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 ()

CurveSharedPtr	GetCurve ()

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...

void	ClearBoundingBox ()

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

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

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. 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...

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

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

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)

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

virtual PointGeomSharedPtr	v_GetVertex (int i) const override

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

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

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

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

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

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 &dist)

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

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

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

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

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

◆ ~Geometry2D()

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

virtual

Definition at line 61 of file Geometry2D.cpp.

62 {

63 }

Member Function Documentation

◆ GetCurve()

CurveSharedPtr Nektar::SpatialDomains::Geometry2D::GetCurve ( )

inline

Definition at line 76 of file Geometry2D.h.

     {
         return m_curve;
     }

References m_curve.

◆ 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 &	dist
	)

protected

Definition at line 65 of file Geometry2D.cpp.

 {
     // Maximum iterations for convergence
     const int MaxIterations = NekConstants::kNewtonIterations;
     // |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.size(), Jac, 1) / ((NekDouble)Jac.size());
     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.size());
     Array<OneD, NekDouble> DxD2(ptsx.size());
     Array<OneD, NekDouble> DyD1(ptsx.size());
     Array<OneD, NekDouble> DyD2(ptsx.size());
  
     // 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
     NekDouble resid = sqrt(F1 * F1 + F2 * F2);
     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 (!(std::isfinite(Lcoords[0]) && std::isfinite(Lcoords[1])))
         {
             dist = 1e16;
             std::ostringstream ss;
             ss << "nan or inf found in NewtonIterationForLocCoord in element "
                << GetGlobalID();
             WARNINGL1(false, ss.str());
             return;
         }
         if (fabs(Lcoords[0]) > LcoordDiv || fabs(Lcoords[1]) > LcoordDiv)
         {
             break; // lcoords have diverged so stop iteration
         }
     }
  
     m_xmap->LocCoordToLocCollapsed(Lcoords, eta);
     if (ClampLocCoords(eta, 0.))
     {
         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;
         dist = sqrt(F1 * F1 + F2 * F2);
     }
     else
     {
         dist = 0.;
     }
  
     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());
         }
     }
 }

References Nektar::SpatialDomains::Geometry::ClampLocCoords(), Nektar::SpatialDomains::Geometry::GetGlobalID(), Nektar::NekConstants::kNewtonIterations, Nektar::SpatialDomains::Geometry::m_geomFactors, Nektar::SpatialDomains::Geometry::m_xmap, tinysimd::sqrt(), Vmath::Vsum(), and WARNINGL1.

Referenced by v_GetLocCoords().

◆ v_FindDistance()

NekDouble Nektar::SpatialDomains::Geometry2D::v_FindDistance	(	const Array< OneD, const NekDouble > &	xs,
		Array< OneD, NekDouble > &	xi
	)

overrideprotectedvirtual

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 354 of file Geometry2D.cpp.

 {
     if (m_geomFactors->GetGtype() == eRegular)
     {
         xiOut = Array<OneD, NekDouble>(2, 0.0);
  
         GetLocCoords(xs, xiOut);
         ClampLocCoords(xiOut);
  
         Array<OneD, NekDouble> gloCoord(3);
         gloCoord[0] = GetCoord(0, xiOut);
         gloCoord[1] = GetCoord(1, xiOut);
         gloCoord[2] = GetCoord(2, xiOut);
  
         return sqrt((xs[0] - gloCoord[0]) * (xs[0] - gloCoord[0]) +
                     (xs[1] - gloCoord[1]) * (xs[1] - gloCoord[1]) +
                     (xs[2] - gloCoord[2]) * (xs[2] - gloCoord[2]));
     }
     // If deformed edge then the inverse mapping is non-linear so need to
     // numerically solve for the local coordinate
     else if (m_geomFactors->GetGtype() == eDeformed)
     {
         // Choose starting based on closest quad
         Array<OneD, NekDouble> xi(2, 0.0), eta(2, 0.0);
         m_xmap->LocCollapsedToLocCoord(eta, xi);
  
         // Armijo constants:
         // https://en.wikipedia.org/wiki/Backtracking_line_search
         const NekDouble c1 = 1e-4, c2 = 0.9;
  
         int nq = m_xmap->GetTotPoints();
  
         Array<OneD, NekDouble> x(nq), y(nq), z(nq);
         m_xmap->BwdTrans(m_coeffs[0], x);
         m_xmap->BwdTrans(m_coeffs[1], y);
         m_xmap->BwdTrans(m_coeffs[2], z);
  
