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.

size_t	dimension () const
	Compute the dimension of the basis.

FunctionValue	function (size_t i, const VectorRd &x) const
	Evaluate the i-th basis function at point x.

constexpr const BasisType &	ancestor () const
	Return the ancestor (basis that the gradient was taken of)

Static Public Attributes
static constexpr const TensorRankE	tensorRank = Vector

static constexpr 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

Public Types

Public Member Functions

Static Public Attributes

Detailed Description