Nektar::Utilities::Triangle Class Reference

A 2-dimensional three-sided element. More...

#include <MeshElements.h>

Inheritance diagram for Nektar::Utilities::Triangle:

Collaboration diagram for Nektar::Utilities::Triangle:

Public Member Functions
	Triangle (ElmtConfig pConf, std::vector< NodeSharedPtr > pNodeList, std::vector< int > pTagList)
	Create a triangle element.
	Triangle (const Triangle &pSrc)
virtual	~Triangle ()
virtual SpatialDomains::GeometrySharedPtr	GetGeom (int coordDim)
	Generate a Nektar++ geometry object for this element.
virtual void	Complete (int order)
	Complete this object.
Public Member Functions inherited from Nektar::Utilities::Element
	Element (ElmtConfig pConf, unsigned int pNumNodes, unsigned int pGotNodes)
unsigned int	GetId () const
	Returns the ID of the element (or associated edge or face for boundary elements).
unsigned int	GetDim () const
	Returns the expansion dimension of the element.
ElmtConfig	GetConf () const
	Returns the configuration of the element.
std::string	GetTag () const
	Returns the tag which defines the element shape.
NodeSharedPtr	GetVertex (unsigned int i) const
	Access a vertex node.
EdgeSharedPtr	GetEdge (unsigned int i) const
	Access an edge.
FaceSharedPtr	GetFace (unsigned int i) const
	Access a face.
std::vector< NodeSharedPtr >	GetVertexList () const
	Access the list of vertex nodes.
std::vector< EdgeSharedPtr >	GetEdgeList () const
	Access the list of edges.
std::vector< FaceSharedPtr >	GetFaceList () const
	Access the list of faces.
std::vector< NodeSharedPtr >	GetVolumeNodes () const
	Access the list of volume nodes.
void	SetVolumeNodes (std::vector< NodeSharedPtr > &nodes)
LibUtilities::PointsType	GetCurveType () const
void	SetCurveType (LibUtilities::PointsType cT)
unsigned int	GetNodeCount () const
	Returns the total number of nodes (vertices, edge nodes and face nodes and volume nodes).
std::vector< int >	GetTagList () const
	Access the list of tags associated with this element.
unsigned int	GetVertexCount () const
	Returns the number of vertices.
unsigned int	GetEdgeCount () const
	Returns the number of edges.
unsigned int	GetFaceCount () const
	Returns the number of faces.
void	SetId (unsigned int p)
	Change the ID of the element.
void	SetVertex (unsigned int p, NodeSharedPtr pNew)
	Replace a vertex with another vertex object.
void	SetEdge (unsigned int p, EdgeSharedPtr pNew)
	Replace an edge with another edge object.
void	SetFace (unsigned int p, FaceSharedPtr pNew)
	Replace a face with another face object.
void	SetEdgeLink (EdgeSharedPtr pLink)
	Set a correspondence between this element and an edge (2D boundary element).
EdgeSharedPtr	GetEdgeLink ()
	Get correspondence between this element and an edge.
void	SetFaceLink (FaceSharedPtr pLink)
	Set a correspondence between this element and a face (3D boundary element).
FaceSharedPtr	GetFaceLink ()
	Get correspondence between this element and a face.
void	SetBoundaryLink (int i, int j)
	Set a correspondence between edge or face i and its representative boundary element m->element[expDim-1][j].
int	GetBoundaryLink (int i)
	Get the location of the boundary face/edge i for this element.
void	SetTagList (const std::vector< int > &tags)
	Set the list of tags associated with this element.
virtual std::string	GetXmlString () const
	Generate a list of vertices (1D), edges (2D), or faces (3D).
std::string	GetXmlCurveString () const
	Generates a string listing the coordinates of all nodes associated with this element.
int	GetMaxOrder ()
	Obtain the order of an element by looking at edges.
void	Print ()

Static Public Member Functions
static ElementSharedPtr	create (ElmtConfig pConf, std::vector< NodeSharedPtr > pNodeList, std::vector< int > pTagList)
	Creates an instance of this class.
static unsigned int	GetNumNodes (ElmtConfig pConf)
	Return the number of nodes defining a triangle.

