ) | const |
Return a copy of the underlying one-dimensional polynomials given to the constructor of this class.
Definition at line 672 of file tensor_product_polynomials.cc.
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inlineprotected |
Each tensor product polynomial i is a product of one-dimensional polynomials in each space direction. Compute the indices of these one-dimensional polynomials for each space direction, given the index i.
Definition at line 83 of file tensor_product_polynomials.cc.
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inlineprotected |
Definition at line 99 of file tensor_product_polynomials.cc.
void TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::output_indices | ( | std::ostream & | ) | const |
Definition at line 128 of file tensor_product_polynomials.cc.
void TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::set_numbering | ( | const std::vector< unsigned int > & | ) |
Definition at line 195 of file tensor_product_polynomials.cc.
double TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::compute_value | ( | const unsigned int | , |
const Point< 0 > & | ) const |
Definition at line 225 of file tensor_product_polynomials.cc.
Tensor< 1, 0 > TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::compute_grad | ( | const unsigned int | , |
const Point< 0 > & | ) const |
Definition at line 275 of file tensor_product_polynomials.cc.
Tensor< 2, 0 > TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::compute_grad_grad | ( | const unsigned int | , |
const Point< 0 > & | ) const |
Definition at line 333 of file tensor_product_polynomials.cc.
void TensorProductPolynomials< 0, Polynomials::Polynomial< double > >::evaluate | ( | const Point< 0 > & | , |
std::vector< double > & | , | ||
std::vector< Tensor< 1, 0 > > & | , | ||
std::vector< Tensor< 2, 0 > > & | , | ||
std::vector< Tensor< 3, 0 > > & | , | ||
std::vector< Tensor< 4, 0 > > & | ) const |
Definition at line 637 of file tensor_product_polynomials.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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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.
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friend |
TensorProductPolynomialsBubbles has a TensorProductPolynomials class so we declare it as a friend class.
Definition at line 277 of file tensor_product_polynomials.h.
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friend |
TensorProductPolynomialsConst has a TensorProductPolynomials class so we declare it as a friend class.
Definition at line 277 of file tensor_product_polynomials.h.
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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 82 of file tensor_product_polynomials.h.
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protected |
Copy of the vector pols
of polynomials given to the constructor.
Definition at line 258 of file tensor_product_polynomials.h.
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protected |
Index map for reordering the polynomials.
Definition at line 263 of file tensor_product_polynomials.h.
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protected |
Index map for reordering the polynomials.
Definition at line 268 of file tensor_product_polynomials.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.