time_harmonic_linear_elasticity_elements.h

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//LIC// ====================================================================
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//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// 
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//LIC//====================================================================
//Header file for general linear elasticity elements

//Include guards to prevent multiple inclusion of the header
#ifndef OOMPH_TIME_HARMONIC_LINEAR_ELASTICITY_ELEMENTS_HEADER
#define OOMPH_TIME_HARMONIC_LINEAR_ELASTICITY_ELEMENTS_HEADER

// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
  #include <oomph-lib-config.h>
#endif


#ifdef OOMPH_HAS_MPI
#include "mpi.h"
#endif

#include<complex>


//OOMPH-LIB headers
#include "../generic/Qelements.h"
#include "../generic/mesh.h"
#include "../generic/hermite_elements.h"
#include "./time_harmonic_elasticity_tensor.h"
#include "../generic/projection.h"

namespace oomph
{
//=======================================================================
/// A base class for elements that solve the equations of time-harmonic linear 
/// elasticity in Cartesian coordinates.
/// Combines a few generic functions that are shared by 
/// TimeHarmonicLinearElasticityEquations
/// and TimeHarmonicLinearElasticityEquationsWithPressure (Note: The latter
/// don't exist yet but will be written as soon as somebody needs them...)
//=======================================================================
 template <unsigned DIM>
  class TimeHarmonicLinearElasticityEquationsBase : public virtual FiniteElement
  {
    public:
   
   /// \short Return the index at which the i-th real or imag unknown 
   /// displacement component is stored. The default value is appropriate for
   /// single-physics problems: 
   virtual inline std::complex<unsigned> 
    u_index_time_harmonic_linear_elasticity(const unsigned i) const
    {
     return std::complex<unsigned>(i,i+DIM);
    }
   
   /// Compute vector of FE interpolated displacement u at local coordinate s
   void interpolated_u_time_harmonic_linear_elasticity(
    const Vector<double> &s, 
    Vector<std::complex<double> >& disp) 
    const
   {
    //Find number of nodes
    unsigned n_node = nnode();
    
    //Local shape function
    Shape psi(n_node);
    
    //Find values of shape function
    shape(s,psi);
    
    for (unsigned i=0;i<DIM;i++)
     {
      //Index at which the nodal value is stored
      std::complex<unsigned> u_nodal_index = 
       u_index_time_harmonic_linear_elasticity(i);
      
      //Initialise value of u
      disp[i] = std::complex<double>(0.0,0.0);
      
      //Loop over the local nodes and sum
      for(unsigned l=0;l<n_node;l++) 
       {
        const std::complex<double> u_value(
         nodal_value(l,u_nodal_index.real()),
         nodal_value(l,u_nodal_index.imag()));
        
        disp[i] += u_value*psi[l];
       }
     }
   }
   
   /// Return FE interpolated displacement u[i] at local coordinate s
   std::complex<double> interpolated_u_time_harmonic_linear_elasticity(
    const Vector<double> &s, 
    const unsigned &i) const
    {
     //Find number of nodes
     unsigned n_node = nnode();
     
     //Local shape function
     Shape psi(n_node);
     
     //Find values of shape function
     shape(s,psi);
     
     //Get nodal index at which i-th velocity is stored
     std::complex<unsigned> u_nodal_index = 
      u_index_time_harmonic_linear_elasticity(i);
     
     //Initialise value of u
     std::complex<double> interpolated_u(0.0,0.0);
     
     //Loop over the local nodes and sum
     for(unsigned l=0;l<n_node;l++) 
      {
       const std::complex<double> u_value(
        nodal_value(l,u_nodal_index.real()),
        nodal_value(l,u_nodal_index.imag()));
 
       interpolated_u += u_value*psi[l];
      }
     
     return(interpolated_u);
    }
   
   
   /// \short Function pointer to function that specifies the body force
   /// as a function of the Cartesian coordinates and time FCT(t,x,b) -- 
   /// x and b are  Vectors! 
   typedef void (*BodyForceFctPt)(const double& t,
                                  const Vector<double>& x,
                                  Vector<std::complex<double> >& b);
   
