Taxisym_poroelasticity_elements.cc

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//LIC// ====================================================================
//LIC// This file forms part of oomph-lib, the object-oriented, 
//LIC// multi-physics finite-element library, available 
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//LIC// 
//LIC//    Version 1.0; svn revision $LastChangedRevision$
//LIC//
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//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
//LIC// This library is free software; you can redistribute it and/or
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//LIC//====================================================================
#include "Taxisym_poroelasticity_elements.h"

namespace oomph
{

 //////////////////////////////////////////////////////////////////////////////
 //////////////////////////////////////////////////////////////////////////////
 /// Lowest-order Raviart-Thomas based Darcy/axisym lin elast equation element
 //////////////////////////////////////////////////////////////////////////////
 //////////////////////////////////////////////////////////////////////////////

 //==========================================================================
 /// \short Constructor. Order 0 elements have 1 pressure dof and no internal
 /// flux dofs
 //==========================================================================
 template<>
 TAxisymmetricPoroelasticityElement<0>::TAxisymmetricPoroelasticityElement() :
  TElement<2,3>(),
  AxisymmetricPoroelasticityEquations(),
  Sign_edge(3,1)
 {
  P_internal_data_index=this->add_internal_data(new Data(1));
 }

 //==========================================================================
 /// Destructor
 //==========================================================================
 template<>
 TAxisymmetricPoroelasticityElement<0>::~TAxisymmetricPoroelasticityElement()
 {
 }

 //==========================================================================
 /// Return the number of edge basis functions for flux q
 //==========================================================================
 template<>
 unsigned TAxisymmetricPoroelasticityElement<0>::nq_basis_edge() const
 {
  return 3;
 }

 //==========================================================================
 /// Return the number of internal basis functions for flux q
 //==========================================================================
 template<>
 unsigned TAxisymmetricPoroelasticityElement<0>::nq_basis_internal() const
 {
  return 0;
 }

 //==========================================================================
 /// Compute the local form of the q basis at local coordinate s
 //==========================================================================
 template<>
 void TAxisymmetricPoroelasticityElement<0>::get_q_basis_local(
   const Vector<double> &s,
   Shape &q_basis) const
 {
  // RT_0 basis functions
  q_basis(0,0) = Sign_edge[0]*std::sqrt(2)*s[0];
  q_basis(0,1) = Sign_edge[0]*std::sqrt(2)*s[1];

  q_basis(1,0) = Sign_edge[1]*(s[0]-1);
  q_basis(1,1) = Sign_edge[1]*s[1];

  q_basis(2,0) = Sign_edge[2]*s[0];
  q_basis(2,1) = Sign_edge[2]*(s[1]-1);
 }

 //===========================================================================
 /// Compute the local form of the q basis and dbasis/ds at local coordinate s
 //==========================================================================
 template<>
 void TAxisymmetricPoroelasticityElement<0>::get_div_q_basis_local(
   const Vector<double> &s,
   Shape &div_q_basis_ds) const
 {
  div_q_basis_ds(0) = Sign_edge[0]*2*std::sqrt(2);
  div_q_basis_ds(1) = Sign_edge[1]*2;
  div_q_basis_ds(2) = Sign_edge[2]*2;

  // Scale the basis by the ratio of the length of the edge to the length of
  // the corresponding edge on the reference element
  scale_basis(div_q_basis_ds);
 }

 //==========================================================================
 /// Return the number of flux_interpolation points along each 
 /// edge of the element
 //==========================================================================
 template<>
 unsigned TAxisymmetricPoroelasticityElement<0>::
 nedge_flux_interpolation_point() const
 {
  return 1;
 }

 //==========================================================================
 /// Return the total number of pressure basis functions
 //==========================================================================
 template<>
 unsigned TAxisymmetricPoroelasticityElement<0>::np_basis() const
 {
  return 1;
 }

 //==========================================================================
 /// Return the pressure basis
 //==========================================================================
 template<>
 void TAxisymmetricPoroelasticityElement<0>::get_p_basis(
   const Vector<double> &s,
   Shape &p_basis) const
 {
  p_basis(0) = 1.0;
 }

 //==========================================================================
 /// The number of values stored at each node
 //==========================================================================
 template<>
 const unsigned TAxisymmetricPoroelasticityElement<0>::Initial_Nvalue[6] =
  {2,2,2,3,3,3};


