A 3-dimensional four-faced element. More...

#include <MeshElements.h>

Inheritance diagram for Nektar::Utilities::Tetrahedron:

Collaboration diagram for Nektar::Utilities::Tetrahedron:

Public Member Functions
	Tetrahedron (ElmtConfig pConf, std::vector< NodeSharedPtr > pNodeList, std::vector< int > pTagList)
	Create a tetrahedron element.
	Tetrahedron (const Tetrahedron &pSrc)
virtual	~Tetrahedron ()
virtual SpatialDomains::GeometrySharedPtr	GetGeom (int coordDim)
	Generate a Nektar++ geometry object for this element.
virtual void	Complete (int order)

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 tetrahedron.

Public Attributes
int	m_orientationMap [4]
int	m_origVertMap [4]

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

Protected Member Functions
void	OrientTet ()
	Orient tetrahedron to align degenerate vertices.

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 3-dimensional four-faced element.

Definition at line 1399 of file MeshElements.h.

Constructor & Destructor Documentation

Nektar::Utilities::Tetrahedron::Tetrahedron	(	ElmtConfig	pConf,
		std::vector< NodeSharedPtr >	pNodeList,
		std::vector< int >	pTagList
	)

Create a tetrahedron element.

Definition at line 840 of file MeshElements.cpp.

            : Element(pConf, GetNumNodes(pConf), pNodeList.size())
        {
            m_tag = "A";
            m_dim = 3;
            m_taglist = pTagList;
            int n = m_conf.m_order-1;
            // Create a map to relate edge nodes to a pair of vertices
            // defining an edge.
            map<pair<int,int>, int> edgeNodeMap;
            map<pair<int,int>, int>::iterator it;
            edgeNodeMap[pair<int,int>(1,2)] = 5;
            edgeNodeMap[pair<int,int>(2,3)] = 5 + n;
            edgeNodeMap[pair<int,int>(1,3)] = 5 + 2*n;
            edgeNodeMap[pair<int,int>(1,4)] = 5 + 3*n;
            edgeNodeMap[pair<int,int>(2,4)] = 5 + 4*n;
            edgeNodeMap[pair<int,int>(3,4)] = 5 + 5*n;
            
            // Add vertices
            for (int i = 0; i < 4; ++i)
            {
                m_vertex.push_back(pNodeList[i]);
            }
            // Create edges (with corresponding set of edge points)
            int eid = 0;
            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)));
                m_edge.back()->m_id = eid++;
            }
            
            // Reorient the tet to ensure collapsed coordinates align between
            // adjacent elements.
            if (m_conf.m_reorient)
            {
                OrientTet();
            }
            else
            {
                // If we didn't need to orient the tet then set up the
                // orientation map as the identity mapping.
                for (int i = 0; i < 4; ++i)
                {
                    m_orientationMap[i] = i;
                }
            }
            
