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Reference documentation for deal.II version 8.1.0
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#include <polynomials_adini.h>
Public Member Functions | |
PolynomialsAdini () | |
void | compute (const Point< 2 > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, 2 > > &grads, std::vector< Tensor< 2, 2 > > &grad_grads) const |
double | compute_value (const unsigned int i, const Point< 2 > &p) const |
Tensor< 1, 2 > | compute_grad (const unsigned int i, const Point< 2 > &p) const |
Tensor< 2, 2 > | compute_grad_grad (const unsigned int i, const Point< 2 > &p) const |
Tensor< 2, 2 > | compute_grad_grad_2 (const unsigned int i, const Point< 2 > &p) const |
Private Attributes | |
Table< 2, double > | coef |
Table< 2, double > | dx |
Table< 2, double > | dy |
Table< 2, double > | dxx |
Table< 2, double > | dyy |
Table< 2, double > | dxy |
The cubic polynomial space for the Adini element
This space consists of the cubic space P3 augmented by the functions xy3 and x3y.
The basis of the space is chosen to match the node functionals of the Adini element.
Definition at line 42 of file polynomials_adini.h.
PolynomialsAdini::PolynomialsAdini | ( | ) |
Constructor for the polynomials of the described space
void PolynomialsAdini::compute | ( | const Point< 2 > & | unit_point, |
std::vector< double > & | values, | ||
std::vector< Tensor< 1, 2 > > & | grads, | ||
std::vector< Tensor< 2, 2 > > & | grad_grads | ||
) | const |
Computes 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.
Computes the value of the i
th polynomial at unit_point
.
Consider using compute() instead.
Computes the gradient of the i
th polynomial at unit_point
.
Consider using compute() instead.
Tensor<2,2> PolynomialsAdini::compute_grad_grad | ( | const unsigned int | i, |
const Point< 2 > & | p | ||
) | const |
Computes the second derivative (grad_grad) of the i
th polynomial at unit_point
.
Consider using compute() instead.
Store the coefficients of the polynominals in the order
Definition at line 121 of file polynomials_adini.h.
Store the coefficients of the x-derivative of the polynominals in the order
Definition at line 129 of file polynomials_adini.h.
Store the coefficients of the y-derivative of the polynominals in the order
Definition at line 136 of file polynomials_adini.h.
Store the coefficients of the second x-derivative of the polynominals in the order
Definition at line 142 of file polynomials_adini.h.
Store the coefficients of the second y-derivative of the polynominals in the order
Definition at line 148 of file polynomials_adini.h.
Store the coefficients of the second mixed derivative of the polynominals in the order
Definition at line 154 of file polynomials_adini.h.