eighth_sphere_domain.h

Go to the documentation of this file.

//LIC// ====================================================================
//LIC// This file forms part of oomph-lib, the object-oriented, 
//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
//LIC// 
//LIC//    Version 1.0; svn revision $LastChangedRevision$
//LIC//
//LIC// $LastChangedDate$
//LIC// 
//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
//LIC// This library is free software; you can redistribute it and/or
//LIC// modify it under the terms of the GNU Lesser General Public
//LIC// License as published by the Free Software Foundation; either
//LIC// version 2.1 of the License, or (at your option) any later version.
//LIC// 
//LIC// This library is distributed in the hope that it will be useful,
//LIC// but WITHOUT ANY WARRANTY; without even the implied warranty of
//LIC// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
//LIC// Lesser General Public License for more details.
//LIC// 
//LIC// You should have received a copy of the GNU Lesser General Public
//LIC// License along with this library; if not, write to the Free Software
//LIC// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
//LIC// 02110-1301  USA.
//LIC// 
//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
//LIC// 
//LIC//====================================================================
//Include guards
#ifndef OOMPH_EIGHTH_SPHERE_DOMAIN_HEADER
#define OOMPH_EIGHTH_SPHERE_DOMAIN_HEADER

// Generic oomph-lib includes
#include "../generic/quadtree.h"
#include "../generic/domain.h"
#include "../generic/geom_objects.h"

namespace oomph
{


//=================================================================
/// \short Eighth sphere as domain. Domain is 
/// parametrised by four macro elements
//=================================================================
class EighthSphereDomain : public Domain 
{ 

public: 

 /// \short Constructor: Pass the radius of the sphere.
 EighthSphereDomain(const double& radius) : Radius(radius)
  {
   // There are four macro elements
   unsigned nmacro=4;

   // Resize
   Macro_element_pt.resize(nmacro);

   // Create the 3D Q macro elements
   for (unsigned i=0;i<nmacro;i++)
    {
     Macro_element_pt[i]=new QMacroElement<3>(this,i);
    }
  }

 /// Broken copy constructor
 EighthSphereDomain(const EighthSphereDomain&) 
  { 
   BrokenCopy::broken_copy("EighthSphereDomain");
  } 
 
 /// Broken assignment operator
 void operator=(const EighthSphereDomain&) 
  {
   BrokenCopy::broken_assign("EighthSphereDomain");
  }


 /// Destructor: Kill macro elements
 ~EighthSphereDomain()
  {
   for (unsigned i=0;i<4;i++)
    {
     delete Macro_element_pt[i];
    }
  }
 

 /// \short Vector representation of the  imacro-th macro element
 /// boundary idirect (L/R/D/U/B/F) at time level t 
 /// (t=0: present; t>0: previous):
 /// f(s). 
 void macro_element_boundary(const unsigned& t,
                             const unsigned& imacro,
                             const unsigned& idirect,
                             const Vector<double>& s,
                             Vector<double>& f)
  {
   
   using namespace OcTreeNames;
   
#ifdef WARN_ABOUT_SUBTLY_CHANGED_OOMPH_INTERFACES
   // Warn about time argument being moved to the front
   OomphLibWarning(
    "Order of function arguments has changed between versions 0.8 and 0.85",
    "EighthSphereDomain::macro_element_boundary(...)",
    OOMPH_EXCEPTION_LOCATION);
#endif

   // Which macro element?
   // --------------------
   switch(imacro)
    {
     
     // Macro element 0: Central box
    case 0:

     if (idirect == L)
      {
       r_centr_L(t,s,f);
      }
     else if (idirect == R)
      {
       r_centr_R(t,s,f);
      }
     else if (idirect == D)
      {
       r_centr_D(t,s,f);
      }
     else if (idirect == U)
      {
       r_centr_U(t,s,f);
      }
     else if (idirect == B)
      {
       r_centr_B(t,s,f);
      }
     else if (idirect == F)
      {
       r_centr_F(t,s,f);
      }
     else
      {
       std::ostringstream error_message;
       error_message << "idirect is " 
                     << OcTree::Direct_string[idirect] 
                     << "not one of L, R, U, D, B, F" << std::endl;

       throw OomphLibError(error_message.str(),
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
      }
     
     break;
     