            // Face-vertex IDs
            int face_ids[4][3] = {
                {0,1,2}, {0,1,3}, {1,2,3}, {0,2,3}
            };
            // Face-edge IDs
            int face_edges[4][3];
            // Create faces
            for (int j = 0; j < 4; ++j)
            {
                vector<NodeSharedPtr> faceVertices;
                vector<EdgeSharedPtr> faceEdges;
                vector<NodeSharedPtr> faceNodes;
                // Extract the edges for this face. We need to do this because
                // of the reorientation which might have been applied (see the
                // additional note below).
                for (int k = 0; k < 3; ++k)
                {
                    faceVertices.push_back(m_vertex[face_ids[j][k]]);
                    NodeSharedPtr a = m_vertex[face_ids[j][k]];
                    NodeSharedPtr b = m_vertex[face_ids[j][(k+1)%3]];
                    for (unsigned int i = 0; i < m_edge.size(); ++i)
                    {
                        if ( ((*(m_edge[i]->m_n1)==*a) && (*(m_edge[i]->m_n2)==*b))
                                || ((*(m_edge[i]->m_n1)==*b) && (*(m_edge[i]->m_n2) == *a)) )
                        {
                            face_edges[j][k] = i;
                            faceEdges.push_back(m_edge[i]);
                            break;
                        }
                    }
                }
                // When face curvature is supplied, it may have been the case
                // that our tetrahedron was reoriented. In this case, faces have
                // different vertex IDs and so we have to rotate the face
                // curvature so that the two align appropriately.
                if (m_conf.m_faceNodes)
                {
                    const int nFaceNodes = n*(n-1)/2;
                    // Get the vertex IDs of whatever face we are processing.
                    vector<int> faceIds(3);
                    faceIds[0] = faceVertices[0]->m_id;
                    faceIds[1] = faceVertices[1]->m_id;
                    faceIds[2] = faceVertices[2]->m_id;
                    // Find out the original face number as we were given it in
                    // the constructor using the orientation map.
                    int origFace = -1;
                    for (int i = 0; i < 4; ++i)
                    {
                        if (m_orientationMap[i] == j)
                        {
                            origFace = i;
                            break;
                        }
                    }
                    ASSERTL0(origFace >= 0, "Couldn't find face");
                    // Now get the face nodes for the original face.
                    int N = 4 + 6*n + origFace * nFaceNodes;
                    for (int i = 0; i < nFaceNodes; ++i)
                    {
                        faceNodes.push_back(pNodeList[N+i]);
                    }
                    // Find the original face vertex IDs.
                    vector<int> origFaceIds(3);
                    origFaceIds[0] = pNodeList[face_ids[origFace][0]]->m_id;
                    origFaceIds[1] = pNodeList[face_ids[origFace][1]]->m_id;
                    origFaceIds[2] = pNodeList[face_ids[origFace][2]]->m_id;
                    // Construct a HOTriangle object which performs the
                    // orientation magically for us.
                    HOTriangle<NodeSharedPtr> hoTri(origFaceIds, faceNodes);
                    hoTri.Align(faceIds);
                    // Copy the face nodes back again.
                    faceNodes = hoTri.surfVerts;
                }
                m_face.push_back(FaceSharedPtr(
                    new Face(faceVertices, faceNodes, faceEdges, m_conf.m_faceCurveType)));
            }
            vector<EdgeSharedPtr> tmp(6);
            tmp[0] = m_edge[face_edges[0][0]];
            tmp[1] = m_edge[face_edges[0][1]];
            tmp[2] = m_edge[face_edges[0][2]];
            tmp[3] = m_edge[face_edges[1][2]];
            tmp[4] = m_edge[face_edges[1][1]];
            tmp[5] = m_edge[face_edges[2][1]];
            m_edge = tmp;
        }

Nektar::Utilities::Tetrahedron::Tetrahedron ( const Tetrahedron & pSrc )

virtual Nektar::Utilities::Tetrahedron::~Tetrahedron ( )

inlinevirtual

Definition at line 1423 of file MeshElements.h.

{}

Member Function Documentation

void Nektar::Utilities::Tetrahedron::Complete ( int order )

virtual

Reimplemented from Nektar::Utilities::Element.

Definition at line 1033 of file MeshElements.cpp.

References Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauMAlpha2Beta0, Nektar::LibUtilities::eNodalTetEvenlySpaced, Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, GetGeom(), Nektar::Utilities::Element::m_conf, Nektar::Utilities::Element::m_edge, Nektar::Utilities::Element::m_face, 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));
            LibUtilities::BasisKey B2(
                LibUtilities::eOrtho_C, order+1,
                LibUtilities::PointsKey(
                    order+1,LibUtilities::eGaussRadauMAlpha2Beta0));
            
            // Create a standard nodal tetrahedron in order to get the
            // Vandermonde matrix to perform interpolation to nodal points.
            StdRegions::StdNodalTetExpSharedPtr nodalTet = 
                MemoryManager<StdRegions::StdNodalTetExp>::AllocateSharedPtr(
                    B0, B1, B2, LibUtilities::eNodalTetEvenlySpaced);
            