   /// \short Constructor: Set null pointers for constitutive law and for
   /// isotropic growth function. Set physical parameter values to 
   /// default values, and set body force to zero.
    TimeHarmonicLinearElasticityEquationsBase() : Elasticity_tensor_pt(0),
    Omega_sq_pt(&Default_omega_sq_value), Body_force_fct_pt(0) {}
   
   /// Return the pointer to the elasticity_tensor
   TimeHarmonicElasticityTensor* &elasticity_tensor_pt()
    {return Elasticity_tensor_pt;}
   
   /// Access function to the entries in the elasticity tensor
   inline double E(const unsigned &i,const unsigned &j,
                   const unsigned &k, const unsigned &l) const
   {
    return (*Elasticity_tensor_pt)(i,j,k,l);
   }
   
   ///Access function for square of non-dim frequency
   const double& omega_sq() const {return *Omega_sq_pt;}
   
   /// Access function for square of non-dim frequency
   double* &omega_sq_pt() {return Omega_sq_pt;}
   
   /// Access function: Pointer to body force function
   BodyForceFctPt& body_force_fct_pt() {return Body_force_fct_pt;}
   
   /// Access function: Pointer to body force function (const version)
   BodyForceFctPt body_force_fct_pt() const {return Body_force_fct_pt;}
   
   /// \short Return the Cauchy stress tensor, as calculated
   /// from the elasticity tensor at specified local coordinate
   /// Virtual so separaete versions can (and must!) be provided
   /// for displacement and pressure-displacement formulations.
   virtual void get_stress(const Vector<double> &s, 
                           DenseMatrix<std::complex<double> > &sigma) const=0;
   
   /// \short Return the strain tensor
   void get_strain(const Vector<double> &s, 
                   DenseMatrix<std::complex<double> >&strain) const;
   
   /// \short Evaluate body force at Eulerian coordinate x at present time
   /// (returns zero vector if no body force function pointer has been set)
   inline void body_force(const Vector<double>& x, 
                          Vector<std::complex<double> >& b) const
   {
    //If no function has been set, return zero vector
    if(Body_force_fct_pt==0)
     {
      // Get spatial dimension of element
      unsigned n=dim();
      for (unsigned i=0;i<n;i++)
       {
        b[i] = std::complex<double>(0.0,0.0);
       }
     }
    else
     {
       // Get time from timestepper of first node (note that this must
       // work -- body force only makes sense for elements that can be
       // deformed and thefore store displacements (at their nodes)
       double time=node_pt(0)->time_stepper_pt()->time_pt()->time();
       
       // Get body force
       (*Body_force_fct_pt)(time,x,b);
     }
   }
   
   /// \short The number of "DOF types" that degrees of freedom in this element
   /// are sub-divided into: for now lump them all into one DOF.
   /// Can be adjusted later
   unsigned ndof_types() const
   {
    return 1;
   }
   
   /// \short Create a list of pairs for all unknowns in this element,
   /// so that the first entry in each pair contains the global equation
   /// number of the unknown, while the second one contains the number
   /// of the "DOF type" that this unknown is associated with.
   /// (Function can obviously only be called if the equation numbering
   /// scheme has been set up.) 
   void get_dof_numbers_for_unknowns(
    std::list<std::pair<unsigned long,unsigned> >& dof_lookup_list) const
   {

    // temporary pair (used to store DOF lookup prior to being added 
    // to list)
    std::pair<unsigned long,unsigned> dof_lookup;
    
    // number of nodes
    const unsigned n_node = this->nnode();
    
    //Integer storage for local unknown
    int local_unknown=0;
    
    //Loop over the nodes
    for(unsigned n=0;n<n_node;n++)
     {
      //Loop over dimension (real and imag)
      for(unsigned i=0;i<2*DIM;i++)
       {
        //If the variable is free
        local_unknown = nodal_local_eqn(n,i);
        
        // ignore pinned values
        if (local_unknown >= 0)
         {
          // store DOF lookup in temporary pair: First entry in pair
          // is global equation number; second entry is DOF type
          dof_lookup.first = this->eqn_number(local_unknown);
          dof_lookup.second = 0;
          
          // add to list
          dof_lookup_list.push_front(dof_lookup);
          
         }
       }
     }
   }
   
   
    protected:
   
