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Reference documentation for deal.II version 8.1.0
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#include <polynomials_bdm.h>
Public Member Functions | |
PolynomialsBDM (const unsigned int k) | |
void | compute (const Point< dim > &unit_point, std::vector< Tensor< 1, dim > > &values, std::vector< Tensor< 2, dim > > &grads, std::vector< Tensor< 3, dim > > &grad_grads) const |
unsigned int | n () const |
unsigned int | degree () const |
std::string | name () const |
Static Public Member Functions | |
static unsigned int | compute_n_pols (unsigned int degree) |
Private Attributes | |
const PolynomialSpace< dim > | polynomial_space |
std::vector < Polynomials::Polynomial < double > > | monomials |
unsigned int | n_pols |
Threads::Mutex | mutex |
std::vector< double > | p_values |
std::vector< Tensor< 1, dim > > | p_grads |
std::vector< Tensor< 2, dim > > | p_grad_grads |
This class implements the Hdiv-conforming, vector-valued Brezzi-Douglas-Marini polynomials as described in the book by Brezzi and Fortin.
These polynomial spaces are based on the space Pk, realized by a PolynomialSpace constructed with Legendre polynomials. Since these shape functions are not sufficient, additional functions are added. These are the following vector valued polynomials:
Definition at line 63 of file polynomials_bdm.h.
PolynomialsBDM< dim >::PolynomialsBDM | ( | const unsigned int | k | ) |
Constructor. Creates all basis functions for BDM polynomials of given degree.
void PolynomialsBDM< dim >::compute | ( | const Point< dim > & | unit_point, |
std::vector< Tensor< 1, dim > > & | values, | ||
std::vector< Tensor< 2, dim > > & | grads, | ||
std::vector< Tensor< 3, dim > > & | grad_grads | ||
) | const |
Computes the value and the first and second derivatives of each BDM polynomial 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 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.
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inline |
Returns the number of BDM polynomials.
Definition at line 187 of file polynomials_bdm.h.
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inline |
Returns the degree of the BDM space, which is one less than the highest polynomial degree.
Definition at line 195 of file polynomials_bdm.h.
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inline |
Return the name of the space, which is BDM
.
Definition at line 203 of file polynomials_bdm.h.
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static |
Return the number of polynomials in the space BDM(degree)
without requiring to build an object of PolynomialsBDM. This is required by the FiniteElement classes.
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private |
An object representing the polynomial space used here. The constructor fills this with the monomial basis.
Definition at line 145 of file polynomials_bdm.h.
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private |
Storage for monomials. In 2D, this is just the polynomial of order k. In 3D, we need all polynomials from degree zero to k.
Definition at line 154 of file polynomials_bdm.h.
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private |
Number of BDM polynomials.
Definition at line 160 of file polynomials_bdm.h.
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mutableprivate |
A mutex that guards the following scratch arrays.
Definition at line 166 of file polynomials_bdm.h.
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mutableprivate |
Auxiliary memory.
Definition at line 171 of file polynomials_bdm.h.
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mutableprivate |
Auxiliary memory.
Definition at line 176 of file polynomials_bdm.h.
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mutableprivate |
Auxiliary memory.
Definition at line 181 of file polynomials_bdm.h.