#include <QuadGeom.h>

Inheritance diagram for Nektar::SpatialDomains::QuadGeom:

Public Member Functions
	QuadGeom ()

	QuadGeom (const QuadGeom &in)

	QuadGeom (const int id, std::array< SegGeom , kNverts > edges, Curve curve=nullptr)

	~QuadGeom () override=default

Public Member Functions inherited from Nektar::SpatialDomains::Geometry2D
	Geometry2D ()

	Geometry2D (const int coordim, Curve *curve)

	~Geometry2D () override=default

Curve *	GetCurve ()

void	SetCurve (Curve *curvePtr)

Public Member Functions inherited from Nektar::SpatialDomains::Geometry
	Geometry ()
	Default constructor.

	Geometry (int coordim)
	Constructor when supplied a coordinate dimension.

virtual	~Geometry ()=default

int	GetCoordim () const
	Return the coordinate dimension of this object (i.e. the dimension of the space in which this object is embedded).

void	SetCoordim (int coordim)
	Sets the coordinate dimension of this object (i.e. the dimension of the space in which this object is embedded).

GeomFactorsUniquePtr	GenGeomFactors (LibUtilities::PointsKeyVector &keyTgt)
	Used by Expansion to generate associated GeomFactors.

LibUtilities::ShapeType	GetShapeType (void)
	Get the geometric shape type of this object.

int	GetGlobalID (void) const
	Get the ID of this object.

void	SetGlobalID (int globalid)
	Set the ID of this object.

int	GetVid (int i) const
	Returns global id of vertex `i` of this object.

int	GetEid (int i) const
	Get the ID of edge `i` of this object.

int	GetFid (int i) const
	Get the ID of face `i` of this object.

int	GetTid (int i) const
	Get the ID of trace `i` of this object.

PointGeom *	GetVertex (int i) const
	Returns vertex `i` of this object.

Geometry1D *	GetEdge (int i) const
	Returns edge `i` of this object.

Geometry2D *	GetFace (int i) const
	Returns face `i` of this object.

StdRegions::Orientation	GetEorient (const int i) const
	Returns the orientation of edge `i` with respect to the ordering of edges in the standard element.

StdRegions::Orientation	GetForient (const int i) const
	Returns the orientation of face `i` with respect to the ordering of faces in the standard element.

int	GetNumVerts () const
	Get the number of vertices of this object.

int	GetNumEdges () const
	Get the number of edges of this object.

int	GetNumFaces () const
	Get the number of faces of this object.

int	GetShapeDim () const
	Get the object's shape dimension.

StdRegions::StdExpansionSharedPtr	GetXmap () const
	Return the mapping object Geometry::m_xmap that represents the coordinate transformation from standard element to physical element.

const Array< OneD, const NekDouble > &	GetCoeffs (const int i) const
	Return the coefficients of the transformation Geometry::m_xmap in coordinate direction `i`.

void	FillGeom ()
	Populate the coordinate mapping Geometry::m_coeffs information from any children geometry elements.

std::array< NekDouble, 6 >	GetBoundingBox ()
	Generates the bounding box for the element.

void	ClearBoundingBox ()

bool	ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, NekDouble tol=0.0)
	Determine whether an element contains a particular Cartesian coordinate \((x,y,z)\).

bool	ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, Array< OneD, NekDouble > &locCoord, NekDouble tol)
	Determine whether an element contains a particular Cartesian coordinate \((x,y,z)\).

bool	ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, Array< OneD, NekDouble > &locCoord, NekDouble tol, NekDouble &dist)
	Determine whether an element contains a particular Cartesian coordinate \(\vec{x} = (x,y,z)\).

NekDouble	GetLocCoords (const Array< OneD, const NekDouble > &coords, Array< OneD, NekDouble > &Lcoords)
	Determine the local collapsed coordinates that correspond to a given Cartesian coordinate for this geometry object.

NekDouble	GetCoord (const int i, const Array< OneD, const NekDouble > &Lcoord)
	Given local collapsed coordinate `Lcoord`, return the value of physical coordinate in direction `i`.

int	PreliminaryCheck (const Array< OneD, const NekDouble > &gloCoord)
	A fast and robust check if a given global coord is outside of a deformed element. For regular elements, this check is unnecessary.

bool	MinMaxCheck (const Array< OneD, const NekDouble > &gloCoord)
	Check if given global coord is within the BoundingBox of the element.

bool	ClampLocCoords (Array< OneD, NekDouble > &locCoord, NekDouble tol=std::numeric_limits< NekDouble >::epsilon())
	Clamp local coords to be within standard regions [-1, 1]^dim.

NekDouble	FindDistance (const Array< OneD, const NekDouble > &xs, Array< OneD, NekDouble > &xi)

int	GetVertexEdgeMap (int i, int j) const
	Returns the standard element edge IDs that are connected to a given vertex.

int	GetVertexFaceMap (int i, int j) const
	Returns the standard element face IDs that are connected to a given vertex.

int	GetEdgeFaceMap (int i, int j) const
	Returns the standard element edge IDs that are connected to a given face.

int	GetEdgeNormalToFaceVert (int i, int j) const
	Returns the standard lement edge IDs that are normal to a given face vertex.

int	GetDir (const int i, const int j=0) const
	Returns the element coordinate direction corresponding to a given face coordinate direction.

