Geometry2D.cpp

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////////////////////////////////////////////////////////////////////////////////
//
//  File:  Geometry2D.cpp
//
//  For more information, please see: http://www.nektar.info/
//
//  The MIT License
//
//  Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
//  Department of Aeronautics, Imperial College London (UK), and Scientific 
//  Computing and Imaging Institute, University of Utah (USA).
//
//  License for the specific language governing rights and limitations under
//  Permission is hereby granted, free of charge, to any person obtaining a
//  copy of this software and associated documentation files (the "Software"),
//  to deal in the Software without restriction, including without limitation
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//  and/or sell copies of the Software, and to permit persons to whom the
//  Software is furnished to do so, subject to the following conditions:
//
//  The above copyright notice and this permission notice shall be included
//  in all copies or substantial portions of the Software.
//
//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
//  OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
//  THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
//  FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
//  DEALINGS IN THE SOFTWARE.
//
//  Description:  2D geometry information
//
//
////////////////////////////////////////////////////////////////////////////////
#include <SpatialDomains/Geometry2D.h>
#include <SpatialDomains/SegGeom.h>
#include <boost/shared_ptr.hpp>

#include <iomanip>

using namespace std;

namespace Nektar
{
    namespace SpatialDomains
    {
        Geometry2D::Geometry2D()
        {
        }

        Geometry2D::Geometry2D(const int coordim):
            Geometry(coordim)
        {
            ASSERTL0(m_coordim > 1,
                     "Coordinate dimension should be at least 2 for a 2D geometry");
        }

        Geometry2D::~Geometry2D()
        {
        }

        int Geometry2D::GetFid() const
        {
            return v_GetFid();
        }

        const LibUtilities::BasisSharedPtr Geometry2D::GetEdgeBasis(const int i)
        {
            return v_GetEdgeBasis(i);
        }

        const Geometry2DSharedPtr Geometry2D::GetFace(int i) const
        {
            return v_GetFace(i);
        }

        StdRegions::Orientation Geometry2D::GetFaceOrient(const int i) const
        {
            return v_GetFaceOrient(i);
        }

        const Geometry1DSharedPtr Geometry2D::GetEdge(int i) const
        {
            return v_GetEdge(i);
        }

        StdRegions::Orientation Geometry2D::GetCartesianEorient(const int i) const
        {
            return v_GetCartesianEorient(i);
        }

        int Geometry2D::WhichEdge(SegGeomSharedPtr edge)
        {
            return v_WhichEdge(edge);
        }

        int Geometry2D::WhichFace(Geometry2DSharedPtr face)
        {
            return v_WhichFace(face);
        }

        void 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)
        {
            // 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());
                }
            }
        }

        int Geometry2D::v_GetFid() const 
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            return 0;
        }

        const LibUtilities::BasisSharedPtr Geometry2D::v_GetEdgeBasis(const int i)
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            LibUtilities::BasisSharedPtr returnval;
            return returnval;
        }


        int Geometry2D::v_GetEid(int i) const
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            return 0;
        }

        const Geometry1DSharedPtr Geometry2D::v_GetEdge(int i) const
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            SegGeomSharedPtr returnval;
            return returnval;
        }

        PointGeomSharedPtr Geometry2D::v_GetVertex(int i) const
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            PointGeomSharedPtr returnval;
            return returnval;
        }

        StdRegions::Orientation Geometry2D::v_GetEorient(const int i) const
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            return StdRegions::eForwards;
        }

        const Geometry2DSharedPtr Geometry2D::v_GetFace(int i) const
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            Geometry2DSharedPtr returnval;
            return returnval;
        }

        StdRegions::Orientation Geometry2D::v_GetFaceOrient(const int i) const
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            return StdRegions::eDir1FwdDir1_Dir2FwdDir2;
        }

        StdRegions::Orientation Geometry2D::v_GetCartesianEorient(const int i) const
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            return StdRegions::eForwards;
        }

        int Geometry2D::v_WhichEdge(SegGeomSharedPtr edge)
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            return 0;
        }

        int Geometry2D::v_WhichFace(Geometry2DSharedPtr face)
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function is only valid for shape type geometries");
            return 0;
        }

        int Geometry2D::v_GetShapeDim() const
        {
            return 2;
        }

        bool Geometry2D::v_ContainsPoint(
                const Array<OneD, const NekDouble>& gloCoord,
                      NekDouble tol)
        {
            NEKERROR(ErrorUtil::efatal,
                     "This function has not been defined for this geometry");
            return false;
        }


  }; //end of namespace
}; //end of namespace