Static Public Attributes
static LibUtilities::ShapeType	m_type
	Element type.

Additional Inherited Members
Protected Attributes inherited from Nektar::Utilities::Element
unsigned int	m_id
	ID of the element.
unsigned int	m_dim
	Dimension of the element.
ElmtConfig	m_conf
	Contains configuration of the element.
std::string	m_tag
	Tag character describing the element.
std::vector< int >	m_taglist
	List of integers specifying properties of the element.
std::vector< NodeSharedPtr >	m_vertex
	List of element vertex nodes.
std::vector< EdgeSharedPtr >	m_edge
	List of element edges.
std::vector< FaceSharedPtr >	m_face
	List of element faces.
std::vector< NodeSharedPtr >	m_volumeNodes
	List of element volume nodes.
LibUtilities::PointsType	m_curveType
	Volume curve type.
EdgeSharedPtr	m_edgeLink
	Pointer to the corresponding edge if element is a 2D boundary.
FaceSharedPtr	m_faceLink
	Pointer to the corresponding face if element is a 3D boundary.
std::map< int, int >	m_boundaryLinks
	Array mapping faces/edges to the location of the appropriate boundary elements in m->element.
SpatialDomains::GeometrySharedPtr	m_geom
	Nektar++ geometry object for this element.

Detailed Description

A 2-dimensional three-sided element.

Definition at line 1327 of file MeshElements.h.

Constructor & Destructor Documentation

Triangle::Triangle	(	ElmtConfig	pConf,
		std::vector< NodeSharedPtr >	pNodeList,
		std::vector< int >	pTagList
	)

Create a triangle element.

Definition at line 486 of file MeshElements.cpp.

References Nektar::LibUtilities::eNodalTriEvenlySpaced, Nektar::iterator, Nektar::Utilities::Element::m_conf, Nektar::Utilities::Element::m_curveType, Nektar::Utilities::Element::m_dim, Nektar::Utilities::Element::m_edge, Nektar::Utilities::ElmtConfig::m_edgeCurveType, Nektar::Utilities::ElmtConfig::m_faceNodes, Nektar::Utilities::ElmtConfig::m_order, Nektar::Utilities::ElmtConfig::m_reorient, Nektar::Utilities::Element::m_tag, Nektar::Utilities::Element::m_taglist, Nektar::Utilities::Element::m_vertex, and Nektar::Utilities::Element::m_volumeNodes.

            : Element(pConf, GetNumNodes(pConf), pNodeList.size()) 
        {
            m_tag     = "T";
            m_dim     = 2;
            m_taglist = pTagList;
            m_curveType = LibUtilities::eNodalTriEvenlySpaced;
            int n     = m_conf.m_order-1;

            // Create a map to relate edge nodes to a pair of vertices
            // defining an edge. This is based on the ordering produced by
            // gmsh.
            map<pair<int,int>, int> edgeNodeMap;
            map<pair<int,int>, int>::iterator it;
            edgeNodeMap[pair<int,int>(1,2)] = 4;
            edgeNodeMap[pair<int,int>(2,3)] = 4 + n;
            edgeNodeMap[pair<int,int>(3,1)] = 4 + 2*n;

            // Add vertices. This logic will determine (in 2D) whether the
            // element is clockwise (sum > 0) or counter-clockwise (sum < 0).
            NekDouble sum = 0.0;
            for (int i = 0; i < 3; ++i) {
                int o = (i+1) % 3;
                m_vertex.push_back(pNodeList[i]);
                sum += (pNodeList[o]->m_x - pNodeList[i]->m_x) *
                       (pNodeList[o]->m_y + pNodeList[i]->m_y);
            }