GeomType	CalcGeomType ()

void	Reset (CurveMap &curvedEdges, CurveMap &curvedFaces)
	Reset this geometry object: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

void	ResetNonRecursive (CurveMap &curvedEdges, CurveMap &curvedFaces)
	Reset this geometry object non-recursively: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

void	Setup ()

Static Public Member Functions
static StdRegions::Orientation	GetFaceOrientation (const QuadGeom &face1, const QuadGeom &face2, bool doRot=false, int dir=0, NekDouble angle=0.0, NekDouble tol=1e-8)
	Get the orientation of face1.

static StdRegions::Orientation	GetFaceOrientation (std::array< PointGeom , 4 > face1, std::array< PointGeom , 4 > face2, bool doRot=false, int dir=0, NekDouble angle=0.0, NekDouble tol=1e-8)

Static Public Attributes
static const int	kNedges = 4

static const int	kNverts = 4

static const int	kNfacets = kNedges

static const std::string	XMLElementType

Static Public Attributes inherited from Nektar::SpatialDomains::Geometry2D
static const int	kDim = 2

Protected Member Functions
NekDouble	v_GetCoord (const int i, const Array< OneD, const NekDouble > &Lcoord) override
	Given local collapsed coordinate `Lcoord`, return the value of physical coordinate in direction `i`.

GeomType	v_CalcGeomType () override

GeomFactorsUniquePtr	v_GenGeomFactors (LibUtilities::PointsKeyVector &keyTgt) override
	Used by Expansion to generate associated GeomFactors.

void	v_FillGeom () override

int	v_GetDir (const int faceidx, const int facedir) const override
	Returns the element coordinate direction corresponding to a given face coordinate direction.

void	v_Reset (CurveMap &curvedEdges, CurveMap &curvedFaces) override
	Reset this geometry object: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

void	v_Setup () override

void	PreSolveStraightEdge ()

int	v_AllLeftCheck (const Array< OneD, const NekDouble > &gloCoord) override

int	v_GetNumVerts () const final
	Get the number of vertices of this object.

int	v_GetNumEdges () const final
	Get the number of edges of this object.

PointGeom *	v_GetVertex (const int i) const final
	Returns vertex `i` of this object.

Geometry1D *	v_GetEdge (const int i) const final
	Returns edge `i` of this object.

StdRegions::Orientation	v_GetEorient (const int i) const final
	Returns the orientation of edge `i` with respect to the ordering of edges in the standard element.

Protected Member Functions inherited from Nektar::SpatialDomains::Geometry2D
NekDouble	v_GetLocCoords (const Array< OneD, const NekDouble > &coords, Array< OneD, NekDouble > &Lcoords) override
	Determine the local collapsed coordinates that correspond to a given Cartesian coordinate for this geometry object.

void	NewtonIterationForLocCoord (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &ptsx, const Array< OneD, const NekDouble > &ptsy, Array< OneD, NekDouble > &Lcoords, NekDouble &dist)

void	SolveStraightEdgeQuad (const Array< OneD, const NekDouble > &coords, Array< OneD, NekDouble > &Lcoords)

void	v_CalculateInverseIsoParam () override

int	v_GetShapeDim () const override
	Get the object's shape dimension.

NekDouble	v_FindDistance (const Array< OneD, const NekDouble > &xs, Array< OneD, NekDouble > &xi) override

Protected Member Functions inherited from Nektar::SpatialDomains::Geometry
virtual int	v_GetVid (int i) const
	Get the ID of vertex `i` of this object.

virtual Geometry2D *	v_GetFace (const int i) const
	Returns face `i` of this object.

virtual StdRegions::Orientation	v_GetForient (const int i) const
	Returns the orientation of face `i` with respect to the ordering of faces in the standard element.

virtual int	v_GetNumFaces () const
	Get the number of faces of this object.

virtual StdRegions::StdExpansionSharedPtr	v_GetXmap () const
	Return the mapping object Geometry::m_xmap that represents the coordinate transformation from standard element to physical element.

virtual bool	v_ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, Array< OneD, NekDouble > &locCoord, NekDouble tol, NekDouble &dist)
	Determine whether an element contains a particular Cartesian coordinate \(\vec{x} = (x,y,z)\).

virtual int	v_GetVertexEdgeMap (int i, int j) const
	Returns the standard element edge IDs that are connected to a given vertex.

virtual int	v_GetVertexFaceMap (int i, int j) const
	Returns the standard element face IDs that are connected to a given vertex.

virtual int	v_GetEdgeFaceMap (int i, int j) const
	Returns the standard element edge IDs that are connected to a given face.

virtual int	v_GetEdgeNormalToFaceVert (const int i, const int j) const
	Returns the standard lement edge IDs that are normal to a given face vertex.

void	SetUpCoeffs (const int nCoeffs)
	Initialise the Geometry::m_coeffs array.