   /// Pointer to the elasticity tensor
   TimeHarmonicElasticityTensor *Elasticity_tensor_pt;
   
   /// Square of nondim frequency
   double* Omega_sq_pt;

   /// Pointer to body force function
   BodyForceFctPt Body_force_fct_pt;
   
   /// Static default value for square of frequency 
   static double Default_omega_sq_value;
   
  };
 
 
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////


//=======================================================================
/// A class for elements that solve the equations of linear elasticity
/// in cartesian coordinates.
//=======================================================================
 template <unsigned DIM>
  class TimeHarmonicLinearElasticityEquations : 
  public TimeHarmonicLinearElasticityEquationsBase<DIM>
  {
    public:
   
   /// \short  Constructor
   TimeHarmonicLinearElasticityEquations() {}
   
   /// Number of values required at node n.
   unsigned required_nvalue(const unsigned &n) const {return 2*DIM;}
   
   /// \short Return the residuals for the solid equations (the discretised
   /// principle of virtual displacements)
   void fill_in_contribution_to_residuals(Vector<double> &residuals)
   {
    fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity(
     residuals,GeneralisedElement::Dummy_matrix,0);
   }
   
   
   /// The jacobian is calculated by finite differences by default,
   /// We need only to take finite differences w.r.t. positional variables
   /// For this element
   void fill_in_contribution_to_jacobian(Vector<double> &residuals,
                                         DenseMatrix<double> &jacobian)
   {
    //Add the contribution to the residuals
    this->fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity(
     residuals,jacobian,1);
   }
   
   /// \short Return the Cauchy stress tensor, as calculated
   /// from the elasticity tensor at specified local coordinate
   void get_stress(const Vector<double> &s, 
                   DenseMatrix<std::complex<double> >&sigma) const;
   
   ///Output exact solution x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]
   void output_fct(std::ostream &outfile, 
                   const unsigned &nplot, 
                   FiniteElement::SteadyExactSolutionFctPt exact_soln_pt);
   
   /// Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]
   void output(std::ostream &outfile) 
   {
    unsigned n_plot=5;
    output(outfile,n_plot);
   }
   
   /// Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]
   void output(std::ostream &outfile, const unsigned &n_plot);
   
   
   /// C-style output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]
   void output(FILE* file_pt) 
   {
    unsigned n_plot=5;
    output(file_pt,n_plot);
   }
   
   /// Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]
   void output(FILE* file_pt, const unsigned &n_plot);
   
   
   /// \short Compute norm of solution: square of the L2 norm
   void compute_norm(double& norm);

    private:
   
   /// \short Private helper function to compute residuals and (if requested
   /// via flag) also the Jacobian matrix.
   virtual void fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity(
    Vector<double> &residuals,DenseMatrix<double> &jacobian,unsigned flag);
   
  }; 
 

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


//===========================================================================
/// An Element that solves the equations of linear elasticity 
/// in Cartesian coordinates, using QElements for the geometry
//============================================================================
 template<unsigned DIM, unsigned NNODE_1D>
  class QTimeHarmonicLinearElasticityElement : public virtual QElement<DIM,NNODE_1D>,
  public virtual TimeHarmonicLinearElasticityEquations<DIM>
  {
    public:
   
   /// Constructor
    QTimeHarmonicLinearElasticityElement() : QElement<DIM,NNODE_1D>(), 
    TimeHarmonicLinearElasticityEquations<DIM>() { }
   
   /// Output function
   void output(std::ostream &outfile) 
   {TimeHarmonicLinearElasticityEquations<DIM>::output(outfile);}
   
   /// Output function
   void output(std::ostream &outfile, const unsigned &n_plot)
   {TimeHarmonicLinearElasticityEquations<DIM>::output(outfile,n_plot);}
   
   
   /// C-style output function
   void output(FILE* file_pt) 
   {TimeHarmonicLinearElasticityEquations<DIM>::output(file_pt);}
   
   /// C-style output function
   void output(FILE* file_pt, const unsigned &n_plot)
   {TimeHarmonicLinearElasticityEquations<DIM>::output(file_pt,n_plot);}
   
  };
 