//===========================================================================
  ///  Face index associated with edge flux degree of freedom
//===========================================================================
 template<>
 const unsigned TAxisymmetricPoroelasticityElement<0>::
 Face_index_of_edge_flux[3] = {2,0,1};

 //==========================================================================
 /// Conversion scheme from an edge degree of freedom to the node it's stored
 /// at
 //==========================================================================
 template<>
 const unsigned TAxisymmetricPoroelasticityElement<0>::Q_edge_conv[3] = {3,4,5};


 //==========================================================================
 /// The points along each edge where the fluxes are taken to be
 //==========================================================================
 template<>
 const double TAxisymmetricPoroelasticityElement<0>::
 Flux_interpolation_point[1] = {0.5};



///////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////
 /// Second-orderRaviart-Thomas based Darcy/axisym lin elast equation element
///////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////

 //==========================================================================
 /// \short Constructor. Order 1 elements have 3 pressure dofs and 2 internal
 /// velocity dofs
 //==========================================================================
 template<>
 TAxisymmetricPoroelasticityElement<1>::TAxisymmetricPoroelasticityElement() :
  TElement<2,3>(),
  AxisymmetricPoroelasticityEquations(),
  Sign_edge(3,1)
 {
  // RT_1 elements have 2 internal degrees of freedom for u, and 3 for p
  Q_internal_data_index=this->add_internal_data(new Data(2));
  P_internal_data_index=this->add_internal_data(new Data(3));
 }

 //==========================================================================
 /// Destructor
 //==========================================================================
 template<>
 TAxisymmetricPoroelasticityElement<1>::~TAxisymmetricPoroelasticityElement()
 {}

 //==========================================================================
 /// Return the number of edge basis functions for flux q
 //==========================================================================
 template<>
 unsigned TAxisymmetricPoroelasticityElement<1>::nq_basis_edge() const
 {
  return 6;
 }

 //==========================================================================
 /// Return the number of internal basis functions for flux q
 //==========================================================================
 template<>
 unsigned TAxisymmetricPoroelasticityElement<1>::nq_basis_internal() const
 {
  return 2;
 }

 //==========================================================================
 /// Returns the local form of the q basis at local coordinate s
 //==========================================================================
 template<>
 void TAxisymmetricPoroelasticityElement<1>::get_q_basis_local(
   const Vector<double> &s,
   Shape &q_basis) const
 {
  // RT_1 basis functions
  Vector<double> g1_vect,g2_vect;
  g1_vect=edge_flux_interpolation_point(0,0);
  g2_vect=edge_flux_interpolation_point(0,1);
  double g1=g1_vect[0];
  double g2=g2_vect[0];

  q_basis(0,0) = Sign_edge[0]*std::sqrt(2.0)*s[0]*(s[1]-g2)/(g1-g2);
  q_basis(0,1) = Sign_edge[0]*std::sqrt(2.0)*s[1]*(s[1]-g2)/(g1-g2);

  q_basis(1,0) = Sign_edge[0]*std::sqrt(2.0)*s[0]*(s[1]-g1)/(g2-g1);
  q_basis(1,1) = Sign_edge[0]*std::sqrt(2.0)*s[1]*(s[1]-g1)/(g2-g1);

  g1_vect=edge_flux_interpolation_point(1,0);
  g2_vect=edge_flux_interpolation_point(1,1);
  g1=g1_vect[0];
  g2=g2_vect[0];
  q_basis(2,0) = Sign_edge[1]*(s[0]-1.0)*(s[1]-g1)/(g2-g1);
  q_basis(2,1) = Sign_edge[1]*s[1]*(s[1]-g1)/(g2-g1);

  q_basis(3,0) = Sign_edge[1]*(s[0]-1.0)*(s[1]-g2)/(g1-g2);
  q_basis(3,1) = Sign_edge[1]*s[1]*(s[1]-g2)/(g1-g2);

  g1_vect=edge_flux_interpolation_point(2,0);
  g2_vect=edge_flux_interpolation_point(2,1);

  g1=g1_vect[0];
  g2=g2_vect[0];
  q_basis(4,0) = Sign_edge[2]*s[0]*(s[0]-g2)/(g1-g2);
  q_basis(4,1) = Sign_edge[2]*(s[1]-1.0)*(s[0]-g2)/(g1-g2);

  q_basis(5,0) = Sign_edge[2]*s[0]*(s[0]-g1)/(g2-g1);
  q_basis(5,1) = Sign_edge[2]*(s[1]-1.0)*(s[0]-g1)/(g2-g1);

  q_basis(6,0) = s[1]*s[0];
  q_basis(6,1) = s[1]*(s[1]-1.0);

  q_basis(7,0) = s[0]*(s[0]-1.0);
  q_basis(7,1) = s[0]*s[1];
 }

 //==========================================================================
 /// Returns the local form of the q basis and dbasis/ds at local coordinate s
 //==========================================================================
 template<>
 void TAxisymmetricPoroelasticityElement<1>::get_div_q_basis_local(
   const Vector<double> &s,
   Shape &div_q_basis_ds) const
 {

