G4BogackiShampine23.cc

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//
// G4BogackiShampine23 implementation
//
//  Bogacki-Shampine - 4 - 3(2) non-FSAL implementation
//
//  Implementation of the method proposed in the publication
//   "A 3(2) pair of Runge - Kutta formulas"
//    by P. Bogacki and L. F. Shampine,
//    Appl. Math. Lett., vol. 2, no. 4, pp. 321-325, Jan. 1989.
// 
// The Bogacki shampine method has the following Butcher's tableau
//
// 0  |
// 1/2|1/2
// 3/4|0        3/4
// 1  |2/9      1/3     4/9
// -------------------
//    |2/9      1/3     4/9    0
//    |7/24 1/4 1/3 1/8
//
// Created: Somnath Banerjee, Google Summer of Code 2015, 20 May 2015
// Supervision: John Apostolakis, CERN
// --------------------------------------------------------------------

#include "G4BogackiShampine23.hh"
#include "G4LineSection.hh"
#include "G4FieldUtils.hh"

using namespace field_utils;

G4BogackiShampine23::G4BogackiShampine23(G4EquationOfMotion* EqRhs,
                                         G4int integrationVariables)
  : G4MagIntegratorStepper(EqRhs, integrationVariables)
{
  SetIntegrationOrder(3);
  SetFSAL(true);
}

void G4BogackiShampine23::makeStep(const G4double yInput[],
                                   const G4double dydx[],
                                   const G4double hstep,
                                   G4double yOutput[],
                                   G4double* dydxOutput,
                                   G4double* yError) const
{

  G4double yTemp[G4FieldTrack::ncompSVEC];
  for(G4int i = GetNumberOfVariables(); i < GetNumberOfStateVariables(); ++i)
  { 
    yOutput[i] = yTemp[i] = yInput[i];
  }

  G4double ak2[G4FieldTrack::ncompSVEC],
           ak3[G4FieldTrack::ncompSVEC];

  const G4double b21 = 0.5 ,
                 b31 = 0., b32 = 3.0 / 4.0,
                 b41 = 2.0 / 9.0, b42 = 1.0 / 3.0, b43 = 4.0 / 9.0;

  const G4double dc1 = b41 - 7.0 / 24.0,  dc2 = b42 - 1.0 / 4.0,
                 dc3 = b43 - 1.0 / 3.0,   dc4 = - 1.0 / 8.0;
 
  // RightHandSide(yInput, dydx);
  for(G4int i = 0; i < GetNumberOfVariables(); ++i)
  {
    yTemp[i] = yInput[i] + b21 * hstep * dydx[i];
  }
    
  RightHandSide(yTemp, ak2);
  for(G4int i = 0; i < GetNumberOfVariables(); ++i)
  {
    yTemp[i] = yInput[i] + hstep * (b31 * dydx[i] + b32 * ak2[i]);
  }

  RightHandSide(yTemp, ak3);
  for(G4int i = 0; i < GetNumberOfVariables(); ++i)
  {
    yOutput[i] = yInput[i] + hstep * (b41*dydx[i] + b42*ak2[i] + b43*ak3[i]);
  }
    
  if (dydxOutput && yError)
  {
    RightHandSide(yOutput, dydxOutput);
    for(G4int i = 0; i < GetNumberOfVariables(); ++i)
    {
      yError[i] = hstep * (dc1 * dydx[i] + dc2 * ak2[i] + 
                           dc3 * ak3[i] + dc4 * dydxOutput[i]);
    }
  }
}

void G4BogackiShampine23::Stepper(const G4double yInput[],
                                  const G4double dydx[],
                                  G4double hstep,
                                  G4double yOutput[],
                                  G4double yError[])
{
  copy(fyIn, yInput);
  copy(fdydx, dydx);
  fhstep = hstep;

  makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);

  copy(yOutput, fyOut);
}

void G4BogackiShampine23::Stepper(const G4double yInput[],
                                  const G4double dydx[],
                                  G4double hstep,
                                  G4double yOutput[],
                                  G4double yError[],
                                  G4double dydxOutput[])
{
  copy(fyIn, yInput);
  copy(fdydx, dydx);
  fhstep = hstep;

  makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);

  copy(yOutput, fyOut);
  copy(dydxOutput, fdydxOut);
}

G4double G4BogackiShampine23::DistChord() const
{
  G4double yMid[G4FieldTrack::ncompSVEC];
  makeStep(fyIn, fdydx, fhstep / 2., yMid);

  const G4ThreeVector begin = makeVector(fyIn, Value3D::Position);
  const G4ThreeVector mid = makeVector(yMid, Value3D::Position);
  const G4ThreeVector end = makeVector(fyOut, Value3D::Position);

  return G4LineSection::Distline(mid, begin, end);
}