            // Create edges (with corresponding set of edge points)
            for (it = edgeNodeMap.begin(); it != edgeNodeMap.end(); ++it)
            {
                vector<NodeSharedPtr> edgeNodes;
                if (m_conf.m_order > 1) {
                    for (int j = it->second; j < it->second + n; ++j) {
                        edgeNodes.push_back(pNodeList[j-1]);
                    }
                }
                m_edge.push_back(EdgeSharedPtr(new Edge(pNodeList[it->first.first-1],
                                                        pNodeList[it->first.second-1],
                                                        edgeNodes,
                                                        m_conf.m_edgeCurveType)));
            }

            if (pConf.m_reorient)
            {
                if (sum > 0.0)
                {
                    reverse(m_edge.begin(), m_edge.end());
                }
            }

            if (m_conf.m_faceNodes)
            {
                m_volumeNodes.insert(m_volumeNodes.begin(),
                                   pNodeList.begin()+3*m_conf.m_order,
                                   pNodeList.end());
            }
        }

Nektar::Utilities::Triangle::Triangle

(

const Triangle &

pSrc

)

virtual Nektar::Utilities::Triangle::~Triangle ( )

inlinevirtual

Definition at line 1351 of file MeshElements.h.

{}

Member Function Documentation

void Triangle::Complete ( int  order )

virtual

Complete this object.

Reimplemented from Nektar::Utilities::Element.

Definition at line 583 of file MeshElements.cpp.

References Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauMAlpha1Beta0, Nektar::LibUtilities::eNodalTriEvenlySpaced, Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, GetGeom(), Nektar::Utilities::Element::m_conf, Nektar::Utilities::Element::m_edge, Nektar::Utilities::ElmtConfig::m_faceNodes, Nektar::Utilities::ElmtConfig::m_order, Nektar::Utilities::ElmtConfig::m_volumeNodes, and Nektar::Utilities::Element::m_volumeNodes.

        {
            int i, j;
            
            // Create basis key for a nodal tetrahedron.
            LibUtilities::BasisKey B0(
                LibUtilities::eOrtho_A, order+1,
                LibUtilities::PointsKey(
                    order+1,LibUtilities::eGaussLobattoLegendre));
            LibUtilities::BasisKey B1(
                LibUtilities::eOrtho_B, order+1,
                LibUtilities::PointsKey(
                    order+1,LibUtilities::eGaussRadauMAlpha1Beta0));
            
            // Create a standard nodal triangle in order to get the
            // Vandermonde matrix to perform interpolation to nodal points.
            StdRegions::StdNodalTriExpSharedPtr nodalTri = 
                MemoryManager<StdRegions::StdNodalTriExp>::AllocateSharedPtr(
                    B0, B1, LibUtilities::eNodalTriEvenlySpaced);
            
            SpatialDomains::TriGeomSharedPtr geom = 
                boost::dynamic_pointer_cast<SpatialDomains::TriGeom>(
                    this->GetGeom(3));
            
            // Create basis key for a triangle.
            LibUtilities::BasisKey C0(
                LibUtilities::eOrtho_A, order+1,
                LibUtilities::PointsKey(
                    order+1,LibUtilities::eGaussLobattoLegendre));
            LibUtilities::BasisKey C1(
                LibUtilities::eOrtho_B, order+1,
                LibUtilities::PointsKey(
                    order+1,LibUtilities::eGaussRadauMAlpha1Beta0));
            
            // Create a triangle.
            LocalRegions::TriExpSharedPtr tri = 
                MemoryManager<LocalRegions::TriExp>::AllocateSharedPtr(
                    C0, C1, geom);
            
            // Get coordinate array for tetrahedron.
            int nqtot = tri->GetTotPoints();
            Array<OneD, NekDouble> alloc(6*nqtot);
            Array<OneD, NekDouble> xi(alloc);
            Array<OneD, NekDouble> yi(alloc+  nqtot);
            Array<OneD, NekDouble> zi(alloc+2*nqtot);
            Array<OneD, NekDouble> xo(alloc+3*nqtot);
            Array<OneD, NekDouble> yo(alloc+4*nqtot);
            Array<OneD, NekDouble> zo(alloc+5*nqtot);
            Array<OneD, NekDouble> tmp;
            
            tri->GetCoords(xi, yi, zi);
            
            for (i = 0; i < 3; ++i)
            {
                Array<OneD, NekDouble> coeffs(nodalTri->GetNcoeffs());
                tri->FwdTrans(alloc+i*nqtot, coeffs);
                // Apply Vandermonde matrix to project onto nodal space.
                nodalTri->ModalToNodal(coeffs, tmp=alloc+(i+3)*nqtot);
            }
            