     
     // Macro element 1:right
    case 1:
     
     // Which direction?
     if (idirect==L)
      {
       r_right_L(t,s,f);
      }
     else if (idirect==R)
      {
       r_right_R(t,s,f);
      }
     else if (idirect==D)
      {
       r_right_D(t,s,f);
      }
     else if (idirect==U)
      {
       r_right_U(t,s,f);
      }
     else if (idirect==B)
      {
       r_right_B(t,s,f);
      }
     else if (idirect==F)
      {
       r_right_F(t,s,f);
      }
     else
      {
       std::ostringstream error_message;
       error_message << "idirect is " 
                     << OcTree::Direct_string[idirect] 
                     << "not one of L, R, U, D, B, F" << std::endl;

       throw OomphLibError(error_message.str(),
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
      }
     
     break;   
     
     // Macro element 2: Up
    case 2:
     
     // Which direction?
     if (idirect==L)
      {
       r_up_L(t,s,f);
      }
     else if (idirect==R)
      {
       r_up_R(t,s,f);
      }
     else if (idirect==D)
      {
       r_up_D(t,s,f);
      }
     else if (idirect==U)
      {
       r_up_U(t,s,f);
      }
     else if (idirect==B)
      {
       r_up_B(t,s,f);
      }
     else if (idirect==F)
      {
       r_up_F(t,s,f);
      }
     else
      {
       std::ostringstream error_message;
       error_message << "idirect is " 
                     << OcTree::Direct_string[idirect] 
                     << "not one of L, R, U, D, B, F" << std::endl;
       
       throw OomphLibError(error_message.str(),
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
      }
     
     break;
     
     // Macro element 3: Front
    case 3:
     // Which direction?
     if (idirect==L)
      {
       r_front_L(t,s,f);
      }
     else if (idirect==R)
      {
       r_front_R(t,s,f);
      }
     else if (idirect==D)
      {
       r_front_D(t,s,f);
      }
     else if (idirect==U)
      {
       r_front_U(t,s,f);
      }
     else if (idirect==B)
      {
       r_front_B(t,s,f);
      }
     else if (idirect==F)
      {
       r_front_F(t,s,f);
      }
     else
      {
       std::ostringstream error_message;
       error_message << "idirect is " 
                     << OcTree::Direct_string[idirect] 
                     << "not one of L, R, U, D, B, F" << std::endl;
       
       throw OomphLibError(error_message.str(),
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
      }
     
     break;
     
    default:
     
     std::ostringstream error_message;
     error_message << "imacro is " 
                   << OcTree::Direct_string[idirect] 
                   << ", but should be in the range 0-3" << std::endl;
     
     throw OomphLibError(error_message.str(),
                         OOMPH_CURRENT_FUNCTION,
                         OOMPH_EXCEPTION_LOCATION);
    }

  }


private:
 
 // Radius of the sphere
 double Radius;

 /// \short Boundary of central box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_centr_L(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);
 
 /// \short Boundary of central box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_centr_R(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f); 
 
 /// \short Boundary of central box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_centr_D(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of central box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_centr_U(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of central box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_centr_B(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of central box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_centr_F(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of right box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_right_L(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);
 
 /// \short Boundary of right box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_right_R(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of  right box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_right_D(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of right box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_right_U(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of  right box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_right_B(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of  right box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_right_F(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of top left box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_up_L(const unsigned& t, const Vector<double>& zeta, 
             Vector<double>& f);

 /// \short Boundary of top left box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_up_R(const unsigned& t, const Vector<double>& zeta, 
             Vector<double>& f);
 
 /// \short Boundary of top left box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
void r_up_D(const unsigned& t, const Vector<double>& zeta, 
            Vector<double>& f);