Protected Attributes
std::array< PointGeom *, kNverts >	m_verts

std::array< SegGeom *, kNedges >	m_edges

std::array< StdRegions::Orientation, kNedges >	m_eorient

Protected Attributes inherited from Nektar::SpatialDomains::Geometry2D
Curve *	m_curve

Array< OneD, int >	m_manifold

Array< OneD, Array< OneD, NekDouble > >	m_edgeNormal

Protected Attributes inherited from Nektar::SpatialDomains::Geometry
int	m_coordim
	Coordinate dimension of this geometry object.

StdRegions::StdExpansionSharedPtr	m_xmap
	\(\chi\) mapping containing isoparametric transformation.

GeomState	m_state
	Enumeration to dictate whether coefficients are filled.

bool	m_setupState
	Wether or not the setup routines have been run.

LibUtilities::ShapeType	m_shapeType
	Type of shape.

int	m_globalID
	Global ID.

std::vector< Array< OneD, NekDouble > >	m_coeffs
	Array containing expansion coefficients of `m_xmap`.

Array< OneD, NekDouble >	m_boundingBox
	Array containing bounding box.

Array< OneD, Array< OneD, NekDouble > >	m_isoParameter

Array< OneD, Array< OneD, NekDouble > >	m_invIsoParam

int	m_straightEdge

Private Member Functions
void	SetUpXmap ()

Detailed Description

Definition at line 52 of file QuadGeom.h.

Constructor & Destructor Documentation

◆ QuadGeom() [1/3]

Nektar::SpatialDomains::QuadGeom::QuadGeom ( )

Definition at line 54 of file QuadGeom.cpp.

{
    m_shapeType = LibUtilities::eQuadrilateral;
}

References Nektar::LibUtilities::eQuadrilateral, and Nektar::SpatialDomains::Geometry::m_shapeType.

◆ QuadGeom() [2/3]

Nektar::SpatialDomains::QuadGeom::QuadGeom ( const QuadGeom & in )

Definition at line 93 of file QuadGeom.cpp.

                                     : Geometry2D(in)
{
    // From Geometry
    m_shapeType = in.m_shapeType;
    m_globalID  = in.m_globalID;
 
    // From QuadGeom
    m_verts = in.m_verts;
    m_edges = in.m_edges;
    for (int i = 0; i < kNedges; i++)
    {
        m_eorient[i] = in.m_eorient[i];
    }
}

References kNedges, m_edges, m_eorient, Nektar::SpatialDomains::Geometry::m_globalID, Nektar::SpatialDomains::Geometry::m_shapeType, and m_verts.

◆ QuadGeom() [3/3]

Nektar::SpatialDomains::QuadGeom::QuadGeom	(	const int	id,
		std::array< SegGeom *, kNverts >	edges,
		Curve *	curve = `nullptr`
	)

◆ ~QuadGeom()

Nektar::SpatialDomains::QuadGeom::~QuadGeom ( )

overridedefault

Member Function Documentation

◆ GetFaceOrientation() [1/2]

StdRegions::Orientation Nektar::SpatialDomains::QuadGeom::GetFaceOrientation	(	const QuadGeom &	face1,
		const QuadGeom &	face2,
		bool	doRot = `false`,
		int	dir = `0`,
		NekDouble	angle = `0.0`,
		NekDouble	tol = `1e-8`
	)

static

Get the orientation of face1.

Definition at line 228 of file QuadGeom.cpp.

{
    return GetFaceOrientation(face1.m_verts, face2.m_verts, doRot, dir, angle,
                              tol);
}

References GetFaceOrientation(), and m_verts.

Referenced by Nektar::MultiRegions::DisContField::FindPeriodicTraces(), and GetFaceOrientation().

◆ GetFaceOrientation() [2/2]

StdRegions::Orientation Nektar::SpatialDomains::QuadGeom::GetFaceOrientation	(	std::array< PointGeom *, 4 >	face1,
		std::array< PointGeom *, 4 >	face2,
		bool	doRot = `false`,
		int	dir = `0`,
		NekDouble	angle = `0.0`,
		NekDouble	tol = `1e-8`
	)

static

Calculate the orientation of face2 to face1 (note this is not face1 to face2!).

Definition at line 242 of file QuadGeom.cpp.

{
    int i, j, vmap[4] = {-1, -1, -1, -1};
 
    if (doRot)
    {
        PointGeom rotPt;
 
        for (i = 0; i < 4; ++i)
        {
            rotPt.Rotate((*face1[i]), dir, angle);
            for (j = 0; j < 4; ++j)
            {
                if (rotPt.dist(*face2[j]) < tol)
                {
                    vmap[j] = i;
                    break;
                }
            }
        }
    }
    else
    {
 
        NekDouble x, y, z, x1, y1, z1, cx = 0.0, cy = 0.0, cz = 0.0;
 
        // For periodic faces, we calculate the vector between the centre
        // points of the two faces. (For connected faces this will be
        // zero). We can then use this to determine alignment later in the
        // algorithm.
        for (i = 0; i < 4; ++i)
        {
            cx += (*face2[i])(0) - (*face1[i])(0);
            cy += (*face2[i])(1) - (*face1[i])(1);
            cz += (*face2[i])(2) - (*face1[i])(2);
        }
        cx /= 4;
        cy /= 4;
        cz /= 4;
 
