Tporoelasticity_elements.cc

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 "Tporoelasticity_elements.h"

namespace oomph
{
 /// Lowest-order Raviart-Thomas based Darcy equation element

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

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

 /// Return the total number of computational basis functions for u
 template<>
 unsigned TPoroelasticityElement<0>::nq_basis() const
 {
  return 3;
 }

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

 /// Returns the local form of the q basis at local coordinate s
 template<>
 void TPoroelasticityElement<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);
 }

 /// Returns the local form of the q basis and dbasis/ds at local coordinate s
 template<>
 void TPoroelasticityElement<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);
 }

 /// Returns the number of gauss points along each edge of the element
 template<>
 unsigned TPoroelasticityElement<0>::nedge_gauss_point() const
 {
  return 1;
 }

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

 /// Return the pressure basis
 template<>
 void TPoroelasticityElement<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 TPoroelasticityElement<0>::Initial_Nvalue[6] =
  //{0,0,0,1,1,1};
  {2,2,2,3,3,3};

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

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

 /// Second-order Raviart-Thomas based Darcy equation element

 /// \short Constructor. Order 1 elements have 3 pressure dofs and 2 internal
 /// velocity dofs
 template<>
 TPoroelasticityElement<1>::TPoroelasticityElement() :
  TElement<2,3>(), PoroelasticityEquations<2>(), 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<>
 TPoroelasticityElement<1>::~TPoroelasticityElement()
 {
 }

 /// Return the total number of computational basis functions for u
 template<>
 unsigned TPoroelasticityElement<1>::nq_basis() const
 {
  return 8;
 }

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

 /// Returns the local form of the q basis at local coordinate s
 template<>
 void TPoroelasticityElement<1>::get_q_basis_local(const Vector<double> &s,
                                                   Shape &q_basis) const
 {
  // RT_1 basis functions

  double g1,g2;

  g1=edge_gauss_point(0,0);
  g2=edge_gauss_point(0,1);
  q_basis(0,0) = Sign_edge[0]*std::sqrt(2)*s[0]*(s[1]-g2)/(g1-g2);
  q_basis(0,1) = Sign_edge[0]*std::sqrt(2)*s[1]*(s[1]-g2)/(g1-g2);

  q_basis(1,0) = Sign_edge[0]*std::sqrt(2)*s[0]*(s[1]-g1)/(g2-g1);
  q_basis(1,1) = Sign_edge[0]*std::sqrt(2)*s[1]*(s[1]-g1)/(g2-g1);

  g1=edge_gauss_point(1,0);
  g2=edge_gauss_point(1,1);
  q_basis(2,0) = Sign_edge[1]*(s[0]-1)*(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)*(s[1]-g2)/(g1-g2);
  q_basis(3,1) = Sign_edge[1]*s[1]*(s[1]-g2)/(g1-g2);

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

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

  q_basis(7,0) = s[0]*(s[0]-1);
  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 TPoroelasticityElement<1>::get_div_q_basis_local(
   const Vector<double> &s,
   Shape &div_q_basis_ds) const
 {
  double g1,g2;

  g1=edge_gauss_point(0,0);
  g2=edge_gauss_point(0,1);
  div_q_basis_ds(0) = Sign_edge[0]*std::sqrt(2)*(3*s[1]-2*g2)/(g1-g2);
  div_q_basis_ds(1) = Sign_edge[0]*std::sqrt(2)*(2*g1-3*s[1])/(g1-g2);

  g1=edge_gauss_point(1,0);
  g2=edge_gauss_point(1,1);
  div_q_basis_ds(2) = Sign_edge[1]*(2*g1-3*s[1])/(g1-g2);
  div_q_basis_ds(3) = Sign_edge[1]*(3*s[1]-2*g2)/(g1-g2);

  g1=edge_gauss_point(2,0);
  g2=edge_gauss_point(2,1);
  div_q_basis_ds(4) = Sign_edge[2]*(3*s[0]-2*g2)/(g1-g2);
  div_q_basis_ds(5) = Sign_edge[2]*(2*g1-3*s[0])/(g1-g2);

  div_q_basis_ds(6) = 3*s[1]-1;
  div_q_basis_ds(7) = 3*s[0]-1;

  // 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 gauss points along each edge of the element
 template<>
 unsigned TPoroelasticityElement<1>::nedge_gauss_point() const
 {
  return 2;
 }

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

 /// Return the pressure basis
 template<>
 void TPoroelasticityElement<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 TPoroelasticityElement<1>::Initial_Nvalue[6] =
  {2,2,2,4,4,4};

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

 /// The points along each edge where the fluxes are taken to be
 template<>
 const double TPoroelasticityElement<1>::Gauss_point[2] =
  {0.5-std::sqrt(3.0)/6.0,
   0.5+std::sqrt(3.0)/6.0};

 // Force building of templates
 template class TPoroelasticityElement<0>;
 template class TPoroelasticityElement<1>;

} // End of oomph namespace