         Array<OneD, NekDouble> xderxi1(nq, 0.0), yderxi1(nq, 0.0),
             zderxi1(nq, 0.0), xderxi2(nq, 0.0), yderxi2(nq, 0.0),
             zderxi2(nq, 0.0), xderxi1xi1(nq, 0.0), yderxi1xi1(nq, 0.0),
             zderxi1xi1(nq, 0.0), xderxi1xi2(nq, 0.0), yderxi1xi2(nq, 0.0),
             zderxi1xi2(nq, 0.0), xderxi2xi1(nq, 0.0), yderxi2xi1(nq, 0.0),
             zderxi2xi1(nq, 0.0), xderxi2xi2(nq, 0.0), yderxi2xi2(nq, 0.0),
             zderxi2xi2(nq, 0.0);
  
         // Get first & second derivatives & partial derivatives of x,y,z values
         std::array<NekDouble, 3> xc_derxi, yc_derxi, zc_derxi;
  
         m_xmap->PhysDeriv(x, xderxi1, xderxi2);
         m_xmap->PhysDeriv(y, yderxi1, yderxi2);
         m_xmap->PhysDeriv(z, zderxi1, zderxi2);
  
         m_xmap->PhysDeriv(xderxi1, xderxi1xi1, xderxi1xi2);
         m_xmap->PhysDeriv(yderxi1, yderxi1xi1, yderxi1xi2);
         m_xmap->PhysDeriv(zderxi1, zderxi1xi1, zderxi1xi2);
  
         m_xmap->PhysDeriv(yderxi2, yderxi2xi1, yderxi2xi2);
         m_xmap->PhysDeriv(xderxi2, xderxi2xi1, xderxi2xi2);
         m_xmap->PhysDeriv(zderxi2, zderxi2xi1, zderxi2xi2);
  
         // Minimisation loop (Quasi-newton method)
         NekDouble fx_prev = std::numeric_limits<NekDouble>::max();
         for (int i = 0; i < NekConstants::kNewtonIterations; ++i)
         {
             // Compute the objective function, f(x_k) and its derivatives
             NekDouble xc = m_xmap->PhysEvaluate(xi, x, xc_derxi);
             NekDouble yc = m_xmap->PhysEvaluate(xi, y, yc_derxi);
             NekDouble zc = m_xmap->PhysEvaluate(xi, z, zc_derxi);
  
             NekDouble xc_derxi1xi1 = m_xmap->PhysEvaluate(xi, xderxi1xi1);
             NekDouble yc_derxi1xi1 = m_xmap->PhysEvaluate(xi, yderxi1xi1);
             NekDouble zc_derxi1xi1 = m_xmap->PhysEvaluate(xi, zderxi1xi1);
  
             NekDouble xc_derxi1xi2 = m_xmap->PhysEvaluate(xi, xderxi1xi2);
             NekDouble yc_derxi1xi2 = m_xmap->PhysEvaluate(xi, yderxi1xi2);
             NekDouble zc_derxi1xi2 = m_xmap->PhysEvaluate(xi, zderxi1xi2);
  
             NekDouble xc_derxi2xi2 = m_xmap->PhysEvaluate(xi, xderxi2xi2);
             NekDouble yc_derxi2xi2 = m_xmap->PhysEvaluate(xi, yderxi2xi2);
             NekDouble zc_derxi2xi2 = m_xmap->PhysEvaluate(xi, zderxi2xi2);
  
             // Objective function is the distance to the search point
             NekDouble xdiff = xc - xs[0];
             NekDouble ydiff = yc - xs[1];
             NekDouble zdiff = zc - xs[2];
  
             NekDouble fx = xdiff * xdiff + ydiff * ydiff + zdiff * zdiff;
  
             NekDouble fx_derxi1 = 2.0 * xdiff * xc_derxi[0] +
                                   2.0 * ydiff * yc_derxi[0] +
                                   2.0 * zdiff * zc_derxi[0];
  
             NekDouble fx_derxi2 = 2.0 * xdiff * xc_derxi[1] +
                                   2.0 * ydiff * yc_derxi[1] +
                                   2.0 * zdiff * zc_derxi[1];
  
             NekDouble fx_derxi1xi1 =
                 2.0 * xdiff * xc_derxi1xi1 + 2.0 * xc_derxi[0] * xc_derxi[0] +
                 2.0 * ydiff * yc_derxi1xi1 + 2.0 * yc_derxi[0] * yc_derxi[0] +
                 2.0 * zdiff * zc_derxi1xi1 + 2.0 * zc_derxi[0] * zc_derxi[0];
  