            // Now extract points from the co-ordinate arrays into the
            // edge/face/volume nodes. First, extract edge-interior nodes.
            for (i = 0; i < 3; ++i)
            {
                int pos = 3 + i*(order-1);
                m_edge[i]->m_edgeNodes.clear();
                for (j = 0; j < order-1; ++j)
                {
                    m_edge[i]->m_edgeNodes.push_back(
                        NodeSharedPtr(new Node(0, xo[pos+j], yo[pos+j], zo[pos+j])));
                }
            }

            // Extract face-interior nodes.
            int pos = 3 + 3*(order-1);
            for (i = pos; i < (order+1)*(order+2)/2; ++i)
            {
                m_volumeNodes.push_back(
                    NodeSharedPtr(new Node(0, xo[i], yo[i], zo[i])));
            }
            
            m_conf.m_order       = order;
            m_conf.m_faceNodes   = true;
            m_conf.m_volumeNodes = true;
        }

static ElementSharedPtr Nektar::Utilities::Triangle::create ( ElmtConfig  pConf, std::vector< NodeSharedPtr >  pNodeList, std::vector< int >  pTagList  )

inlinestatic

Creates an instance of this class.

Definition at line 1330 of file MeshElements.h.

References Nektar::Utilities::Element::GetEdgeList().

            {
                ElementSharedPtr e = boost::shared_ptr<Element>(
                    new Triangle(pConf, pNodeList, pTagList));
                vector<EdgeSharedPtr> m_edges = e->GetEdgeList();
                for (int i = 0; i < m_edges.size(); ++i)
                {
                    m_edges[i]->m_elLink.push_back(pair<ElementSharedPtr, int>(e,i));
                }
                return e;
            }

SpatialDomains::GeometrySharedPtr Triangle::GetGeom ( int  coordDim )

virtual

Generate a Nektar++ geometry object for this element.

Reimplemented from Nektar::Utilities::Element.

Definition at line 547 of file MeshElements.cpp.

References Nektar::SpatialDomains::SegGeom::GetEdgeOrientation(), Nektar::Utilities::Element::m_edge, Nektar::Utilities::Element::m_id, and Nektar::Utilities::Element::m_vertex.

Referenced by Complete().

        {
            SpatialDomains::SegGeomSharedPtr   edges[3];
            SpatialDomains::PointGeomSharedPtr verts[3];
            SpatialDomains::TriGeomSharedPtr   ret;
            
            for (int i = 0; i < 3; ++i)
            {
                edges[i] = m_edge  [i]->GetGeom(coordDim);
                verts[i] = m_vertex[i]->GetGeom(coordDim);
            }
            
            StdRegions::Orientation edgeorient[3] = {
                SpatialDomains::SegGeom::GetEdgeOrientation(*edges[0], *edges[1]),
                SpatialDomains::SegGeom::GetEdgeOrientation(*edges[1], *edges[2]),
                SpatialDomains::SegGeom::GetEdgeOrientation(*edges[2], *edges[0])
            };
            
            ret = MemoryManager<SpatialDomains::TriGeom>::
                AllocateSharedPtr(m_id, verts, edges, edgeorient);

            return ret;
        }

unsigned int Triangle::GetNumNodes ( ElmtConfig  pConf )

static

Return the number of nodes defining a triangle.

Definition at line 574 of file MeshElements.cpp.

References Nektar::Utilities::ElmtConfig::m_faceNodes, and Nektar::Utilities::ElmtConfig::m_order.

Referenced by Nektar::Utilities::InputGmsh::GetNnodes().

        {
            int n = pConf.m_order;
            if (!pConf.m_faceNodes)
                return (n+1)+2*(n-1)+1;
            else
                return (n+1)*(n+2)/2;
        }

Member Data Documentation

LibUtilities::ShapeType Triangle::m_type

static

Initial value:

 GetElementFactory().
            RegisterCreatorFunction(LibUtilities::eTriangle, Triangle::create, "Triangle")

Element type.

Definition at line 1345 of file MeshElements.h.