Inheritance diagram for Nektar::Utilities::NodalUtilTriMonomial:

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Public Member Functions
	NodalUtilTriMonomial (int degree, Array< OneD, NekDouble > r, Array< OneD, NekDouble > s)

virtual	~NodalUtilTriMonomial ()

Public Member Functions inherited from Nektar::LibUtilities::NodalUtilTriangle
	NodalUtilTriangle (int degree, Array< OneD, NekDouble > r, Array< OneD, NekDouble > s)
	Construct the nodal utility class for a triangle. More...

virtual	~NodalUtilTriangle ()

Public Member Functions inherited from Nektar::LibUtilities::NodalUtil
NekVector< NekDouble >	GetWeights ()
	Obtain the integration weights for the given nodal distribution. More...

SharedMatrix	GetVandermonde ()
	Return the Vandermonde matrix for the nodal distribution. More...

SharedMatrix	GetVandermondeForDeriv (int dir)
	Return the Vandermonde matrix of the derivative of the basis functions for the nodal distribution. More...

SharedMatrix	GetDerivMatrix (int dir)
	Return the derivative matrix for the nodal distribution. More...

SharedMatrix	GetInterpolationMatrix (Array< OneD, Array< OneD, NekDouble > > &xi)
	Construct the interpolation matrix used to evaluate the basis at the points `xi` inside the element. More...

Protected Member Functions
virtual NekVector< NekDouble >	v_OrthoBasis (const int mode)
	Return the value of the modal functions for the triangular element at the nodal points m_xi for a given mode. More...

virtual NekVector< NekDouble >	v_OrthoBasisDeriv (const int dir, const int mode)
	Return the value of the derivative of the modal functions for the triangular element at the nodal points m_xi for a given mode. More...

virtual std::shared_ptr< NodalUtil >	v_CreateUtil (Array< OneD, Array< OneD, NekDouble > > &xi)
	Construct a NodalUtil object of the appropriate element type for a given set of points. More...

Protected Member Functions inherited from Nektar::LibUtilities::NodalUtilTriangle
virtual NekDouble	v_ModeZeroIntegral ()
	Return the value of the integral of the zero-th mode for this element. More...

virtual int	v_NumModes ()
	Calculate the number of degrees of freedom for this element. More...

Protected Member Functions inherited from Nektar::LibUtilities::NodalUtil
	NodalUtil (int degree, int dim)
	Set up the NodalUtil object. More...

Additional Inherited Members
Protected Attributes inherited from Nektar::LibUtilities::NodalUtilTriangle
std::vector< std::pair< int, int > >	m_ordering
	Mapping from the \( (i,j) \) indexing of the basis to a continuous ordering. More...

Array< OneD, Array< OneD, NekDouble > >	m_eta
	Collapsed coordinates \( (\eta_1, \eta_2) \) of the nodal points. More...

Protected Attributes inherited from Nektar::LibUtilities::NodalUtil
int	m_dim
	Dimension of the nodal element. More...

int	m_degree
	Degree of the nodal element. More...

int	m_numPoints
	Total number of nodal points. More...

Array< OneD, Array< OneD, NekDouble > >	m_xi
	Coordinates of the nodal points defining the basis. More...

Detailed Description

Definition at line 406 of file ProcessVarOpti.cpp.

Constructor & Destructor Documentation

◆ NodalUtilTriMonomial()

Nektar::Utilities::NodalUtilTriMonomial::NodalUtilTriMonomial	(	int	degree,
		Array< OneD, NekDouble >	r,
		Array< OneD, NekDouble >	s
	)

inline

Definition at line 409 of file ProcessVarOpti.cpp.

         : NodalUtilTriangle(degree, r, s)
     {
     }

◆ ~NodalUtilTriMonomial()

virtual Nektar::Utilities::NodalUtilTriMonomial::~NodalUtilTriMonomial ( )

inlinevirtual

Definition at line 415 of file ProcessVarOpti.cpp.

416 {

417 }

Member Function Documentation

◆ v_CreateUtil()

virtual std::shared_ptr<NodalUtil> Nektar::Utilities::NodalUtilTriMonomial::v_CreateUtil ( Array< OneD, Array< OneD, NekDouble > > & xi )

inlineprotectedvirtual

Construct a NodalUtil object of the appropriate element type for a given set of points.

This function is used inside NodalUtil::GetInterpolationMatrix so that the (potentially non-square) Vandermonde matrix can be constructed to create the interpolation matrix at an arbitrary set of points in the domain.

Parameters

xi	Distribution of nodal points to create utility with.

Reimplemented from Nektar::LibUtilities::NodalUtilTriangle.

Definition at line 443 of file ProcessVarOpti.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr().

     {
         return MemoryManager<NodalUtilTriMonomial>::AllocateSharedPtr(
             m_degree, xi[0], xi[1]);
     }

◆ v_OrthoBasis()

virtual NekVector<NekDouble> Nektar::Utilities::NodalUtilTriMonomial::v_OrthoBasis ( const int mode )

inlineprotectedvirtual

Return the value of the modal functions for the triangular element at the nodal points m_xi for a given mode.

In a triangle, we use the orthogonal basis

\[ \psi_{m(ij)} = \sqrt{2} P^{(0,0)}_i(\xi_1) P_j^{(2i+1,0)}(\xi_2) (1-\xi_2)^i \]

where \( m(ij) \) is the mapping defined in NodalUtilTriangle::m_ordering and \( J_n^{(\alpha,\beta)}(z) \) denotes the standard Jacobi polynomial.

Parameters

mode	The mode of the orthogonal basis to evaluate.

Returns: Vector containing orthogonal basis evaluated at the points m_xi.

Reimplemented from Nektar::LibUtilities::NodalUtilTriangle.

Definition at line 420 of file ProcessVarOpti.cpp.

References CG_Iterations::modes.

     {
         // Monomial basis.
         std::pair<int, int> modes = m_ordering[mode];
         NekVector<NekDouble> ret(m_numPoints);
 
         for (int i = 0; i < m_numPoints; ++i)
         {
             ret(i) =
                 pow(m_xi[0][i], modes.first) * pow(m_xi[1][i], modes.second);
         }
 
         return ret;
     }

◆ v_OrthoBasisDeriv()

virtual NekVector<NekDouble> Nektar::Utilities::NodalUtilTriMonomial::v_OrthoBasisDeriv	(	const int	dir,
		const int	mode
	)

inlineprotectedvirtual

Return the value of the derivative of the modal functions for the triangular element at the nodal points m_xi for a given mode.

Note that this routine must use the chain rule combined with the collapsed coordinate derivatives as described in Sherwin & Karniadakis (2nd edition), pg 150.

Parameters

dir	Coordinate direction in which to evaluate the derivative.
mode	The mode of the orthogonal basis to evaluate.

Returns: Vector containing the derivative of the orthogonal basis evaluated at the points m_xi.

Reimplemented from Nektar::LibUtilities::NodalUtilTriangle.

Definition at line 435 of file ProcessVarOpti.cpp.

References Nektar::ErrorUtil::efatal, and NEKERROR.

     {
         boost::ignore_unused(dir, mode);
         NEKERROR(ErrorUtil::efatal, "OrthoBasisDeriv: not supported");
         return NekVector<NekDouble>();
     }

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ NodalUtilTriMonomial()

◆ ~NodalUtilTriMonomial()

Member Function Documentation

◆ v_CreateUtil()

◆ v_OrthoBasis()

◆ v_OrthoBasisDeriv()