        // Now construct a mapping which takes us from the vertices of one
        // face to the other. That is, vertex j of face2 corresponds to
        // vertex vmap[j] of face1.
        for (i = 0; i < 4; ++i)
        {
            x = (*face1[i])(0);
            y = (*face1[i])(1);
            z = (*face1[i])(2);
            for (j = 0; j < 4; ++j)
            {
                x1 = (*face2[j])(0) - cx;
                y1 = (*face2[j])(1) - cy;
                z1 = (*face2[j])(2) - cz;
                if (sqrt((x1 - x) * (x1 - x) + (y1 - y) * (y1 - y) +
                         (z1 - z) * (z1 - z)) < 1e-8)
                {
                    vmap[j] = i;
                    break;
                }
            }
        }
    }
 
    // Use the mapping to determine the eight alignment options between
    // faces.
    if (vmap[1] == (vmap[0] + 1) % 4)
    {
        switch (vmap[0])
        {
            case 0:
                return StdRegions::eDir1FwdDir1_Dir2FwdDir2;
                break;
            case 1:
                return StdRegions::eDir1BwdDir2_Dir2FwdDir1;
                break;
            case 2:
                return StdRegions::eDir1BwdDir1_Dir2BwdDir2;
                break;
            case 3:
                return StdRegions::eDir1FwdDir2_Dir2BwdDir1;
                break;
        }
    }
    else
    {
        switch (vmap[0])
        {
            case 0:
                return StdRegions::eDir1FwdDir2_Dir2FwdDir1;
                break;
            case 1:
                return StdRegions::eDir1BwdDir1_Dir2FwdDir2;
                break;
            case 2:
                return StdRegions::eDir1BwdDir2_Dir2BwdDir1;
                break;
            case 3:
                return StdRegions::eDir1FwdDir1_Dir2BwdDir2;
                break;
        }
    }
    NEKERROR(ErrorUtil::efatal, "unable to determine face orientation");
    return StdRegions::eDir1FwdDir1_Dir2FwdDir2;
}

◆ PreSolveStraightEdge()

void Nektar::SpatialDomains::QuadGeom::PreSolveStraightEdge ( )

protected

Definition at line 556 of file QuadGeom.cpp.

{
    int i0, i1, j1, j2;
    if (fabs(m_isoParameter[0][3]) >= fabs(m_isoParameter[1][3]))
    {
        i0 = 0;
        i1 = 1;
    }
    else
    {
        i1 = 0;
        i0 = 1;
        m_straightEdge |= 2;
    }
    NekDouble gamma = m_isoParameter[i1][3] / m_isoParameter[i0][3];
    std::vector<NekDouble> c(3);
    for (int i = 0; i < 3; ++i)
    {
        c[i] = m_isoParameter[i1][i] - gamma * m_isoParameter[i0][i];
    }
    if (fabs(c[1]) >= fabs(c[2]))
    {
        j1 = 1;
        j2 = 2;
    }
    else
    {
        j1 = 2;
        j2 = 1;
        m_straightEdge |= 4;
    }
    NekDouble beta = c[j2] / c[j1];
    if (i0 == 1)
    {
        Vmath::Vcopy(4, m_isoParameter[1], 1, m_isoParameter[0], 1);
    }
    if (j1 == 2)
    {
        NekDouble temp        = m_isoParameter[0][j1];
        m_isoParameter[0][j1] = m_isoParameter[0][j2];
        m_isoParameter[0][j2] = temp;
    }
    m_isoParameter[0][2] -= m_isoParameter[0][1] * beta;
    m_isoParameter[1][0] = c[0];
    m_isoParameter[1][1] = 1. / c[j1];
    m_isoParameter[1][2] = beta;
    m_isoParameter[1][3] = gamma;
}

References Nektar::LibUtilities::beta, Nektar::SpatialDomains::Geometry::m_isoParameter, Nektar::SpatialDomains::Geometry::m_straightEdge, and Vmath::Vcopy().

Referenced by v_CalcGeomType().

◆ SetUpXmap()

void Nektar::SpatialDomains::QuadGeom::SetUpXmap ( )

private

Definition at line 194 of file QuadGeom.cpp.

{
    int order0 = std::max(m_edges[0]->GetXmap()->GetBasis(0)->GetNumModes(),
                          m_edges[2]->GetXmap()->GetBasis(0)->GetNumModes());
    int order1 = std::max(m_edges[1]->GetXmap()->GetBasis(0)->GetNumModes(),
                          m_edges[3]->GetXmap()->GetBasis(0)->GetNumModes());
 
    std::array<LibUtilities::BasisKey, 2> basis = {
        LibUtilities::BasisKey(
            LibUtilities::eModified_A, order0,
            LibUtilities::PointsKey(order0 + 1,
                                    LibUtilities::eGaussLobattoLegendre)),
        LibUtilities::BasisKey(
            LibUtilities::eModified_A, order1,
            LibUtilities::PointsKey(order1 + 1,
                                    LibUtilities::eGaussLobattoLegendre))};
 
    m_xmap = GetStdQuadFactory().CreateInstance(basis);
}

References Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eModified_A, Nektar::SpatialDomains::GetStdQuadFactory(), Nektar::SpatialDomains::Geometry::GetXmap(), m_edges, and Nektar::SpatialDomains::Geometry::m_xmap.