 /// \short Boundary of top left box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_up_U(const unsigned& t, const Vector<double>& zeta, 
             Vector<double>& f);

 /// \short Boundary of top left box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_up_B(const unsigned& t, const Vector<double>& zeta, 
             Vector<double>& f);

 /// \short Boundary of top left box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_up_F(const unsigned& t, const Vector<double>& zeta, 
             Vector<double>& f); 

/// \short Boundary of top left box macro element
/// zeta \f$ \in [-1,1]^2 \f$
 void r_front_L(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);
 
 /// \short Boundary of top left box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_front_R(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of top left box macro element 
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_front_D(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

 /// \short Boundary of top left box macro element
 /// zeta \f$ \in [-1,1]^2 \f$
 void r_front_U(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);
 
/// \short Boundary of top left box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
 void r_front_B(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);
 
/// \short Boundary of top left box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
 void r_front_F(const unsigned& t, const Vector<double>& zeta, 
                Vector<double>& f);

};

////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////



//=================================================================
/// Boundary of central box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_centr_L(const unsigned& t,
                                  const Vector<double>& zeta, 
                                  Vector<double>& f)
{                                                          
 f[0]=0;
 f[1]=Radius*0.25*(1.0+zeta[0]);
 f[2]=Radius*0.25*(1.0+zeta[1]);
}


//================================================================= 
///  Boundary of central box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_centr_R(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{                                                          
 f[0]=Radius*0.5;
 f[1]=Radius*0.25*(1.0+zeta[0]);
 f[2]=Radius*0.25*(1.0+zeta[1]);
}




//================================================================= 
///  Boundary of central box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_centr_D(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{                                                          
 f[0]=Radius*0.25*(1.0+zeta[0]);
 f[1]=0;
 f[2]=Radius*0.25*(1.0+zeta[1]);
}


//=================================================================
///  Boundary of central box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_centr_U(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{                                                          
 f[0]=Radius*0.25*(1.0+zeta[0]);
 f[1]=Radius*0.5;
 f[2]=Radius*0.25*(1.0+zeta[1]);
}



//=================================================================
///  Boundary of central box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_centr_B(const unsigned& t,
                                  const Vector<double>& zeta, 
                                  Vector<double>& f)
{                                                          
 f[0]=Radius*0.25*(1.0+zeta[0]);
 f[1]=Radius*0.25*(1.0+zeta[1]);
 f[2]=0.0;
}

//=================================================================
///  Boundary of central box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_centr_F(const unsigned& t,
                                  const Vector<double>& zeta, 
                                  Vector<double>& f)
{                                                          
 f[0]=Radius*0.25*(1.0+zeta[0]);
 f[1]=Radius*0.25*(1.0+zeta[1]);
 f[2]=Radius*0.5;
}



//=================================================================
///  Boundary of right box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_right_L(const unsigned& t,
                                  const Vector<double>& zeta, 
                                  Vector<double>& f)
{
 r_centr_R(t,zeta,f);
}


//=================================================================
///  Boundary of right box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_right_R(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{ 
 double k0=0.5*(1.0+zeta[0]);
 double k1=0.5*(1.0+zeta[1]);
 Vector<double> p(3);
 Vector<double> point1(3);
 Vector<double> point2(3);
 
 point1[0]=Radius-0.5*Radius*k0;
 point1[1]=0.5*Radius*k0;
 point1[2]=0.0;
 point2[0]=0.5*Radius-k0*Radius/6.0;
 point2[1]=k0*Radius/3.0;
 point2[2]=0.5*Radius-k0*Radius/6.0;
 
 for(unsigned i=0; i<3; i++)
  {
   p[i]=point1[i]+k1*(point2[i]-point1[i]);
  }
 double alpha=Radius/std::sqrt(p[0]*p[0]+p[1]*p[1]+p[2]*p[2]);
 
 for(unsigned i=0; i<3; i++)
  {
   f[i]=alpha*p[i];
  }
 
}

//=================================================================
///  Boundary of  right box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_right_D(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{ 
// position vector on sphere   
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=-1.0;
 temp_zeta[1]=zeta[1];
 r_right_R(t,temp_zeta,on_sphere);
 