//============================================================================
/// FaceGeometry of a linear 2D QTimeHarmonicLinearElasticityElement element
//============================================================================
 template<>
  class FaceGeometry<QTimeHarmonicLinearElasticityElement<2,2> > :
 public virtual QElement<1,2>
  {
    public:
   /// Constructor must call the constructor of the underlying solid element
    FaceGeometry() : QElement<1,2>() {}
  };
 
 
 
//============================================================================
/// FaceGeometry of a quadratic 2D QTimeHarmonicLinearElasticityElement element
//============================================================================
 template<>
  class FaceGeometry<QTimeHarmonicLinearElasticityElement<2,3> > :
 public virtual QElement<1,3>
  {
    public:
   /// Constructor must call the constructor of the underlying element
    FaceGeometry() : QElement<1,3>() {}
  };
 
 
 
//============================================================================
/// FaceGeometry of a cubic 2D QTimeHarmonicLinearElasticityElement element
//============================================================================
 template<>
  class FaceGeometry<QTimeHarmonicLinearElasticityElement<2,4> > :
  public virtual QElement<1,4>
  {
    public:
   /// Constructor must call the constructor of the underlying element
    FaceGeometry() : QElement<1,4>() {}
  };
  
  
//============================================================================
/// FaceGeometry of a linear 3D QTimeHarmonicLinearElasticityElement element
//============================================================================
  template<>
   class FaceGeometry<QTimeHarmonicLinearElasticityElement<3,2> > :
  public virtual QElement<2,2>
   {
     public:
    /// Constructor must call the constructor of the underlying element
     FaceGeometry() : QElement<2,2>() {}
   };
  
//============================================================================
/// FaceGeometry of a quadratic 3D QTimeHarmonicLinearElasticityElement element
//============================================================================
  template<>
   class FaceGeometry<QTimeHarmonicLinearElasticityElement<3,3> > :
  public virtual QElement<2,3>
   {
     public:
    /// Constructor must call the constructor of the underlying element
     FaceGeometry() : QElement<2,3>() {}
   };
  
  
//============================================================================
/// FaceGeometry of a cubic 3D QTimeHarmonicLinearElasticityElement element
//============================================================================
  template<>
   class FaceGeometry<QTimeHarmonicLinearElasticityElement<3,4> > :
  public virtual QElement<2,4>
   {
     public:
    /// Constructor must call the constructor of the underlying element
     FaceGeometry() : QElement<2,4>() {}
   };

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


//==========================================================
/// Time-harmonic linear elasticity upgraded to become projectable
//==========================================================
 template<class TIME_HARMONIC_LINEAR_ELAST_ELEMENT>
 class ProjectableTimeHarmonicLinearElasticityElement : 
  public virtual ProjectableElement<TIME_HARMONIC_LINEAR_ELAST_ELEMENT>
 {
  
 public:
  
  /// \short Constructor [this was only required explicitly
  /// from gcc 4.5.2 onwards...]
  ProjectableTimeHarmonicLinearElasticityElement(){}
  
  
  /// \short Specify the values associated with field fld. 
  /// The information is returned in a vector of pairs which comprise 
  /// the Data object and the value within it, that correspond to field fld. 
  /// In the underlying time-harmonic linear elasticity elements the 
  /// real and complex parts of the displacements are stored
  /// at the nodal values
  Vector<std::pair<Data*,unsigned> > data_values_of_field(const unsigned& fld)
   {   
    // Create the vector
    Vector<std::pair<Data*,unsigned> > data_values;
    
    // Loop over all nodes and extract the fld-th nodal value
    unsigned nnod=this->nnode();
    for (unsigned j=0;j<nnod;j++)
     {
      // Add the data value associated with the displacement components
      data_values.push_back(std::make_pair(this->node_pt(j),fld));
     }
    
    // Return the vector
    return data_values;
    
   }

  /// \short Number of fields to be projected: 2*dim, corresponding to 
  /// real and imag parts of the displacement components
  unsigned nfields_for_projection()
   {
    return 2*this->dim();
   }
  
  /// \short Number of history values to be stored for fld-th field. 
  /// (includes present value!)
  unsigned nhistory_values_for_projection(const unsigned &fld)
   {
#ifdef PARANOID
    if (fld>3)
     {
      std::stringstream error_stream;
      error_stream 
       << "Elements only store four fields so fld can't be"
       << " " << fld << std::endl;
      throw OomphLibError(
       error_stream.str(),
       OOMPH_CURRENT_FUNCTION,
       OOMPH_EXCEPTION_LOCATION);
     }
#endif
   return this->node_pt(0)->ntstorage();   
   }
  