Referenced by v_Reset(), and v_Setup().

◆ v_AllLeftCheck()

int Nektar::SpatialDomains::QuadGeom::v_AllLeftCheck ( const Array< OneD, const NekDouble > & gloCoord )

overrideprotectedvirtual

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 108 of file QuadGeom.cpp.

{
    int nc = 1, d0 = m_manifold[0], d1 = m_manifold[1];
    if (0 == m_edgeNormal.size())
    {
        m_edgeNormal = Array<OneD, Array<OneD, NekDouble>>(m_verts.size());
        Array<OneD, Array<OneD, NekDouble>> x(2);
        x[0] = Array<OneD, NekDouble>(3);
        x[1] = Array<OneD, NekDouble>(3);
        m_verts[0]->GetCoords(x[0]);
        int i0 = 1, i1 = 0, direction = 1;
        for (size_t i = 0; i < m_verts.size(); ++i)
        {
            i0 ^= 1;
            i1 ^= 1;
            m_verts[(i + 1) % m_verts.size()]->GetCoords(x[i1]);
            if (m_edges[i]->GetXmap()->GetBasis(0)->GetNumModes() > 2)
            {
                continue;
            }
            m_edgeNormal[i]    = Array<OneD, NekDouble>(2);
            m_edgeNormal[i][0] = x[i0][d1] - x[i1][d1];
            m_edgeNormal[i][1] = x[i1][d0] - x[i0][d0];
        }
        if (m_coordim == 3)
        {
            for (size_t i = 0; i < m_verts.size(); ++i)
            {
                if (m_edgeNormal[i].size() == 2)
                {
                    m_verts[i]->GetCoords(x[0]);
                    m_verts[(i + 2) % m_verts.size()]->GetCoords(x[1]);
                    if (m_edgeNormal[i][0] * (x[1][d0] - x[0][d0]) <
                        m_edgeNormal[i][1] * (x[0][d1] - x[1][d1]))
                    {
                        direction = -1;
                    }
                    break;
                }
            }
        }
        if (direction == -1)
        {
            for (size_t i = 0; i < m_verts.size(); ++i)
            {
                if (m_edgeNormal[i].size() == 2)
                {
                    m_edgeNormal[i][0] = -m_edgeNormal[i][0];
                    m_edgeNormal[i][1] = -m_edgeNormal[i][1];
                }
            }
        }
    }
 
    Array<OneD, NekDouble> vertex(3);
    for (size_t i = 0; i < m_verts.size(); ++i)
    {
        int i1 = (i + 1) % m_verts.size();
        if (m_verts[i]->GetGlobalID() < m_verts[i1]->GetGlobalID())
        {
            m_verts[i]->GetCoords(vertex);
        }
        else
        {
            m_verts[i1]->GetCoords(vertex);
        }
        if (m_edgeNormal[i].size() == 0)
        {
            nc = 0; // not sure
            continue;
        }
        if (m_edgeNormal[i][0] * (gloCoord[d0] - vertex[d0]) <
            m_edgeNormal[i][1] * (vertex[d1] - gloCoord[d1]))
        {
            return -1; // outside
        }
    }
    // 3D manifold needs to check the distance
    if (m_coordim == 3)
    {
        nc = 0;
    }
    // nc: 1 (side element), 0 (maybe inside), -1 (outside)
    return nc;
}

References Nektar::SpatialDomains::Geometry::GetGlobalID(), Nektar::SpatialDomains::Geometry::GetXmap(), Nektar::SpatialDomains::Geometry::m_coordim, Nektar::SpatialDomains::Geometry2D::m_edgeNormal, m_edges, Nektar::SpatialDomains::Geometry2D::m_manifold, and m_verts.

◆ v_CalcGeomType()

GeomType Nektar::SpatialDomains::QuadGeom::v_CalcGeomType ( )

overrideprotectedvirtual

Set up GeoFac for this geometry using Coord quadrature distribution

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 352 of file QuadGeom.cpp.

{
    if (!m_setupState)
    {
        QuadGeom::v_Setup();
    }
    QuadGeom::v_FillGeom();
 
    GeomType Gtype = eRegular;
 
    // We will first check whether we have a regular or deformed
    // geometry. We will define regular as those cases where the
    // Jacobian and the metric terms of the derivative are constants
    // (i.e. not coordinate dependent)
 
    // Check to see if expansions are linear
    // If not linear => deformed geometry
    if ((m_xmap->GetBasisNumModes(0) != 2) ||
        (m_xmap->GetBasisNumModes(1) != 2))
    {
        Gtype = eDeformed;
    }
 