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.5*Radius;
 on_center[1]=0.0;
 on_center[2]=0.5*Radius*0.5*(zeta[1]+1.0);   
 // strait line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[0]+1.0)*(on_sphere[i]-on_center[i]);
  }
}


//=================================================================
///  Boundary of right box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_right_U(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{ 
 // position vector on sphere
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=1.0;
 temp_zeta[1]=zeta[1];
 r_right_R(t,temp_zeta,on_sphere);
 
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.5*Radius;
 on_center[1]=0.5*Radius;
 on_center[2]=0.5*Radius*0.5*(zeta[1]+1.0);   
 // strait line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[0]+1.0)*(on_sphere[i]-on_center[i]);
  }
}

//=================================================================
///  Boundary of  right box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_right_B(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{
 // position vector on sphere
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=zeta[1];
 temp_zeta[1]=-1.0;
 r_right_R(t,temp_zeta,on_sphere);
 
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.5*Radius;
 on_center[1]=0.5*Radius*0.5*(zeta[1]+1.0);
 on_center[2]=0.0;   
 // strait line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[0]+1.0)*(on_sphere[i]-on_center[i]);
  }
}


//=================================================================
///  Boundary of  right box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_right_F(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{

 // position vector on sphere
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=zeta[1];
 temp_zeta[1]=1.0;
 r_right_R(t,temp_zeta,on_sphere);
      
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.5*Radius;
 on_center[1]=0.5*Radius*0.5*(zeta[1]+1.0);
 on_center[2]=0.5*Radius;   
 // strait line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[0]+1.0)*(on_sphere[i]-on_center[i]);
  }
}

//=================================================================
///  Boundary of top left box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_up_L(const unsigned& t,
                               const Vector<double>& zeta, 
                                Vector<double>& f)
{
 // position vector on sphere
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=-1.0;
 temp_zeta[1]=zeta[1];
 r_up_U(t,temp_zeta,on_sphere);
 
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.0;
 on_center[1]=0.5*Radius;
 on_center[2]=0.5*Radius*0.5*(zeta[1]+1.0);   
 // strait line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[0]+1.0)*(on_sphere[i]-on_center[i]);
  }
}


//=================================================================
///  Boundary of top left box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_up_R(const unsigned& t,
                                const Vector<double>& zeta, 
                                Vector<double>& f)
{
 r_right_U(t,zeta,f);
}


//=================================================================
///  Boundary of top left box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_up_D(const unsigned& t,
                                const Vector<double>& zeta, 
                                Vector<double>& f)
{
 r_centr_U(t,zeta,f);
}

//=================================================================
///  Boundary of top left box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_up_U(const unsigned& t,
                                const Vector<double>& zeta, 
                                Vector<double>& f)
{   

 double k0=0.5*(1.0+zeta[0]);
 double k1=0.5*(1.0+zeta[1]);
 Vector<double> p(3);
 Vector<double> point1(3);
 Vector<double> point2(3);
 
 point1[0]=0.5*Radius*k0;
 point1[1]=Radius-0.5*Radius*k0;
 point1[2]=0;
 point2[0]=k0*Radius/3.0;
 point2[1]=0.5*Radius-k0*Radius/6.0;
 point2[2]=0.5*Radius-k0*Radius/6.0;
 
 for(unsigned i=0; i<3; i++)
  {
   p[i]=point1[i]+k1*(point2[i]-point1[i]);
  }
 double alpha=Radius/std::sqrt(p[0]*p[0]+p[1]*p[1]+p[2]*p[2]);
 
 for(unsigned i=0; i<3; i++)
  {
   f[i]=alpha*p[i];
  }  
 
}

//=================================================================
///  Boundary of top left box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_up_B(const unsigned& t,
                                const Vector<double>& zeta, 
                                Vector<double>& f)
{
 // position vector on sphere
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=zeta[0];
 temp_zeta[1]=-1.0;
 r_up_U(t,temp_zeta,on_sphere);
 
