G4BulirschStoer Class Reference

#include <G4BulirschStoer.hh>

Public Types
enum class	step_result { success , fail }

Public Member Functions
	G4BulirschStoer (G4EquationOfMotion *equation, G4int nvar, G4double eps_rel, G4double max_dt=DBL_MAX)
void	set_max_dt (G4double max_dt)
void	set_max_relative_error (G4double eps_rel)
step_result	try_step (const G4double in[], const G4double dxdt[], G4double &t, G4double out[], G4double &dt)
void	reset ()
void	SetEquationOfMotion (G4EquationOfMotion *equation)
G4EquationOfMotion *	GetEquationOfMotion ()
G4int	GetNumberOfVariables () const

Detailed Description

Definition at line 43 of file G4BulirschStoer.hh.

Member Enumeration Documentation

step_result

enum class G4BulirschStoer::step_result

strong

Enumerator
success
fail

Definition at line 47 of file G4BulirschStoer.hh.

    {
      success,
      fail
    };

Constructor & Destructor Documentation

G4BulirschStoer()

G4BulirschStoer::G4BulirschStoer	(	G4EquationOfMotion *	equation,
		G4int	nvar,
		G4double	eps_rel,
		G4double	max_dt = DBL_MAX
	)

Definition at line 47 of file G4BulirschStoer.cc.

  : fnvar(nvar), m_eps_rel(eps_rel), m_midpoint(equation,nvar),
    m_last_step_rejected(false), m_first(true), m_dt_last(0.0), m_max_dt(max_dt)
{
  /* initialize sequence of stage numbers and work */
 
  for(G4int i = 0; i < m_k_max + 1; ++i)
  {
    m_interval_sequence[i] = 2 * (i + 1);
    if (i == 0)
    {
      m_cost[i] = m_interval_sequence[i];
    }
    else
    {
      m_cost[i] = m_cost[i-1] + m_interval_sequence[i];
    }
    for(G4int k = 0; k < i; ++k)
    {
      const G4double r = static_cast<G4double>(m_interval_sequence[i])
                       / static_cast<G4double>(m_interval_sequence[k]);
      m_coeff[i][k] = 1.0 / (r * r - 1.0); // coefficients for extrapolation
    }
 
    // crude estimate of optimal order
    m_current_k_opt = 4;
 
    // no calculation because log10 might not exist for value_type!
 
    //const G4double logfact = -log10(std::max(eps_rel, 1.0e-12)) * 0.6 + 0.5;
    //m_current_k_opt = std::max(1.,
    //                  std::min(static_cast<G4double>(m_k_max-1), logfact));
  }
}

Member Function Documentation

GetEquationOfMotion()

G4EquationOfMotion * G4BulirschStoer::GetEquationOfMotion ( )

inline

GetNumberOfVariables()

G4int G4BulirschStoer::GetNumberOfVariables ( ) const

inline

reset()

void G4BulirschStoer::reset

(

)

Definition at line 233 of file G4BulirschStoer.cc.

{
  m_first = true;
  m_last_step_rejected = false;
}

Referenced by try_step().

set_max_dt()

void G4BulirschStoer::set_max_dt ( G4double  max_dt )

inline

set_max_relative_error()

void G4BulirschStoer::set_max_relative_error ( G4double  eps_rel )

inline

SetEquationOfMotion()

void G4BulirschStoer::SetEquationOfMotion ( G4EquationOfMotion *  equation )

inline

try_step()

G4BulirschStoer::step_result G4BulirschStoer::try_step	(	const G4double	in[],
		const G4double	dxdt[],
		G4double &	t,
		G4double	out[],
		G4double &	dt
	)

Definition at line 84 of file G4BulirschStoer.cc.