  ///\short Number of positional history values: Read out from
  /// positional timestepper 
  /// (Note: count includes current value!)
  unsigned nhistory_values_for_coordinate_projection()
   {
    return this->node_pt(0)->position_time_stepper_pt()->ntstorage();
   }
  
  /// \short Return Jacobian of mapping and shape functions of field fld
  /// at local coordinate s
  double jacobian_and_shape_of_field(const unsigned &fld, 
                                     const Vector<double> &s, 
                                     Shape &psi)
   {
    unsigned n_dim=this->dim();
    unsigned n_node=this->nnode();
    DShape dpsidx(n_node,n_dim);
        
    // Call the derivatives of the shape functions and return
    // the Jacobian
    return this->dshape_eulerian(s,psi,dpsidx);
   }
  


  /// \short Return interpolated field fld at local coordinate s, at time level
  /// t (t=0: present; t>0: history values)
  double get_field(const unsigned &t, 
                   const unsigned &fld,
                   const Vector<double>& s)
   {
    unsigned n_node=this->nnode();

#ifdef PARANOID
    unsigned n_dim=this->node_pt(0)->ndim();
#endif
    
    //Local shape function
    Shape psi(n_node);
    
    //Find values of shape function
    this->shape(s,psi);
    
    //Initialise value of u
    double interpolated_u = 0.0;
    
    //Sum over the local nodes at that time
    for(unsigned l=0;l<n_node;l++) 
     {
#ifdef PARANOID
      unsigned nvalue=this->node_pt(l)->nvalue();
      if (nvalue!=2*n_dim)
       {        
        std::stringstream error_stream;
        error_stream 
         << "Current implementation only works for non-resized nodes\n"
         << "but nvalue= " << nvalue << "!= 2 dim = " << 2*n_dim << std::endl;
        throw OomphLibError(
         error_stream.str(),
         OOMPH_CURRENT_FUNCTION,
         OOMPH_EXCEPTION_LOCATION);
       }
#endif
      interpolated_u += this->nodal_value(t,l,fld)*psi[l];
     }
    return interpolated_u;     
   }
  
 
  ///Return number of values in field fld
  unsigned nvalue_of_field(const unsigned &fld)
   {
    return this->nnode();
   }
  
  
  ///Return local equation number of value j in field fld.
  int local_equation(const unsigned &fld,
                     const unsigned &j)
   {
#ifdef PARANOID
    unsigned n_dim=this->node_pt(0)->ndim();
    unsigned nvalue=this->node_pt(j)->nvalue();
    if (nvalue!=2*n_dim)
     {        
      std::stringstream error_stream;
      error_stream 
       << "Current implementation only works for non-resized nodes\n"
       << "but nvalue= " << nvalue << "!= 2 dim = " << 2*n_dim << std::endl;
      throw OomphLibError(
         error_stream.str(),
         OOMPH_CURRENT_FUNCTION,
         OOMPH_EXCEPTION_LOCATION);
     }
#endif
    return this->nodal_local_eqn(j,fld);
   }

  
 };


//=======================================================================
/// Face geometry for element is the same as that for the underlying
/// wrapped element
//=======================================================================
 template<class ELEMENT>
 class FaceGeometry<ProjectableTimeHarmonicLinearElasticityElement<ELEMENT> > 
  : public virtual FaceGeometry<ELEMENT>
 {
 public:
  FaceGeometry() : FaceGeometry<ELEMENT>() {}
 };


//=======================================================================
/// Face geometry of the Face Geometry for element is the same as 
/// that for the underlying wrapped element
//=======================================================================
 template<class ELEMENT>
 class FaceGeometry<FaceGeometry<ProjectableTimeHarmonicLinearElasticityElement<ELEMENT> > >
  : public virtual FaceGeometry<FaceGeometry<ELEMENT> >
 {
 public:
  FaceGeometry() : FaceGeometry<FaceGeometry<ELEMENT> >() {}
 };


}

#endif