2D geometry information More...

#include <Geometry2D.h>

Inheritance diagram for Nektar::SpatialDomains::Geometry2D:

Public Member Functions
	Geometry2D ()

	Geometry2D (const int coordim, CurveSharedPtr curve)

virtual	~Geometry2D ()

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

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

virtual	~Geometry ()
	Default destructor. More...

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

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

GeomFactorsSharedPtr	GetGeomFactors ()
	Get the geometric factors for this object, generating them if required. More...

GeomFactorsSharedPtr	GetRefGeomFactors (const Array< OneD, const LibUtilities::BasisSharedPtr > &tbasis)

GeomFactorsSharedPtr	GetMetricInfo ()
	Get the geometric factors for this object. More...

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

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

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

int	GetVid (int i) const
	Get the ID of vertex `i` of this object. More...

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

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

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

PointGeomSharedPtr	GetVertex (int i) const
	Returns vertex `i` of this object. More...

Geometry1DSharedPtr	GetEdge (int i) const
	Returns edge `i` of this object. More...

Geometry2DSharedPtr	GetFace (int i) const
	Returns face `i` of this object. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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. More...

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`. More...

bool	MinMaxCheck (const Array< OneD, const NekDouble > &gloCoord)
	Check if given global coord is within twice the min/max distance of the element. More...

void	ClampLocCoords (Array< OneD, NekDouble > &locCoord, NekDouble tol)
	Clamp local coords to be within standard regions [-1, 1]^dim. More...

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

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

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

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

void	Setup ()

Static Public Attributes
static const int	kDim = 2

Protected Member Functions
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 &resid)

Protected Member Functions inherited from Nektar::SpatialDomains::Geometry
void	GenGeomFactors ()
	Handles generation of geometry factors. More...

virtual Geometry2DSharedPtr	v_GetFace (int i) const
	Returns face `i` of this object. More...

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. More...

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

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

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

virtual bool	v_ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, Array< OneD, NekDouble > &locCoord, NekDouble tol, NekDouble &resid)

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

virtual NekDouble	v_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. More...

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

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

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

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

virtual void	v_Setup ()

virtual void	v_GenGeomFactors ()=0

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

Protected Attributes
PointGeomVector	m_verts

SegGeomVector	m_edges

std::vector< StdRegions::Orientation >	m_eorient

CurveSharedPtr	m_curve

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

GeomFactorsSharedPtr	m_geomFactors
	Geometric factors. More...

GeomState	m_geomFactorsState
	State of the geometric factors. More...

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

GeomState	m_state
	Enumeration to dictate whether coefficients are filled. More...

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

GeomType	m_geomType
	Type of geometry. More...

LibUtilities::ShapeType	m_shapeType
	Type of shape. More...

int	m_globalID
	Global ID. More...

Array< OneD, Array< OneD, NekDouble > >	m_coeffs
	Array containing expansion coefficients of `m_xmap`. More...

Private Member Functions
virtual int	v_GetShapeDim () const
	Get the object's shape dimension. More...

virtual PointGeomSharedPtr	v_GetVertex (int i) const

virtual Geometry1DSharedPtr	v_GetEdge (int i) const
	Returns edge `i` of this object. More...

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

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

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

Additional Inherited Members
Static Protected Member Functions inherited from Nektar::SpatialDomains::Geometry
static GeomFactorsSharedPtr	ValidateRegGeomFactor (GeomFactorsSharedPtr geomFactor)
	Check to see if a geometric factor has already been created that contains the same regular information. More...

Static Protected Attributes inherited from Nektar::SpatialDomains::Geometry
static GeomFactorsVector	m_regGeomFactorsManager

Detailed Description

2D geometry information

Definition at line 68 of file Geometry2D.h.

Constructor & Destructor Documentation

◆ Geometry2D() [1/2]

Nektar::SpatialDomains::Geometry2D::Geometry2D ( )

Definition at line 50 of file Geometry2D.cpp.

51 {

52 }

◆ Geometry2D() [2/2]

Nektar::SpatialDomains::Geometry2D::Geometry2D	(	const int	coordim,
		CurveSharedPtr	curve
	)

Definition at line 54 of file Geometry2D.cpp.

References ASSERTL0, and Nektar::SpatialDomains::Geometry::m_coordim.

     : Geometry(coordim), m_curve(curve)
 {
     ASSERTL0(m_coordim > 1,
              "Coordinate dimension should be at least 2 for a 2D geometry");
 }

◆ ~Geometry2D()

Nektar::SpatialDomains::Geometry2D::~Geometry2D ( )

virtual

Definition at line 61 of file Geometry2D.cpp.