             NekDouble fx_derxi1xi2 =
                 2.0 * xdiff * xc_derxi1xi2 + 2.0 * xc_derxi[1] * xc_derxi[0] +
                 2.0 * ydiff * yc_derxi1xi2 + 2.0 * yc_derxi[1] * yc_derxi[0] +
                 2.0 * zdiff * zc_derxi1xi2 + 2.0 * zc_derxi[1] * zc_derxi[0];
  
             NekDouble fx_derxi2xi2 =
                 2.0 * xdiff * xc_derxi2xi2 + 2.0 * xc_derxi[1] * xc_derxi[1] +
                 2.0 * ydiff * yc_derxi2xi2 + 2.0 * yc_derxi[1] * yc_derxi[1] +
                 2.0 * zdiff * zc_derxi2xi2 + 2.0 * zc_derxi[1] * zc_derxi[1];
  
             // Jacobian
             NekDouble jac[2];
             jac[0] = fx_derxi1;
             jac[1] = fx_derxi2;
  
             // Inverse of 2x2 hessian
             NekDouble hessInv[2][2];
  
             NekDouble det =
                 1 / (fx_derxi1xi1 * fx_derxi2xi2 - fx_derxi1xi2 * fx_derxi1xi2);
             hessInv[0][0] = det * fx_derxi2xi2;
             hessInv[0][1] = det * -fx_derxi1xi2;
             hessInv[1][0] = det * -fx_derxi1xi2;
             hessInv[1][1] = det * fx_derxi1xi1;
  
             // Check for convergence
             if (abs(fx - fx_prev) < 1e-12)
             {
                 fx_prev = fx;
                 break;
             }
             else
             {
                 fx_prev = fx;
             }
  
             NekDouble gamma = 1.0;
             bool conv       = false;
  
             // Search direction: Newton's method
             NekDouble pk[2];
             pk[0] = -(hessInv[0][0] * jac[0] + hessInv[1][0] * jac[1]);
             pk[1] = -(hessInv[0][1] * jac[0] + hessInv[1][1] * jac[1]);
  
             // Backtracking line search
             while (gamma > 1e-10)
             {
                 Array<OneD, NekDouble> xi_pk(2);
                 xi_pk[0] = xi[0] + pk[0] * gamma;
                 xi_pk[1] = xi[1] + pk[1] * gamma;
  
                 Array<OneD, NekDouble> eta_pk(2, 0.0);
                 m_xmap->LocCoordToLocCollapsed(xi_pk, eta_pk);
  
                 if (eta_pk[0] <
                         (-1 - std::numeric_limits<NekDouble>::epsilon()) ||
                     eta_pk[0] >
                         (1 + std::numeric_limits<NekDouble>::epsilon()) ||
                     eta_pk[1] <
                         (-1 - std::numeric_limits<NekDouble>::epsilon()) ||
                     eta_pk[1] > (1 + std::numeric_limits<NekDouble>::epsilon()))
                 {
                     gamma /= 2.0;
                     continue;
                 }
  
                 std::array<NekDouble, 3> xc_pk_derxi, yc_pk_derxi, zc_pk_derxi;
  
                 NekDouble xc_pk = m_xmap->PhysEvaluate(xi_pk, x, xc_pk_derxi);
                 NekDouble yc_pk = m_xmap->PhysEvaluate(xi_pk, y, yc_pk_derxi);
                 NekDouble zc_pk = m_xmap->PhysEvaluate(xi_pk, z, zc_pk_derxi);
  
                 NekDouble xc_pk_diff = xc_pk - xs[0];
                 NekDouble yc_pk_diff = yc_pk - xs[1];
                 NekDouble zc_pk_diff = zc_pk - xs[2];
  
                 NekDouble fx_pk = xc_pk_diff * xc_pk_diff +
                                   yc_pk_diff * yc_pk_diff +
                                   zc_pk_diff * zc_pk_diff;
  
                 NekDouble fx_pk_derxi1 = 2.0 * xc_pk_diff * xc_pk_derxi[0] +
                                          2.0 * yc_pk_diff * yc_pk_derxi[0] +
                                          2.0 * zc_pk_diff * zc_pk_derxi[0];
  
                 NekDouble fx_pk_derxi2 = 2.0 * xc_pk_diff * xc_pk_derxi[1] +
                                          2.0 * yc_pk_diff * yc_pk_derxi[1] +
                                          2.0 * zc_pk_diff * zc_pk_derxi[1];
  
