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Nektar::LibUtilities::NodalUtilQuad Class Reference

Specialisation of the NodalUtil class to support nodal quad elements. More...

#include <NodalUtil.h>

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Public Member Functions

 NodalUtilQuad (int degree, Array< OneD, NekDouble > r, Array< OneD, NekDouble > s)
 Construct the nodal utility class for a quadrilateral. More...
 
virtual ~NodalUtilQuad ()
 
- Public Member Functions inherited from Nektar::LibUtilities::NodalUtil
NekVector< NekDoubleGetWeights ()
 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< NekDoublev_OrthoBasis (const int mode)
 Return the value of the modal functions for the quad element at the nodal points m_xi for a given mode. More...
 
virtual NekVector< NekDoublev_OrthoBasisDeriv (const int dir, const int mode)
 Return the value of the derivative of the modal functions for the quadrilateral element at the nodal points m_xi for a given mode. More...
 
virtual boost::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...
 
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...
 

Protected Attributes

std::vector< std::pair< int,
int > > 
m_ordering
 Mapping from the $ (i,j) $ indexing of the basis to a continuous ordering. 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

Specialisation of the NodalUtil class to support nodal quad elements.

Definition at line 312 of file NodalUtil.h.

Constructor & Destructor Documentation

Nektar::LibUtilities::NodalUtilQuad::NodalUtilQuad ( int  degree,
Array< OneD, NekDouble r,
Array< OneD, NekDouble s 
)

Construct the nodal utility class for a quadrilateral.

The constructor of this class sets up the m_ordering member variable used in the evaluation of the orthogonal basis.

Parameters
degreePolynomial order of this nodal quad.
r$ \xi_1 $-coordinates of nodal points in the standard element.
s$ \xi_2 $-coordinates of nodal points in the standard element.

Definition at line 843 of file NodalUtil.cpp.

References Nektar::LibUtilities::NodalUtil::m_degree, Nektar::LibUtilities::NodalUtil::m_numPoints, m_ordering, and Nektar::LibUtilities::NodalUtil::m_xi.

846  : NodalUtil(degree, 2)
847 {
848  // Set up parent variables.
849  m_numPoints = r.num_elements();
850  m_xi[0] = r;
851  m_xi[1] = s;
852 
853  // Construct a mapping (i,j) -> m from the tensor product space (i,j) to a
854  // single ordering m.
855  for (int j = 0; j <= m_degree; ++j)
856  {
857  for (int i = 0; i <= m_degree; ++i)
858  {
859  m_ordering.push_back(std::make_pair(i,j));
860  }
861  }
862 }
int m_degree
Degree of the nodal element.
Definition: NodalUtil.h:108
NodalUtil(int degree, int dim)
Set up the NodalUtil object.
Definition: NodalUtil.h:101
Array< OneD, Array< OneD, NekDouble > > m_xi
Coordinates of the nodal points defining the basis.
Definition: NodalUtil.h:112
int m_numPoints
Total number of nodal points.
Definition: NodalUtil.h:110
std::vector< std::pair< int, int > > m_ordering
Mapping from the indexing of the basis to a continuous ordering.
Definition: NodalUtil.h:326
virtual Nektar::LibUtilities::NodalUtilQuad::~NodalUtilQuad ( )
inlinevirtual

Definition at line 319 of file NodalUtil.h.

320  {
321  }

Member Function Documentation

virtual boost::shared_ptr<NodalUtil> Nektar::LibUtilities::NodalUtilQuad::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
xiDistribution of nodal points to create utility with.

Implements Nektar::LibUtilities::NodalUtil.

Definition at line 332 of file NodalUtil.h.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and Nektar::LibUtilities::NodalUtil::m_degree.

334  {
336  m_degree, xi[0], xi[1]);
337  }
static boost::shared_ptr< DataType > AllocateSharedPtr()
Allocate a shared pointer from the memory pool.
int m_degree
Degree of the nodal element.
Definition: NodalUtil.h:108
virtual NekDouble Nektar::LibUtilities::NodalUtilQuad::v_ModeZeroIntegral ( )
inlineprotectedvirtual

Return the value of the integral of the zero-th mode for this element.

Note that for the orthogonal basis under consideration, all modes integrate to zero asides from the zero-th mode. This function is used in NodalUtil::GetWeights to determine integration weights.

Implements Nektar::LibUtilities::NodalUtil.

Definition at line 339 of file NodalUtil.h.

340  {
341  return 4.0;
342  }
virtual int Nektar::LibUtilities::NodalUtilQuad::v_NumModes ( )
inlineprotectedvirtual

Calculate the number of degrees of freedom for this element.

Implements Nektar::LibUtilities::NodalUtil.

Definition at line 344 of file NodalUtil.h.

References Nektar::LibUtilities::NodalUtil::m_degree.

345  {
346  return (m_degree + 1) * (m_degree + 1);
347  }
int m_degree
Degree of the nodal element.
Definition: NodalUtil.h:108
NekVector< NekDouble > Nektar::LibUtilities::NodalUtilQuad::v_OrthoBasis ( const int  mode)
protectedvirtual

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

In a quad, we use the orthogonal basis

\[ \psi_{m(ij)} = P^{(0,0)}_i(\xi_1) P_j^{(0,0)}(\xi_2) \]

Parameters
modeThe mode of the orthogonal basis to evaluate.