    // For linear expansions, the mapping from standard to local
    // element is given by the relation:
    // x_i = 0.25 * [ ( x_i^A + x_i^B + x_i^C + x_i^D)       +
    //                (-x_i^A + x_i^B + x_i^C - x_i^D)*xi_1  +
    //                (-x_i^A - x_i^B + x_i^C + x_i^D)*xi_2  +
    //                ( x_i^A - x_i^B + x_i^C - x_i^D)*xi_1*xi_2 ]
    //
    // The jacobian of the transformation and the metric terms
    // dxi_i/dx_j, involve only terms of the form dx_i/dxi_j (both
    // for coordim == 2 or 3). Inspecting the formula above, it can
    // be appreciated that the derivatives dx_i/dxi_j will be
    // constant, if the coefficient of the non-linear term is zero.
    //
    // That is why for regular geometry, we require
    //
    //     x_i^A - x_i^B + x_i^C - x_i^D = 0
    //
    // or equivalently
    //
    //     x_i^A - x_i^B = x_i^D - x_i^C
    //
    // This corresponds to quadrilaterals which are paralellograms.
    m_manifold    = Array<OneD, int>(m_coordim);
    m_manifold[0] = 0;
    m_manifold[1] = 1;
    if (m_coordim == 3)
    {
        PointGeom e01, e21, norm;
        e01.Sub(*m_verts[0], *m_verts[1]);
        e21.Sub(*m_verts[3], *m_verts[1]);
        norm.Mult(e01, e21);
        int tmpi   = 0;
        double tmp = std::fabs(norm[0]);
        if (tmp < fabs(norm[1]))
        {
            tmp  = fabs(norm[1]);
            tmpi = 1;
        }
        if (tmp < fabs(norm[2]))
        {
            tmpi = 2;
        }
        m_manifold[0] = (tmpi + 1) % 3;
        m_manifold[1] = (tmpi + 2) % 3;
        m_manifold[2] = (tmpi + 3) % 3;
    }
 
    if (Gtype == eRegular)
    {
        Array<OneD, Array<OneD, NekDouble>> verts(m_verts.size());
        for (int i = 0; i < m_verts.size(); ++i)
        {
            verts[i] = Array<OneD, NekDouble>(3);
            m_verts[i]->GetCoords(verts[i]);
        }
        // a00 + a01 xi1 + a02 xi2 + a03 xi1 xi2
        // a10 + a11 xi1 + a12 xi2 + a03 xi1 xi2
        m_isoParameter = Array<OneD, Array<OneD, NekDouble>>(2);
        for (int i = 0; i < 2; i++)
        {
            unsigned int d    = m_manifold[i];
            m_isoParameter[i] = Array<OneD, NekDouble>(4, 0.);
            // Karniadakis, Sherwin 2005, Appendix D
            NekDouble A          = verts[0][d];
            NekDouble B          = verts[1][d];
            NekDouble D          = verts[2][d];
            NekDouble C          = verts[3][d];
            m_isoParameter[i][0] = 0.25 * (A + B + C + D);  // 1
            m_isoParameter[i][1] = 0.25 * (-A + B - C + D); // xi1
            m_isoParameter[i][2] = 0.25 * (-A - B + C + D); // xi2
            m_isoParameter[i][3] = 0.25 * (A - B - C + D);  // xi1*xi2
            NekDouble tmp =
                fabs(m_isoParameter[i][1]) + fabs(m_isoParameter[i][2]);
            if (fabs(m_isoParameter[i][3]) > tmp * NekConstants::kNekZeroTol)
            {
                Gtype = eDeformed;
            }
        }
    }
 
    if (Gtype == eRegular)
    {
        v_CalculateInverseIsoParam();
    }
    else if (m_straightEdge)
    {
        PreSolveStraightEdge();
    }
 
    return Gtype;
}

◆ v_FillGeom()

void Nektar::SpatialDomains::QuadGeom::v_FillGeom ( )

overrideprotectedvirtual

Note verts and edges are listed according to anticlockwise convention but points in _coeffs have to be in array format from left to right.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 481 of file QuadGeom.cpp.

{
    // check to see if geometry structure is already filled
    if (m_state != ePtsFilled)
    {
        int i, j, k;
        int nEdgeCoeffs;
 
        if (m_curve)
        {
            int npts     = m_curve->m_points.size();
            int nEdgePts = (int)sqrt(static_cast<NekDouble>(npts));
            Array<OneD, NekDouble> tmp(npts);
            Array<OneD, NekDouble> tmp2(m_xmap->GetTotPoints());
            LibUtilities::PointsKey curveKey(nEdgePts, m_curve->m_ptype);
 
            // Sanity checks:
            // - Curved faces should have square number of points;
            // - Each edge should have sqrt(npts) points.
            ASSERTL0(nEdgePts * nEdgePts == npts,
                     "NUMPOINTS should be a square number in"
                     " quadrilteral " +
                         std::to_string(m_globalID));
 
            for (i = 0; i < kNedges; ++i)
            {
                ASSERTL0(m_edges[i]->GetXmap()->GetNcoeffs() == nEdgePts,
                         "Number of edge points does not correspond to "
                         "number of face points in quadrilateral " +
                             std::to_string(m_globalID));
            }
 
            for (i = 0; i < m_coordim; ++i)
            {
                for (j = 0; j < npts; ++j)
                {
                    tmp[j] = (m_curve->m_points[j]->GetPtr())[i];
                }
 
                // Interpolate m_curve points to GLL points
                LibUtilities::Interp2D(curveKey, curveKey, tmp,
                                       m_xmap->GetBasis(0)->GetPointsKey(),
                                       m_xmap->GetBasis(1)->GetPointsKey(),
                                       tmp2);
 