                 // Check Wolfe conditions using Armijo constants
                 // https://en.wikipedia.org/wiki/Wolfe_conditions
                 NekDouble tmp  = pk[0] * fx_derxi1 + pk[1] * fx_derxi2;
                 NekDouble tmp2 = pk[0] * fx_pk_derxi1 + pk[1] * fx_pk_derxi2;
                 if ((fx_pk - (fx + c1 * gamma * tmp)) <
                         std::numeric_limits<NekDouble>::epsilon() &&
                     (-tmp2 - (-c2 * tmp)) <
                         std::numeric_limits<NekDouble>::epsilon())
                 {
                     conv = true;
                     break;
                 }
  
                 gamma /= 2.0;
             }
  
             if (!conv)
             {
                 break;
             }
  
             xi[0] += gamma * pk[0];
             xi[1] += gamma * pk[1];
         }
  
         xiOut = xi;
         return sqrt(fx_prev);
     }
     else
     {
         ASSERTL0(false, "Geometry type unknown")
     }
  
     return -1.0;
 }

References tinysimd::abs(), ASSERTL0, Nektar::SpatialDomains::Geometry::ClampLocCoords(), Nektar::SpatialDomains::eDeformed, Nektar::SpatialDomains::eRegular, Nektar::SpatialDomains::Geometry::GetCoord(), Nektar::SpatialDomains::Geometry::GetLocCoords(), Nektar::NekConstants::kNewtonIterations, Nektar::SpatialDomains::Geometry::m_coeffs, Nektar::SpatialDomains::Geometry::m_geomFactors, Nektar::SpatialDomains::Geometry::m_xmap, and tinysimd::sqrt().

◆ v_GetEdge()

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

overrideprotectedvirtual

Returns edge i of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 337 of file Geometry2D.cpp.

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

References ASSERTL2, and m_edges.

◆ v_GetEorient()

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

overrideprotectedvirtual

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 343 of file Geometry2D.cpp.

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

References ASSERTL2, and m_eorient.

◆ v_GetLocCoords()

NekDouble Nektar::SpatialDomains::Geometry2D::v_GetLocCoords	(	const Array< OneD, const NekDouble > &	coords,
		Array< OneD, NekDouble > &	Lcoords
	)

overrideprotectedvirtual

Determine the local collapsed coordinates that correspond to a given Cartesian coordinate for this geometry object.

For curvilinear and non-affine elements (i.e. where the Jacobian varies as a function of the standard element coordinates), this is a non-linear optimisation problem that requires the use of a Newton iteration. Note therefore that this can be an expensive operation.

Note that, clearly, the provided Cartesian coordinate lie outside the element. The function therefore returns the minimum distance from some position in the element to . Lcoords will also be constrained to fit within the range \([-1,1]^d\) where \( d \) is the dimension of the element.

Parameters

coords	Input Cartesian global coordinates
Lcoords	Corresponding local coordinates

Returns: Distance between obtained coordinates and provided ones.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 201 of file Geometry2D.cpp.

 {
     NekDouble dist = 0.;
     if (GetMetricInfo()->GetGtype() == eRegular)
     {
         int v2;
         if (m_shapeType == LibUtilities::eTriangle)
         {
             v2 = 2;
         }
         else if (m_shapeType == LibUtilities::eQuadrilateral)
         {
             v2 = 3;
         }
         else
         {
             v2 = 2;
             ASSERTL0(false, "unrecognized 2D element type");
         }
  
         NekDouble coords2 = (m_coordim == 3) ? coords[2] : 0.0;
         PointGeom r(m_coordim, 0, coords[0], coords[1], coords2);
  
         // Edges
         PointGeom er0, e10, e20;
         PointGeom norm, orth1, orth2;
         er0.Sub(r, *m_verts[0]);
         e10.Sub(*m_verts[1], *m_verts[0]);
         e20.Sub(*m_verts[v2], *m_verts[0]);
  
         // Obtain normal to element plane
         norm.Mult(e10, e20);
         // Obtain vector which are proportional to normal of e10 and e20.
         orth1.Mult(norm, e10);
         orth2.Mult(norm, e20);
  
         // Calculate length using L/|dv1| = (x-v0).n1/(dv1.n1) for coordiante 1
         // Then rescale to [-1,1].
         Lcoords[0] = er0.dot(orth2) / e10.dot(orth2);
         Lcoords[0] = 2. * Lcoords[0] - 1.;
         Lcoords[1] = er0.dot(orth1) / e20.dot(orth1);
         Lcoords[1] = 2. * Lcoords[1] - 1.;
  