  Vector<double> g1_vect,g2_vect;
  g1_vect=edge_flux_interpolation_point(0,0);
  g2_vect=edge_flux_interpolation_point(0,1);
  double g1=g1_vect[0];
  double g2=g2_vect[0];
  div_q_basis_ds(0) = Sign_edge[0]*std::sqrt(2.0)*(3.0*s[1]-2.0*g2)/(g1-g2);
  div_q_basis_ds(1) = Sign_edge[0]*std::sqrt(2.0)*(2.0*g1-3.0*s[1])/(g1-g2);

  g1_vect=edge_flux_interpolation_point(1,0);
  g2_vect=edge_flux_interpolation_point(1,1);
  g1=g1_vect[0];
  g2=g2_vect[0];
  div_q_basis_ds(2) = Sign_edge[1]*(2.0*g1-3.0*s[1])/(g1-g2);
  div_q_basis_ds(3) = Sign_edge[1]*(3.0*s[1]-2.0*g2)/(g1-g2);

  g1_vect=edge_flux_interpolation_point(2,0);
  g2_vect=edge_flux_interpolation_point(2,1);
  g1=g1_vect[0];
  g2=g2_vect[0];
  div_q_basis_ds(4) = Sign_edge[2]*(3.0*s[0]-2.0*g2)/(g1-g2);
  div_q_basis_ds(5) = Sign_edge[2]*(2.0*g1-3.0*s[0])/(g1-g2);

  div_q_basis_ds(6) = 3.0*s[1]-1.0;
  div_q_basis_ds(7) = 3.0*s[0]-1.0;
  
  // Scale the basis by the ratio of the length of the edge to the length of
  // the corresponding edge on the reference element
  scale_basis(div_q_basis_ds);
 }

 //==========================================================================
 /// Returns the number of flux_interpolation points along each edge of 
 /// the element
 //==========================================================================
 template<>
 unsigned TAxisymmetricPoroelasticityElement<1>::
 nedge_flux_interpolation_point() const
 {
  return 2;
 }

 //==========================================================================
 /// Return the total number of pressure basis functions
 //==========================================================================
 template<>
 unsigned TAxisymmetricPoroelasticityElement<1>::np_basis() const
 {
  return 3;
 }

 //==========================================================================
 /// Return the pressure basis
 //==========================================================================
 template<>
 void TAxisymmetricPoroelasticityElement<1>::get_p_basis(
   const Vector<double> &s,
   Shape &p_basis) const
 {
  p_basis(0) = 1.0;
  p_basis(1) = s[0];
  p_basis(2) = s[1];
 }

 //==========================================================================
 /// The number of values stored at each node
 //==========================================================================
 template<>
 const unsigned TAxisymmetricPoroelasticityElement<1>::Initial_Nvalue[6] =
  {2,2,2,4,4,4};


//===========================================================================
 ///  Face index associated with edge flux degree of freedom
//===========================================================================
 template<>
 const unsigned TAxisymmetricPoroelasticityElement<1>::
 Face_index_of_edge_flux[3] = {2,0,1};

 
 //==========================================================================
/// Conversion scheme from an edge degree of freedom to the node it's stored at
 //==========================================================================
 template<>
 const unsigned TAxisymmetricPoroelasticityElement<1>::Q_edge_conv[3] = {3,4,5};

 //==========================================================================
 /// The points along each edge where the fluxes are taken to be
 //==========================================================================
 template<>
 const double TAxisymmetricPoroelasticityElement<1>::
 Flux_interpolation_point[2] =
 {0.5-std::sqrt(3.0)/6.0,
  0.5+std::sqrt(3.0)/6.0};
 
 
 //==========================================================================
 // Force building of templates
 //==========================================================================
 template class TAxisymmetricPoroelasticityElement<0>;
 template class TAxisymmetricPoroelasticityElement<1>;

} // End of oomph namespace