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.5*Radius*0.5*(zeta[0]+1.0);
 on_center[1]=0.5*Radius;
 on_center[2]=0.0;   
 // strait line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[1]+1.0)*(on_sphere[i]-on_center[i]);
  }
}



//=================================================================
///  Boundary of top left box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_up_F(const unsigned& t,
                                const Vector<double>& zeta, 
                                Vector<double>& f)
{
 // position vector on sphere
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=zeta[0];
 temp_zeta[1]=1.0;
 r_up_U(t,temp_zeta,on_sphere);
 
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.5*Radius*0.5*(zeta[0]+1.0);
 on_center[1]=0.5*Radius;
 on_center[2]=0.5*Radius;   
 // straight line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[1]+1.0)*(on_sphere[i]-on_center[i]);
  }
}
 

//=================================================================
///  Boundary of top left box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_front_L(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{
 
 // position vector on sphere
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=-1.0;
 temp_zeta[1]=zeta[0];
 r_front_F(t,temp_zeta,on_sphere);
 
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.0;
 on_center[1]=0.5*Radius*0.5*(zeta[0]+1.0);
 on_center[2]=0.5*Radius;   
 // straight line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[1]+1.0)*(on_sphere[i]-on_center[i]);
  }
}
 

//=================================================================
///  Boundary of top left box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_front_R(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{
 Vector<double> zeta2(2);
 zeta2[0]=zeta[1];
 zeta2[1]=zeta[0];
 r_right_F(t,zeta2,f);
}
 

//=================================================================
///  Boundary of top left box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_front_D(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{

 // position vector on sphere
 Vector<double> on_sphere(3);   
 Vector<double> temp_zeta(2);
 temp_zeta[0]=zeta[0];
 temp_zeta[1]=-1.0;
 r_front_F(t,temp_zeta,on_sphere);
 
 // position vector on center box
 Vector<double> on_center(3);
 on_center[0]=0.5*Radius*0.5*(zeta[0]+1.0);
 on_center[1]=0.0;
 on_center[2]=0.5*Radius;   
 // straight line across
 for(unsigned i=0; i<3; i++)
  {
   f[i]=on_center[i]+0.5*(zeta[1]+1.0)*(on_sphere[i]-on_center[i]);
  }
}


//=================================================================
///  Boundary of top left box macro element
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_front_U(const unsigned& t,
                                  const Vector<double>& zeta, 
                                  Vector<double>& f)
{
 r_up_F(t,zeta,f);
}


//=================================================================
///  Boundary of top left box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_front_B(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{
 r_centr_F(t,zeta,f);
}


//=================================================================
/// Boundary of top left box macro element 
/// zeta \f$ \in [-1,1]^2 \f$
//=================================================================
void EighthSphereDomain::r_front_F(const unsigned& t,
                                   const Vector<double>& zeta, 
                                   Vector<double>& f)
{
 double k0=0.5*(1.0+zeta[0]);
 double k1=0.5*(1.0+zeta[1]);
 Vector<double> p(3);
 Vector<double> point1(3);
 Vector<double> point2(3);
 
 point1[0]=0.5*Radius*k0;
 point1[1]=0.0; 
 point1[2]=Radius-k0*0.5*Radius;
 point2[0]=k0*Radius/3.0; 
 point2[1]=0.5*Radius-k0*Radius/6.0; 
 point2[2]=0.5*Radius-k0*Radius/6.0;
 
 for(unsigned i=0; i<3; i++)
  {
   p[i]=point1[i]+k1*(point2[i]-point1[i]);
  }
 double alpha=Radius/std::sqrt(p[0]*p[0]+p[1]*p[1]+p[2]*p[2]);
 
 for(unsigned i=0; i<3; i++)
  {
   f[i]=alpha*p[i];
  }
}




}

#endif