62 {

63 }

Member Function Documentation

◆ NewtonIterationForLocCoord()

void Nektar::SpatialDomains::Geometry2D::NewtonIterationForLocCoord	(	const Array< OneD, const NekDouble > &	coords,
		const Array< OneD, const NekDouble > &	ptsx,
		const Array< OneD, const NekDouble > &	ptsy,
		Array< OneD, NekDouble > &	Lcoords,
		NekDouble &	resid
	)

protected

Definition at line 65 of file Geometry2D.cpp.

References Nektar::SpatialDomains::Geometry::m_geomFactors, Nektar::SpatialDomains::Geometry::m_xmap, Vmath::Vsum(), and WARNINGL1.

Referenced by Nektar::SpatialDomains::QuadGeom::v_GetLocCoords(), and Nektar::SpatialDomains::TriGeom::v_GetLocCoords().

 {
     // Maximum iterations for convergence
     const int MaxIterations = 51;
     // |x-xp|^2 < EPSILON  error    tolerance
     const NekDouble Tol = 1.e-8;
     // |r,s|    > LcoordDIV stop   the search
     const NekDouble LcoordDiv = 15.0;
 
     Array<OneD, const NekDouble> Jac =
         m_geomFactors->GetJac(m_xmap->GetPointsKeys());
 
     NekDouble ScaledTol = Vmath::Vsum(Jac.num_elements(), Jac, 1) /
                           ((NekDouble)Jac.num_elements());
     ScaledTol *= Tol;
 
     NekDouble xmap, ymap, F1, F2;
     NekDouble derx_1, derx_2, dery_1, dery_2, jac;
 
     // save intiial guess for later reference if required.
     NekDouble init0 = Lcoords[0], init1 = Lcoords[1];
 
     Array<OneD, NekDouble> DxD1(ptsx.num_elements());
     Array<OneD, NekDouble> DxD2(ptsx.num_elements());
     Array<OneD, NekDouble> DyD1(ptsx.num_elements());
     Array<OneD, NekDouble> DyD2(ptsx.num_elements());
 
     // Ideally this will be stored in m_geomfactors
     m_xmap->PhysDeriv(ptsx, DxD1, DxD2);
     m_xmap->PhysDeriv(ptsy, DyD1, DyD2);
 
     int cnt = 0;
     Array<OneD, DNekMatSharedPtr> I(2);
     Array<OneD, NekDouble> eta(2);
 
     F1 = F2 = 2000; // Starting value of Function
 
     while (cnt++ < MaxIterations)
     {
         //  evaluate lagrange interpolant at Lcoords
         m_xmap->LocCoordToLocCollapsed(Lcoords, eta);
         I[0] = m_xmap->GetBasis(0)->GetI(eta);
         I[1] = m_xmap->GetBasis(1)->GetI(eta + 1);
 
         // calculate the global point `corresponding to Lcoords
         xmap = m_xmap->PhysEvaluate(I, ptsx);
         ymap = m_xmap->PhysEvaluate(I, ptsy);
 
         F1 = coords[0] - xmap;
         F2 = coords[1] - ymap;
 
         if (F1 * F1 + F2 * F2 < ScaledTol)
         {
             resid = sqrt(F1 * F1 + F2 * F2);
             break;
         }
 
         // Interpolate derivative metric at Lcoords
         derx_1 = m_xmap->PhysEvaluate(I, DxD1);
         derx_2 = m_xmap->PhysEvaluate(I, DxD2);
         dery_1 = m_xmap->PhysEvaluate(I, DyD1);
         dery_2 = m_xmap->PhysEvaluate(I, DyD2);
 
         jac = dery_2 * derx_1 - dery_1 * derx_2;
 
         // use analytical inverse of derivitives which are
         // also similar to those of metric factors.
         Lcoords[0] =
             Lcoords[0] +
             (dery_2 * (coords[0] - xmap) - derx_2 * (coords[1] - ymap)) / jac;
 
         Lcoords[1] =
             Lcoords[1] +
             (-dery_1 * (coords[0] - xmap) + derx_1 * (coords[1] - ymap)) / jac;
 
         if (fabs(Lcoords[0]) > LcoordDiv || fabs(Lcoords[1]) > LcoordDiv)
         {
             break; // lcoords have diverged so stop iteration
         }
     }
 
     resid = sqrt(F1 * F1 + F2 * F2);
 
     if (cnt >= MaxIterations)
     {
         Array<OneD, NekDouble> collCoords(2);
         m_xmap->LocCoordToLocCollapsed(Lcoords, collCoords);
 
         // if coordinate is inside element dump error!
         if ((collCoords[0] >= -1.0 && collCoords[0] <= 1.0) &&
             (collCoords[1] >= -1.0 && collCoords[1] <= 1.0))
         {
             std::ostringstream ss;
 
             ss << "Reached MaxIterations (" << MaxIterations
                << ") in Newton iteration ";
             ss << "Init value (" << setprecision(4) << init0 << "," << init1
                << ","
                << ") ";
             ss << "Fin  value (" << Lcoords[0] << "," << Lcoords[1] << ","
                << ") ";
             ss << "Resid = " << resid << " Tolerance = " << sqrt(ScaledTol);
 
             WARNINGL1(cnt < MaxIterations, ss.str());
         }
     }
 }

◆ v_GetEdge()

Geometry1DSharedPtr Nektar::SpatialDomains::Geometry2D::v_GetEdge ( int i ) const

privatevirtual

Returns edge i of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 194 of file Geometry2D.cpp.