            Array<OneD, NekDouble> x, y, z;
            
            nodalTet->GetNodalPoints(x,y,z);
            
            SpatialDomains::TetGeomSharedPtr geom = 
                boost::dynamic_pointer_cast<SpatialDomains::TetGeom>(
                    this->GetGeom(3));
            
            // Create basis key for a tetrahedron.
            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));
            LibUtilities::BasisKey C2(
                LibUtilities::eOrtho_C, order+1,
                LibUtilities::PointsKey(
                    order+1,LibUtilities::eGaussRadauMAlpha2Beta0));
            
            // Create a tet.
            LocalRegions::TetExpSharedPtr tet = 
                MemoryManager<LocalRegions::TetExp>::AllocateSharedPtr(
                    C0, C1, C2, geom);
            
            // Get coordinate array for tetrahedron.
            int nqtot = tet->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;
            
            tet->GetCoords(xi, yi, zi);
            
            for (i = 0; i < 3; ++i)
            {
                Array<OneD, NekDouble> coeffs(nodalTet->GetNcoeffs());
                tet->FwdTrans(alloc+i*nqtot, coeffs);
                // Apply Vandermonde matrix to project onto nodal space.
                nodalTet->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 < 6; ++i)
            {
                int pos = 4 + 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])));
                }
            }
            // Now extract face-interior nodes.
            for (i = 0; i < 4; ++i)
            {
                int pos = 4 + 6*(order-1) + i*(order-2)*(order-1)/2;
                m_face[i]->m_faceNodes.clear();
                for (j = 0; j < (order-2)*(order-1)/2; ++j)
                {
                    m_face[i]->m_faceNodes.push_back(
                        NodeSharedPtr(new Node(0, xo[pos+j], yo[pos+j], zo[pos+j])));
                }
            }
            
            // Finally extract volume nodes.
            int pos = 4 + 6*(order-1) + 4*(order-2)*(order-1)/2;
            for (i = pos; i < (order+1)*(order+2)*(order+3)/6; ++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::Tetrahedron::create	(	ElmtConfig	pConf,
		std::vector< NodeSharedPtr >	pNodeList,
		std::vector< int >	pTagList
	)

inlinestatic

Creates an instance of this class.

Definition at line 1402 of file MeshElements.h.

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

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

SpatialDomains::GeometrySharedPtr Nektar::Utilities::Tetrahedron::GetGeom ( int coordDim )

virtual

Generate a Nektar++ geometry object for this element.

Reimplemented from Nektar::Utilities::Element.

Definition at line 999 of file MeshElements.cpp.

References Nektar::Utilities::Element::m_face.

Referenced by Complete().

        {
            SpatialDomains::TriGeomSharedPtr tfaces[4];
            SpatialDomains::TetGeomSharedPtr ret;
            
            for (int i = 0; i < 4; ++i)
            {
                tfaces[i] = boost::dynamic_pointer_cast
                    <SpatialDomains::TriGeom>(m_face[i]->GetGeom(coordDim));
            }
            ret = MemoryManager<SpatialDomains::TetGeom>::
                AllocateSharedPtr(tfaces);
            return ret;
        }

unsigned int Nektar::Utilities::Tetrahedron::GetNumNodes ( ElmtConfig pConf )

static

Return the number of nodes defining a tetrahedron.

Definition at line 1019 of file MeshElements.cpp.

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

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

        {
            int n = pConf.m_order;
            if (pConf.m_volumeNodes && pConf.m_faceNodes)
                return (n+1)*(n+2)*(n+3)/6;
            else if (!pConf.m_volumeNodes && pConf.m_faceNodes)
                return 4*(n+1)*(n+2)/2-6*(n+1)+4;
            else
                return 6*(n+1)-8;
        }

void Nektar::Utilities::Tetrahedron::OrientTet ( )

protected

Orient tetrahedron to align degenerate vertices.