Implements Nektar::LibUtilities::NodalUtil.

Definition at line 877 of file NodalUtil.cpp.

References Polylib::jacobfd(), Nektar::LibUtilities::NodalUtil::m_numPoints, m_ordering, Nektar::LibUtilities::NodalUtil::m_xi, and CG_Iterations::modes.

878 {
879  std::vector<NekDouble> jacobi_i(m_numPoints), jacobi_j(m_numPoints);
880  std::pair<int, int> modes = m_ordering[mode];
881 
882  // Calculate Jacobi polynomials
884  m_numPoints, &m_xi[0][0], &jacobi_i[0], NULL, modes.first, 0.0, 0.0);
886  m_numPoints, &m_xi[1][0], &jacobi_j[0], NULL, modes.second, 0.0, 0.0);
887 
888  NekVector<NekDouble> ret(m_numPoints);
889 
890  for (int i = 0; i < m_numPoints; ++i)
891  {
892  ret[i] = jacobi_i[i] * jacobi_j[i];
893  }
894 
895  return ret;
896 }
Array< OneD, Array< OneD, NekDouble > > m_xi
Coordinates of the nodal points defining the basis.
Definition: NodalUtil.h:112
int m_numPoints
Total number of nodal points.
Definition: NodalUtil.h:110
std::vector< std::pair< int, int > > m_ordering
Mapping from the indexing of the basis to a continuous ordering.
Definition: NodalUtil.h:326
void jacobfd(const int np, const double *z, double *poly_in, double *polyd, const int n, const double alpha, const double beta)
Routine to calculate Jacobi polynomials, , and their first derivative, .
Definition: Polylib.cpp:1920
NekVector< NekDouble > Nektar::LibUtilities::NodalUtilQuad::v_OrthoBasisDeriv ( const int  dir,
const int  mode 
)
protectedvirtual

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

Parameters
modeThe mode of the orthogonal basis to evaluate.

Implements Nektar::LibUtilities::NodalUtil.

Definition at line 904 of file NodalUtil.cpp.

References Polylib::jacobd(), Polylib::jacobfd(), Nektar::LibUtilities::NodalUtil::m_numPoints, m_ordering, Nektar::LibUtilities::NodalUtil::m_xi, and CG_Iterations::modes.

906 {
907  std::vector<NekDouble> jacobi_i(m_numPoints), jacobi_j(m_numPoints);
908  std::vector<NekDouble> jacobi_di(m_numPoints), jacobi_dj(m_numPoints);
909  std::pair<int, int> modes = m_ordering[mode];
910 
911  // Calculate Jacobi polynomials and their derivatives. Note that we use both
912  // jacobfd and jacobd since jacobfd is only valid for derivatives in the
913  // open interval (-1,1).
915  m_numPoints, &m_xi[0][0], &jacobi_i[0], NULL, modes.first, 0.0, 0.0);
917  m_numPoints, &m_xi[1][0], &jacobi_j[0], NULL, modes.second, 0.0, 0.0);
919  m_numPoints, &m_xi[0][0], &jacobi_di[0], modes.first, 0.0, 0.0);
921  m_numPoints, &m_xi[1][0], &jacobi_dj[0], modes.second, 0.0, 0.0);
922 
923  NekVector<NekDouble> ret(m_numPoints);
924 
925  if (dir == 0)
926  {
927  for (int i = 0; i < m_numPoints; ++i)
928  {
929  ret[i] = jacobi_di[i] * jacobi_j[i];
930  }
931  }
932  else
933  {
934  for (int i = 0; i < m_numPoints; ++i)
935  {
936  ret[i] = jacobi_i[i] * jacobi_dj[i];
937  }
938  }
939 
940  return ret;
941 }
void jacobd(const int np, const double *z, double *polyd, const int n, const double alpha, const double beta)
Calculate the derivative of Jacobi polynomials.
Definition: Polylib.cpp:2120
Array< OneD, Array< OneD, NekDouble > > m_xi
Coordinates of the nodal points defining the basis.
Definition: NodalUtil.h:112
int m_numPoints
Total number of nodal points.
Definition: NodalUtil.h:110
std::vector< std::pair< int, int > > m_ordering
Mapping from the indexing of the basis to a continuous ordering.
Definition: NodalUtil.h:326
void jacobfd(const int np, const double *z, double *poly_in, double *polyd, const int n, const double alpha, const double beta)
Routine to calculate Jacobi polynomials, , and their first derivative, .
Definition: Polylib.cpp:1920

Member Data Documentation

std::vector<std::pair<int, int> > Nektar::LibUtilities::NodalUtilQuad::m_ordering
protected

Mapping from the $ (i,j) $ indexing of the basis to a continuous ordering.

Definition at line 326 of file NodalUtil.h.

Referenced by NodalUtilQuad(), v_OrthoBasis(), and v_OrthoBasisDeriv().