HArDCore2D::GradientBasis< BasisType > Class Template Reference

Basis for the space of gradients of polynomials. More...

#include <basis.hpp>

Public Types
typedef BasisType::GradientValue	FunctionValue
typedef Eigen::Matrix< double, dimspace, dimspace >	GradientValue
typedef VectorRd	CurlValue
typedef void	DivergenceValue
typedef void	RotorValue
typedef void	HessianValue
typedef BasisType::GeometricSupport	GeometricSupport
typedef BasisType	AncestorType

Public Member Functions
	GradientBasis (const BasisType &basis)
	Constructor. More...
size_t	dimension () const
	Compute the dimension of the basis. More...
FunctionValue	function (size_t i, const VectorRd &x) const
	Evaluate the i-th basis function at point x. More...
constexpr const BasisType &	ancestor () const
	Return the ancestor (basis that the gradient was taken of) More...

Static Public Attributes
constexpr static const TensorRankE	tensorRank = Vector
constexpr static const bool	hasAncestor = true
static const bool	hasFunction = true
static const bool	hasGradient = false
static const bool	hasCurl = false
static const bool	hasDivergence = false
static const bool	hasRotor = false
static const bool	hasHessian = false

Detailed Description

template<typename BasisType>
class HArDCore2D::GradientBasis< BasisType >

Basis for the space of gradients of polynomials.

To construct a basis of G^k, this assumes that the scalar basis it is constructed from is an ancestor basis of P^{k+1}/P^0, space of polynomials of degree k+1 without trivial polynomial with zero gradient (e.g. polynomials with zero average, or a hierarchical basis of P^{k+1} in which we have removed the first, constant, polynomial). This can also be used to create a family of gradients (not necessarily linearly independent, if the ancestor basis is not a basis of P^{k+1}/P^0)

---

The documentation for this class was generated from the following file:

• src/Common/basis.hpp