                // Forwards transform to get coefficient space.
                m_xmap->FwdTrans(tmp2, m_coeffs[i]);
            }
        }
 
        // Now fill in edges.
        Array<OneD, unsigned int> mapArray;
        Array<OneD, int> signArray;
 
        for (i = 0; i < kNedges; i++)
        {
            m_edges[i]->FillGeom();
            m_xmap->GetTraceToElementMap(i, mapArray, signArray, m_eorient[i]);
 
            nEdgeCoeffs = m_edges[i]->GetXmap()->GetNcoeffs();
 
            for (j = 0; j < m_coordim; j++)
            {
                for (k = 0; k < nEdgeCoeffs; k++)
                {
                    m_coeffs[j][mapArray[k]] =
                        signArray[k] * (m_edges[i]->GetCoeffs(j))[k];
                }
            }
        }
 
        m_state = ePtsFilled;
    }
}

References ASSERTL0, Nektar::SpatialDomains::ePtsFilled, Nektar::SpatialDomains::Geometry::GetXmap(), Nektar::LibUtilities::Interp2D(), kNedges, Nektar::SpatialDomains::Geometry::m_coeffs, Nektar::SpatialDomains::Geometry::m_coordim, Nektar::SpatialDomains::Geometry2D::m_curve, m_edges, m_eorient, Nektar::SpatialDomains::Geometry::m_globalID, Nektar::SpatialDomains::Curve::m_points, Nektar::SpatialDomains::Curve::m_ptype, Nektar::SpatialDomains::Geometry::m_state, Nektar::SpatialDomains::Geometry::m_xmap, and tinysimd::sqrt().

Referenced by v_CalcGeomType().

◆ v_GenGeomFactors()

GeomFactorsUniquePtr Nektar::SpatialDomains::QuadGeom::v_GenGeomFactors ( LibUtilities::PointsKeyVector & keyTgt )

overrideprotectedvirtual

Used by Expansion to generate associated GeomFactors.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 467 of file QuadGeom.cpp.

{
    GeomType Gtype = CalcGeomType();
 
    return ObjPoolManager<GeomFactors>::AllocateUniquePtr(
        Gtype, m_coordim, m_xmap, m_coeffs, keyTgt);
}

References Nektar::ObjPoolManager< DataType >::AllocateUniquePtr(), Nektar::SpatialDomains::Geometry::CalcGeomType(), Nektar::SpatialDomains::Geometry::m_coeffs, Nektar::SpatialDomains::Geometry::m_coordim, and Nektar::SpatialDomains::Geometry::m_xmap.

◆ v_GetCoord()

NekDouble Nektar::SpatialDomains::QuadGeom::v_GetCoord	(	const int	i,
		const Array< OneD, const NekDouble > &	Lcoord
	)

overrideprotectedvirtual

Given local collapsed coordinate Lcoord, return the value of physical coordinate in direction i.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 214 of file QuadGeom.cpp.

{
    if (m_state != ePtsFilled)
    {
        NEKERROR(ErrorUtil::efatal, "Geometry is not in physical space");
    }
 
    Array<OneD, NekDouble> tmp(m_xmap->GetTotPoints());
    m_xmap->BwdTrans(m_coeffs[i], tmp);
 
    return m_xmap->PhysEvaluate(Lcoord, tmp);
}

References Nektar::ErrorUtil::efatal, Nektar::SpatialDomains::ePtsFilled, Nektar::SpatialDomains::Geometry::m_coeffs, Nektar::SpatialDomains::Geometry::m_state, Nektar::SpatialDomains::Geometry::m_xmap, and NEKERROR.

◆ v_GetDir()

int Nektar::SpatialDomains::QuadGeom::v_GetDir	(	const int	i,
		const int	j
	)		const

overrideprotectedvirtual

Returns the element coordinate direction corresponding to a given face coordinate direction.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 605 of file QuadGeom.cpp.

{
    return i % 2;
}

◆ v_GetEdge()

Geometry1D * Nektar::SpatialDomains::QuadGeom::v_GetEdge ( const int i ) const

inlinefinalprotectedvirtual

Returns edge i of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 110 of file QuadGeom.h.

    {
        return static_cast<Geometry1D *>(m_edges[i]);
    }

References m_edges.

◆ v_GetEorient()

StdRegions::Orientation Nektar::SpatialDomains::QuadGeom::v_GetEorient ( const int i ) const

inlinefinalprotectedvirtual

Returns the orientation of edge i with respect to the ordering of edges in the standard element.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 115 of file QuadGeom.h.

    {
        return m_eorient[i];
    }

References m_eorient.

◆ v_GetNumEdges()

int Nektar::SpatialDomains::QuadGeom::v_GetNumEdges ( ) const

inlinefinalprotectedvirtual

Get the number of edges of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 100 of file QuadGeom.h.

    {
        return kNedges;
    }

References kNedges.

◆ v_GetNumVerts()

int Nektar::SpatialDomains::QuadGeom::v_GetNumVerts ( ) const

inlinefinalprotectedvirtual

Get the number of vertices of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 95 of file QuadGeom.h.

    {
        return kNverts;
    }

References kNverts.

