Vectorial \( H(\text{div}) \) conforming shape functions on the unit simplex. More...
#include <nedelecshapefunctions.hh>
Detailed Description
class Kaskade::HdivSimplexShapeFunction< ctype, dimension, T >
Vectorial \( H(\text{div}) \) conforming shape functions on the unit simplex.
These form a basis of \( \mathbb{P}_p^d \) of the space of vectorial polynomials of degree at most \( p, p\ge 1 \). A shape function is represented as a linear combination of Lagrangian shape functions.
- Template Parameters
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ctype the coordinate type (a real number type) dimension the dimension of the unit simplex over which the shape functions are defined T the value type (a real number type)
Definition at line 333 of file nedelecshapefunctions.hh.
Public Types | |
| typedef ctype | CoordType |
Public Member Functions | |
| HdivSimplexShapeFunction ()=default | |
| Default constructor. Constructs a vanishing "shape function". Not particularly useful, but it's often convenient to have a default constructible class. More... | |
| template<class Coefficients > | |
| HdivSimplexShapeFunction (Coefficients const &coeff_, std::tuple< int, int, int, int > loc_) | |
| Creates a shape function as a linear combination of Lagrangian shape functions. More... | |
| virtual std::unique_ptr< ShapeFunction< ctype, dim, T, dim > > | clone () const |
| virtual Dune::FieldVector< T, dim > | evaluateFunction (Dune::FieldVector< ctype, dim > const &xi) const |
| Evaluates the shape function at point xi. More... | |
| virtual Dune::FieldMatrix< T, dim, dim > | evaluateDerivative (Dune::FieldVector< CoordType, dim > const &xi) const |
| Evaluates the derivative of the shape function. More... | |
| virtual Tensor< T, dim, dim, dim > | evaluate2ndDerivative (Dune::FieldVector< CoordType, dim > const &xi) const |
| Evaluates the second derivative of the shape function. More... | |
| virtual std::tuple< int, int, int, int > | location () const |
| Returns a tuple (nominalOrder,codim,entity,index) giving detailed information about the location of the shape function. More... | |
Static Public Attributes | |
| static int const | dim = dimension |
| static int const | comps = dim |
| static int const | order = 1 |
Member Typedef Documentation
◆ CoordType
| typedef ctype Kaskade::HdivSimplexShapeFunction< ctype, dimension, T >::CoordType |
Definition at line 340 of file nedelecshapefunctions.hh.
Constructor & Destructor Documentation
◆ HdivSimplexShapeFunction() [1/2]
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default |
Default constructor. Constructs a vanishing "shape function". Not particularly useful, but it's often convenient to have a default constructible class.
- Todo:
- makes only sense if it is assignable - any real need for default constructibility?
Referenced by Kaskade::HdivSimplexShapeFunction< ctype, dimension, T >::clone().
◆ HdivSimplexShapeFunction() [2/2]
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inlineexplicit |
Creates a shape function as a linear combination of Lagrangian shape functions.
- Template Parameters
-
Coefficients an STL container with value type Dune::FieldVector<T,comps>.
- Parameters
-
coeff contains coefficients of linear combinations of Lagrangian shape functions. Note that the coefficients are vectorial, as the Lagrangian shape functions are scalar, but we create vectorial shape functions. loc the topological location information (nominalOrder,codim,entity,index)
Definition at line 357 of file nedelecshapefunctions.hh.
Member Function Documentation
◆ clone()
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inlinevirtual |
Definition at line 363 of file nedelecshapefunctions.hh.
◆ evaluate2ndDerivative()
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inlinevirtual |
Evaluates the second derivative of the shape function.
The result is r[i][j][k] = \( \partial^2 \phi_i / (\partial \xi_j \partial \xi_k) = 0. \)
The point xi is not restricted to be inside the unit simplex, but the meaning of evaluating a shape function outside of the unit simplex is questionable.
Reimplemented from Kaskade::ShapeFunction< ctype, dimension, T, dimension >.
Definition at line 409 of file nedelecshapefunctions.hh.
◆ evaluateDerivative()
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inlinevirtual |
Evaluates the derivative of the shape function.
The point xi is not restricted to be inside the unit simplex, but the meaning of evaluating a shape function outside of the unit simplex is questionable.
Implements Kaskade::ShapeFunction< ctype, dimension, T, dimension >.
Definition at line 389 of file nedelecshapefunctions.hh.
◆ evaluateFunction()
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inlinevirtual |
Evaluates the shape function at point xi.
The point xi is not restricted to be inside the unit simplex, but the meaning of evaluating a shape function outside of the unit simplex is questionable.
Implements Kaskade::ShapeFunction< ctype, dimension, T, dimension >.
Definition at line 375 of file nedelecshapefunctions.hh.
Referenced by Kaskade::HdivSimplexShapeFunction< ctype, dimension, T >::evaluateFunction().
◆ location()
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inlinevirtual |
Returns a tuple (nominalOrder,codim,entity,index) giving detailed information about the location of the shape function.
Each shape function is associated to a certain subentity of the element.
nominalOrder is a nonnegative ordering parameter that is usually the polynomial order of the shape function, but need not coincide.
codim is the codimension of the subentity to which the shape function is associated, entity is the number of the subentity, and index is the number of the shape function among those that are associated to the same subentity.
Implements Kaskade::ShapeFunction< ctype, dimension, T, dimension >.
Definition at line 421 of file nedelecshapefunctions.hh.
Member Data Documentation
◆ comps
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static |
Definition at line 337 of file nedelecshapefunctions.hh.
◆ dim
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static |
Definition at line 336 of file nedelecshapefunctions.hh.
Referenced by Kaskade::HdivSimplexShapeFunction< ctype, dimension, T >::evaluate2ndDerivative(), and Kaskade::HdivSimplexShapeFunction< ctype, dimension, T >::evaluateDerivative().
◆ order
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static |
Definition at line 338 of file nedelecshapefunctions.hh.
The documentation for this class was generated from the following file:
