Reference documentation for deal.II version 9.5.0
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#include <deal.II/base/polynomials_adini.h>
Public Member Functions | |
PolynomialsAdini () | |
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 |
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 |
template<int order> | |
Tensor< order, dim > | compute_derivative (const unsigned int i, const Point< dim > &p) const |
unsigned int | n () const |
virtual unsigned int | degree () const |
virtual std::size_t | memory_consumption () 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 |
const unsigned int | polynomial_degree |
const unsigned int | n_pols |
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 44 of file polynomials_adini.h.
PolynomialsAdini< dim >::PolynomialsAdini |
Constructor for the polynomials of the described space
Definition at line 42 of file polynomials_adini.cc.
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overridevirtual |
Compute 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.
Implements ScalarPolynomialsBase< dim >.
Definition at line 138 of file polynomials_adini.cc.
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overridevirtual |
Compute the value of the i
th polynomial at unit_point
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 193 of file polynomials_adini.cc.
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inlineoverridevirtual |
Compute the first derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 181 of file polynomials_adini.h.
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inlineoverridevirtual |
Compute the second derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 192 of file polynomials_adini.h.
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inlineoverridevirtual |
Compute the third derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 203 of file polynomials_adini.h.
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inlineoverridevirtual |
Compute the fourth derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 214 of file polynomials_adini.h.
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overridevirtual |
Compute the gradient of the i
th polynomial at unit_point
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 209 of file polynomials_adini.cc.
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overridevirtual |
Compute the second derivative (grad_grad) of the i
th polynomial at unit_point
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 233 of file polynomials_adini.cc.
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inlineoverridevirtual |
Return the name of the space, which is PolynomialsAdini
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Implements ScalarPolynomialsBase< dim >.
Definition at line 225 of file polynomials_adini.h.
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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 262 of file polynomials_adini.cc.
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inlineinherited |
Compute the order
th derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
order | The order of the derivative. |
Definition at line 259 of file scalar_polynomials_base.h.
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inlineinherited |
Return the number of polynomials.
Definition at line 240 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 249 of file scalar_polynomials_base.h.
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virtualinherited |
Return an estimate (in bytes) for the memory consumption of this object.
Reimplemented in BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, TensorProductPolynomials< dim, PolynomialType >, and TensorProductPolynomials< dim - 1 >.
Definition at line 39 of file scalar_polynomials_base.cc.
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private |
Store the coefficients of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)
Definition at line 144 of file polynomials_adini.h.
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private |
Store the coefficients of the x-derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)
Definition at line 150 of file polynomials_adini.h.
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private |
Store the coefficients of the y-derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)
Definition at line 156 of file polynomials_adini.h.
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private |
Store the coefficients of the second x-derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)
Definition at line 162 of file polynomials_adini.h.
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private |
Store the coefficients of the second y-derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)
Definition at line 168 of file polynomials_adini.h.
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private |
Store the coefficients of the second mixed derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)
Definition at line 174 of file polynomials_adini.h.
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privateinherited |
The highest polynomial degree of this functions represented by this object.
Definition at line 228 of file scalar_polynomials_base.h.
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privateinherited |
The number of polynomials represented by this object.
Definition at line 233 of file scalar_polynomials_base.h.