◆ v_GetVertex()

PointGeom * Nektar::SpatialDomains::QuadGeom::v_GetVertex ( const int i ) const

inlinefinalprotectedvirtual

Returns vertex i of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 105 of file QuadGeom.h.

    {
        return m_verts[i];
    }

References m_verts.

◆ v_Reset()

void Nektar::SpatialDomains::QuadGeom::v_Reset	(	CurveMap &	curvedEdges,
		CurveMap &	curvedFaces
	)

overrideprotectedvirtual

Reset this geometry object: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 610 of file QuadGeom.cpp.

{
    Geometry::v_Reset(curvedEdges, curvedFaces);
    CurveMap::iterator it = curvedFaces.find(m_globalID);
 
    if (it != curvedFaces.end())
    {
        m_curve = it->second.get();
    }
 
    for (int i = 0; i < 4; ++i)
    {
        m_edges[i]->Reset(curvedEdges, curvedFaces);
    }
 
    SetUpXmap();
    SetUpCoeffs(m_xmap->GetNcoeffs());
}

References Nektar::SpatialDomains::Geometry2D::m_curve, m_edges, Nektar::SpatialDomains::Geometry::m_globalID, Nektar::SpatialDomains::Geometry::m_xmap, Nektar::SpatialDomains::Geometry::SetUpCoeffs(), SetUpXmap(), and Nektar::SpatialDomains::Geometry::v_Reset().

◆ v_Setup()

void Nektar::SpatialDomains::QuadGeom::v_Setup ( )

overrideprotectedvirtual

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 629 of file QuadGeom.cpp.

{
    if (!m_setupState)
    {
        for (int i = 0; i < 4; ++i)
        {
            m_edges[i]->Setup();
        }
        SetUpXmap();
        SetUpCoeffs(m_xmap->GetNcoeffs());
 
        // Check to see if expansions are linear
        m_straightEdge = 1;
        if ((m_xmap->GetBasisNumModes(0) != 2) ||
            (m_xmap->GetBasisNumModes(1) != 2))
        {
            m_straightEdge = 0;
        }
 
        m_setupState = true;
    }
}

References m_edges, Nektar::SpatialDomains::Geometry::m_setupState, Nektar::SpatialDomains::Geometry::m_straightEdge, Nektar::SpatialDomains::Geometry::m_xmap, Nektar::SpatialDomains::Geometry::SetUpCoeffs(), and SetUpXmap().

Referenced by v_CalcGeomType().

Member Data Documentation

◆ kNedges

const int Nektar::SpatialDomains::QuadGeom::kNedges = 4

static

Definition at line 55 of file QuadGeom.h.

Referenced by QuadGeom(), v_FillGeom(), and v_GetNumEdges().

◆ kNfacets

const int Nektar::SpatialDomains::QuadGeom::kNfacets = kNedges

static

Definition at line 57 of file QuadGeom.h.

◆ kNverts

const int Nektar::SpatialDomains::QuadGeom::kNverts = 4

static

Definition at line 56 of file QuadGeom.h.

Referenced by Nektar::SpatialDomains::HexGeom::SetUpFaceOrientation(), Nektar::SpatialDomains::PrismGeom::SetUpFaceOrientation(), and v_GetNumVerts().

◆ m_edges

std::array<SegGeom *, kNedges> Nektar::SpatialDomains::QuadGeom::m_edges

protected

Definition at line 121 of file QuadGeom.h.

Referenced by QuadGeom(), SetUpXmap(), v_AllLeftCheck(), v_FillGeom(), v_GetEdge(), v_Reset(), and v_Setup().

◆ m_eorient

std::array<StdRegions::Orientation, kNedges> Nektar::SpatialDomains::QuadGeom::m_eorient

protected

Definition at line 122 of file QuadGeom.h.

Referenced by QuadGeom(), v_FillGeom(), and v_GetEorient().

◆ m_verts

std::array<PointGeom *, kNverts> Nektar::SpatialDomains::QuadGeom::m_verts

protected

Definition at line 120 of file QuadGeom.h.

Referenced by GetFaceOrientation(), QuadGeom(), v_AllLeftCheck(), v_CalcGeomType(), and v_GetVertex().

◆ XMLElementType

const std::string Nektar::SpatialDomains::QuadGeom::XMLElementType

static

Definition at line 76 of file QuadGeom.h.

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ QuadGeom() [1/3]

◆ QuadGeom() [2/3]

◆ QuadGeom() [3/3]

◆ ~QuadGeom()

Member Function Documentation

◆ GetFaceOrientation() [1/2]

◆ GetFaceOrientation() [2/2]

◆ PreSolveStraightEdge()

◆ SetUpXmap()

◆ v_AllLeftCheck()

◆ v_CalcGeomType()

◆ v_FillGeom()

◆ v_GenGeomFactors()

◆ v_GetCoord()

◆ v_GetDir()

◆ v_GetEdge()

◆ v_GetEorient()

◆ v_GetNumEdges()

◆ v_GetNumVerts()

◆ v_GetVertex()

◆ v_Reset()

◆ v_Setup()

Member Data Documentation

◆ kNedges

◆ kNfacets

◆ kNverts

◆ m_edges

◆ m_eorient

◆ m_verts

◆ XMLElementType