References ASSERTL2, and m_edges.

 {
     ASSERTL2(i >= 0 && i < m_edges.size(), "Index out of range");
     return m_edges[i];
 }

◆ v_GetEorient()

StdRegions::Orientation Nektar::SpatialDomains::Geometry2D::v_GetEorient ( const int i ) const

privatevirtual

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 200 of file Geometry2D.cpp.

References ASSERTL2, and m_eorient.

 {
     ASSERTL2(i >= 0 && i < m_eorient.size(), "Index out of range");
     return m_eorient[i];
 }

◆ v_GetNumEdges()

int Nektar::SpatialDomains::Geometry2D::v_GetNumEdges ( ) const

privatevirtual

Get the number of edges of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 183 of file Geometry2D.cpp.

References m_edges.

 {
     return m_edges.size();
 }

◆ v_GetNumVerts()

int Nektar::SpatialDomains::Geometry2D::v_GetNumVerts ( ) const

privatevirtual

Get the number of vertices of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 178 of file Geometry2D.cpp.

References m_verts.

 {
     return m_verts.size();
 }

◆ v_GetShapeDim()

int Nektar::SpatialDomains::Geometry2D::v_GetShapeDim ( ) const

privatevirtual

Get the object's shape dimension.

For example, a segment is one dimensional and quadrilateral is two dimensional.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 206 of file Geometry2D.cpp.

 {
     return 2;
 }

◆ v_GetVertex()

PointGeomSharedPtr Nektar::SpatialDomains::Geometry2D::v_GetVertex ( int i ) const

privatevirtual

Implements Nektar::SpatialDomains::Geometry.

Definition at line 188 of file Geometry2D.cpp.

References ASSERTL2, and m_verts.

 {
     ASSERTL2(i >= 0 && i < m_verts.size(), "Index out of range");
     return m_verts[i];
 }

Member Data Documentation

◆ kDim

const int Nektar::SpatialDomains::Geometry2D::kDim = 2

static

Definition at line 75 of file Geometry2D.h.

◆ m_curve

CurveSharedPtr Nektar::SpatialDomains::Geometry2D::m_curve

protected

Definition at line 81 of file Geometry2D.h.

Referenced by Nektar::SpatialDomains::QuadGeom::v_FillGeom(), Nektar::SpatialDomains::TriGeom::v_FillGeom(), Nektar::SpatialDomains::QuadGeom::v_Reset(), and Nektar::SpatialDomains::TriGeom::v_Reset().

◆ m_edges

SegGeomVector Nektar::SpatialDomains::Geometry2D::m_edges

protected

Definition at line 79 of file Geometry2D.h.

◆ m_eorient

std::vector<StdRegions::Orientation> Nektar::SpatialDomains::Geometry2D::m_eorient

protected

Definition at line 80 of file Geometry2D.h.

Referenced by Nektar::SpatialDomains::QuadGeom::QuadGeom(), Nektar::SpatialDomains::TriGeom::TriGeom(), Nektar::SpatialDomains::QuadGeom::v_FillGeom(), Nektar::SpatialDomains::TriGeom::v_FillGeom(), and v_GetEorient().

◆ m_verts

PointGeomVector Nektar::SpatialDomains::Geometry2D::m_verts

protected

Definition at line 78 of file Geometry2D.h.

Referenced by Nektar::SpatialDomains::QuadGeom::GetFaceOrientation(), Nektar::SpatialDomains::TriGeom::GetFaceOrientation(), Nektar::SpatialDomains::QuadGeom::QuadGeom(), Nektar::SpatialDomains::TriGeom::TriGeom(), Nektar::SpatialDomains::TriGeom::v_FillGeom(), Nektar::SpatialDomains::QuadGeom::v_GenGeomFactors(), Nektar::SpatialDomains::QuadGeom::v_GetLocCoords(), Nektar::SpatialDomains::TriGeom::v_GetLocCoords(), v_GetNumVerts(), and v_GetVertex().

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geometry2D() [1/2]

◆ Geometry2D() [2/2]

◆ ~Geometry2D()

Member Function Documentation

◆ NewtonIterationForLocCoord()

◆ v_GetEdge()

◆ v_GetEorient()

◆ v_GetNumEdges()

◆ v_GetNumVerts()

◆ v_GetShapeDim()

◆ v_GetVertex()

Member Data Documentation

◆ kDim

◆ m_curve

◆ m_edges

◆ m_eorient

◆ m_verts