         // Set distance
         Array<OneD, NekDouble> eta(2, 0.);
         m_xmap->LocCoordToLocCollapsed(Lcoords, eta);
         if (ClampLocCoords(eta, 0.))
         {
             Array<OneD, NekDouble> xi(2, 0.);
             m_xmap->LocCollapsedToLocCoord(eta, xi);
             xi[0] = (xi[0] + 1.) * 0.5; // re-scaled to ratio [0, 1]
             xi[1] = (xi[1] + 1.) * 0.5;
             for (int i = 0; i < m_coordim; ++i)
             {
                 NekDouble tmp = xi[0] * e10[i] + xi[1] * e20[i] - er0[i];
                 dist += tmp * tmp;
             }
             dist = sqrt(dist);
         }
     }
     else
     {
         v_FillGeom();
         // Determine nearest point of coords  to values in m_xmap
         int npts = m_xmap->GetTotPoints();
         Array<OneD, NekDouble> ptsx(npts), ptsy(npts);
         Array<OneD, NekDouble> tmpx(npts), tmpy(npts);
  
         // Determine 3D manifold orientation
         int idx = 0, idy = 1;
         if (m_coordim == 3)
         {
             PointGeom e01, e21, norm;
             e01.Sub(*m_verts[0], *m_verts[1]);
             e21.Sub(*m_verts[2], *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;
             }
             idx = (tmpi + 1) % 3;
             idy = (tmpi + 2) % 3;
         }
         Array<OneD, NekDouble> tmpcoords(2);
         tmpcoords[0] = coords[idx];
         tmpcoords[1] = coords[idy];
  
         m_xmap->BwdTrans(m_coeffs[idx], ptsx);
         m_xmap->BwdTrans(m_coeffs[idy], ptsy);
  
         const Array<OneD, const NekDouble> za = m_xmap->GetPoints(0);
         const Array<OneD, const NekDouble> zb = m_xmap->GetPoints(1);
  
         // guess the first local coords based on nearest point
         Vmath::Sadd(npts, -tmpcoords[0], ptsx, 1, tmpx, 1);
         Vmath::Sadd(npts, -tmpcoords[1], ptsy, 1, tmpy, 1);
         Vmath::Vmul(npts, tmpx, 1, tmpx, 1, tmpx, 1);
         Vmath::Vvtvp(npts, tmpy, 1, tmpy, 1, tmpx, 1, tmpx, 1);
  
         int min_i = Vmath::Imin(npts, tmpx, 1);
  
         Array<OneD, NekDouble> eta(2, 0.);
         eta[0] = za[min_i % za.size()];
         eta[1] = zb[min_i / za.size()];
         m_xmap->LocCollapsedToLocCoord(eta, Lcoords);
  
         // Perform newton iteration to find local coordinates
         NewtonIterationForLocCoord(tmpcoords, ptsx, ptsy, Lcoords, dist);
     }
     return dist;
 }

◆ v_GetNumEdges()

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

overrideprotectedvirtual

Get the number of edges of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 326 of file Geometry2D.cpp.

 {
     return m_edges.size();
 }

References m_edges.

◆ v_GetNumVerts()

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

overrideprotectedvirtual

Get the number of vertices of this object.

Reimplemented from Nektar::SpatialDomains::Geometry.

Definition at line 321 of file Geometry2D.cpp.

 {
     return m_verts.size();
 }

References m_verts.

◆ v_GetShapeDim()

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

overrideprotectedvirtual

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 349 of file Geometry2D.cpp.

 {
     return 2;
 }

◆ v_GetVertex()

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

overrideprotectedvirtual

Implements Nektar::SpatialDomains::Geometry.

Definition at line 331 of file Geometry2D.cpp.

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

References ASSERTL2, and m_verts.

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 85 of file Geometry2D.h.

Referenced by GetCurve(), 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 83 of file Geometry2D.h.

◆ m_eorient

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

protected

Definition at line 84 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 82 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(), v_GetLocCoords(), v_GetNumVerts(), and v_GetVertex().

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geometry2D() [1/2]

◆ Geometry2D() [2/2]

◆ ~Geometry2D()

Member Function Documentation

◆ GetCurve()

◆ NewtonIterationForLocCoord()

◆ v_FindDistance()

◆ v_GetEdge()

◆ v_GetEorient()

◆ v_GetLocCoords()

◆ v_GetNumEdges()

◆ v_GetNumVerts()

◆ v_GetShapeDim()

◆ v_GetVertex()

Member Data Documentation

◆ kDim

◆ m_curve

◆ m_edges

◆ m_eorient

◆ m_verts