Schema_Adams_Bashforth_order_3.cpp

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#include <Schema_Adams_Bashforth_order_3.h>
#include <Equation_base.h>
#include <TRUSTTrav.h>
 
Implemente_instanciable(Schema_Adams_Bashforth_order_3,"Schema_Adams_Bashforth_order_3",Schema_Adams_Bashforth_base);
// XD schema_adams_bashforth_order_3 schema_temps_base schema_adams_bashforth_order_3 INHERITS_BRACE not_set
 
Sortie& Schema_Adams_Bashforth_order_3::printOn(Sortie& s) const
{
  return  Schema_Adams_Bashforth_base::printOn(s);
}
 
Entree& Schema_Adams_Bashforth_order_3::readOn(Entree& s)
{
  return Schema_Adams_Bashforth_base::readOn(s) ;
}
 
////////////////////////////////
//                            //
// Schema characteristics     //
//                            //
////////////////////////////////
 
/*! @brief Returns the number of temporal values to keep.
 *
 * Here: n-2, n-1, n and n+1, so 4.
 *
 */
int Schema_Adams_Bashforth_order_3::nb_valeurs_temporelles() const
{
  return 4 ;
}
 
/*! @brief Returns the number of time steps strictly beyond which the Adams-Bashforth scheme is applied.
 *
 * Here: we need at least 2 past times, so 1.
 *
 */
inline int Schema_Adams_Bashforth_order_3::nb_pas_dt_seuil() const
{
  return 1 ;
}
 
/*! @brief Returns the number of past temporal values.
 *
 * Here: n-2 and n-1, so 2.
 *
 */
inline int Schema_Adams_Bashforth_order_3::nb_valeurs_passees() const
{
  return 2 ;
}
 
/////////////////////////////////////////
//                                     //
// End of schema characteristics       //
//                                     //
/////////////////////////////////////////
 
static double Ln02(const double time_n_plus_1, const double time_n, const double time_n_minus_1, const double time_n_minus_2)
{
  //Integration of first degree-2 lagrangian polynomial with Simpson's formulae
  //Ln02(time_n_minus_2) = 0
  //Ln02(time_n_minus_1) = 0
  //Ln02(time_n)         = 1
  //Integration bound : time_n and time_n_plus_1
  double result = 0.;
 
  double midpoint = (time_n_plus_1+time_n);
  midpoint *= 0.5;
 
  double scaling_coeff = (time_n_plus_1-time_n);
  scaling_coeff /= 6.;
 
  double denominator = (time_n-time_n_minus_1);
  denominator *= (time_n-time_n_minus_2);
  denominator = 1./denominator;
 
  double numerator = (time_n-time_n_minus_1)*(time_n-time_n_minus_2);
  numerator += 4*(midpoint-time_n_minus_1)*(midpoint-time_n_minus_2);
  numerator += (time_n_plus_1-time_n_minus_1)*(time_n_plus_1-time_n_minus_2);
 
  result = scaling_coeff * numerator * denominator;
  return result;
}
 
static double Ln12(const double time_n_plus_1, const double time_n, const double time_n_minus_1, const double time_n_minus_2)
{
  //Integration of second degree-2 lagrangian polynomial with Simpson's formulae
  //Ln12(time_n_minus_2) = 0
  //Ln12(time_n_minus_1) = 1
  //Ln12(time_n)         = 0
  //Integration bound : time_n and time_n_plus_1
  double result = 0.;
 
  double midpoint = (time_n_plus_1+time_n);
  midpoint *= 0.5;
 
  double scaling_coeff = (time_n_plus_1-time_n);
  scaling_coeff /= 6.;
 
  double denominator = (time_n_minus_1-time_n);
  denominator *= (time_n_minus_1-time_n_minus_2);
  denominator = 1./denominator;
 
  double numerator = 0.;
  numerator += 4*(midpoint-time_n)*(midpoint-time_n_minus_2);
  numerator += (time_n_plus_1-time_n)*(time_n_plus_1-time_n_minus_2);
 
  result = scaling_coeff * numerator * denominator;
  return result;
}
 
void Schema_Adams_Bashforth_order_3::compute_adams_bashforth_coefficients(double time_step, const DoubleTab& times)
{
  if (nb_pas_dt()<100 && limpr() && facteur_securite_pas()==1.0)
    {
      Cerr << finl;
      Cerr << "********************* Warning (printed only on the first 100 time steps) **********************"<< finl;
      Cerr << "The Adams Bashforth order 3 scheme is recommended with a facsec lower than 1.0 for example 0.5."<< finl;
      Cerr << "***********************************************************************************************"<< finl;
      // See $TRUST_ROOT/tests/Reference/Schema_Adams_Bashforth_order_3 test case.
    }
 
  assert(times.size_array() == 4); //2 past times, present and future times, stored in ascending order inside "times" table
 
  if (coefficients().size_array() != 3)
    {
      coefficients().resize(3,RESIZE_OPTIONS::NOCOPY_NOINIT);
    }
 
  double inv_time_step  = 1./time_step;
  double time_n_minus_2 = times[0];
  double time_n_minus_1 = times[1];
  double time_n         = times[2];
  double time_n_plus_1  = times[3];
 
  coefficients()[2] = Ln02(time_n_plus_1,time_n,time_n_minus_1,time_n_minus_2) * inv_time_step;
  coefficients()[1] = Ln12(time_n_plus_1,time_n,time_n_minus_1,time_n_minus_2) * inv_time_step;
  coefficients()[0] = 1-coefficients()[2]-coefficients()[1];
}