{
  if(m_max_dt < dt)
  {
    // given step size is bigger then max_dt set limit and return fail
    //
    dt = m_max_dt;
    return step_result::fail;
  }
 
  if (dt != m_dt_last)
  {
    reset(); // step size changed from outside -> reset
  }
 
  G4bool reject = true;
 
  G4double new_h = dt;
 
  /* m_current_k_opt is the estimated current optimal stage number */
 
  for(G4int k = 0; k <= m_current_k_opt+1; ++k)
  {
    // the stage counts are stored in m_interval_sequence
    //
    m_midpoint.SetSteps(m_interval_sequence[k]);
    if(k == 0)
    {
      m_midpoint.DoStep(in, dxdt, out, dt);
      /* the first step, nothing more to do */
    }
    else
    {
      m_midpoint.DoStep(in, dxdt, m_table[k-1], dt);
      extrapolate(k, out);
      // get error estimate
      for (G4int i = 0; i < fnvar; ++i)
      {
        m_err[i] = out[i] - m_table[0][i];
      }
      const G4double error =
            field_utils::relativeError(out, m_err, dt, m_eps_rel);
      h_opt[k] = calc_h_opt(dt, error, k);
      work[k] = static_cast<G4double>(m_cost[k]) / h_opt[k];
 
      if( (k == m_current_k_opt-1) || m_first)  // convergence before k_opt ?
      {
        if(error < 1.0)
        {
          // convergence
          reject = false;
          if( (work[k] < KFAC2 * work[k-1]) || (m_current_k_opt <= 2) )
          {
            // leave order as is (except we were in first round)
            m_current_k_opt = std::min(m_k_max - 1 , std::max(2 , k + 1));
            new_h = h_opt[k];
            new_h *= static_cast<G4double>(m_cost[k + 1])
                   / static_cast<G4double>(m_cost[k]);
          }
          else
          {
            m_current_k_opt = std::min(m_k_max - 1, std::max(2, k));
            new_h = h_opt[k];
          }
          break;
        }
        else if(should_reject(error , k) && !m_first)
        {
          reject = true;
          new_h = h_opt[k];
          break;
        }
      }
      if(k == m_current_k_opt)  // convergence at k_opt ?
      {
        if(error < 1.0)
        {
          // convergence
          reject = false;
          if(work[k-1] < KFAC2 * work[k])
          {
            m_current_k_opt = std::max( 2 , m_current_k_opt-1 );
            new_h = h_opt[m_current_k_opt];
          }
          else if( (work[k] < KFAC2 * work[k-1]) && !m_last_step_rejected )
          {
            m_current_k_opt = std::min(m_k_max - 1, m_current_k_opt + 1);
            new_h = h_opt[k];
            new_h *= static_cast<G4double>(m_cost[m_current_k_opt])
                   / static_cast<G4double>(m_cost[k]);
          }
          else
          {
            new_h = h_opt[m_current_k_opt];
          }
          break;
        }
        else if(should_reject(error, k))
        {
          reject = true;
          new_h = h_opt[m_current_k_opt];
          break;
        }
      }
      if(k == m_current_k_opt + 1)  // convergence at k_opt+1 ?
      {
        if(error < 1.0)  // convergence
        {
          reject = false;
          if(work[k-2] < KFAC2 * work[k-1])
          {
            m_current_k_opt = std::max(2, m_current_k_opt - 1);
          }
          if((work[k] < KFAC2 * work[m_current_k_opt]) && !m_last_step_rejected)
          {
            m_current_k_opt = std::min(m_k_max - 1 , k);
          }
          new_h = h_opt[m_current_k_opt];
        }
        else
        {
          reject = true;
          new_h = h_opt[m_current_k_opt];
        }
        break;
      }
    }
  }
 
  if(!reject)
  {
    t += dt;
  }
 
  if(!m_last_step_rejected || new_h < dt)
  {
    // limit step size
    new_h = std::min(m_max_dt, new_h);
    m_dt_last = new_h;
    dt = new_h;
  }
 
  m_last_step_rejected = reject;
  m_first = false;
 
  return reject ? step_result::fail : step_result::success;
}

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The documentation for this class was generated from the following files:

• G4BulirschStoer.hh
• G4BulirschStoer.cc