Orientation of tetrahedral elements is required so that the singular vertices of triangular faces (which occur as a part of the collapsed co-ordinate system) align. The algorithm is based on that used in T. Warburton's thesis and in the original Nektar source.

First the vertices are ordered with the highest global vertex at the top degenerate point, and the base degenerate point has second lowest ID. These vertices are swapped if the element is incorrectly oriented.

Definition at line 1190 of file MeshElements.cpp.

References Nektar::iterator, Nektar::Utilities::Element::m_id, m_orientationMap, m_origVertMap, and Nektar::Utilities::Element::m_vertex.

Referenced by Tetrahedron().

        {
            static int face_ids[4][3] = {
                {0,1,2},{0,1,3},{1,2,3},{0,2,3}};
            
            TetOrientSet faces;
            // Create a copy of the original vertex ordering. This is used to
            // construct a mapping, #orientationMap, which maps the original
            // face ordering to the new face ordering.
            for (int i = 0; i < 4; ++i)
            {
                vector<int> nodes(3);
                nodes[0] = m_vertex[face_ids[i][0]]->m_id;
                nodes[1] = m_vertex[face_ids[i][1]]->m_id;
                nodes[2] = m_vertex[face_ids[i][2]]->m_id;
                
                sort(nodes.begin(), nodes.end());
                struct TetOrient faceNodes(nodes, i);
                faces.insert(faceNodes);
            }
            // Store a copy of the original vertex ordering so we can create a
            // permutation map later.
            vector<NodeSharedPtr> origVert = m_vertex;
            // Order vertices with highest global vertex at top degenerate
            // point. Place second highest global vertex at base degenerate
            // point.
            sort(m_vertex.begin(), m_vertex.end());
            
            // Calculate a.(b x c) to determine tet volume; if negative,
            // reverse order of non-degenerate points to correctly orientate
            // the tet.
            double ax  = m_vertex[1]->m_x-m_vertex[0]->m_x;
            double ay  = m_vertex[1]->m_y-m_vertex[0]->m_y;
            double az  = m_vertex[1]->m_z-m_vertex[0]->m_z;
            double bx  = m_vertex[2]->m_x-m_vertex[0]->m_x;
            double by  = m_vertex[2]->m_y-m_vertex[0]->m_y;
            double bz  = m_vertex[2]->m_z-m_vertex[0]->m_z;
            double cx  = m_vertex[3]->m_x-m_vertex[0]->m_x;
            double cy  = m_vertex[3]->m_y-m_vertex[0]->m_y;
            double cz  = m_vertex[3]->m_z-m_vertex[0]->m_z;
            double vol = cx*(ay*bz-az*by)+cy*(az*bx-ax*bz)+cz*(ax*by-ay*bx);
            vol       /= 6.0;
            
            if (fabs(vol) <= 1e-10)
            {
                cerr << "Warning: degenerate tetrahedron, volume = " << vol << endl;
            }
            if (vol < 0)
            {
                swap(m_vertex[0], m_vertex[1]);
            }
            
            TetOrientSet::iterator it;
            
            // Search for the face in the original set of face nodes. Then use
            // this to construct the #orientationMap.
            for (int i = 0; i < 4; ++i)
            {
                vector<int> nodes(3);
                
                nodes[0] = m_vertex[face_ids[i][0]]->m_id;
                nodes[1] = m_vertex[face_ids[i][1]]->m_id;
                nodes[2] = m_vertex[face_ids[i][2]]->m_id;
                sort(nodes.begin(), nodes.end());
                
                struct TetOrient faceNodes(nodes, 0);
                
                it = faces.find(faceNodes);
                m_orientationMap[it->fid] = i;
                for (int j = 0; j < 4; ++j)
                {
                    if (m_vertex[i]->m_id == origVert[j]->m_id)
                    {
                        m_origVertMap[j] = i;
                        break;
                    }
                }
            }
        }