ARK4DenseOutput< Soln, Rhs, IMEXOp > Class Template Reference

#include <ARK4DenseOutput.H>

List of all members.

Detailed Description

template<class Soln, class Rhs, class IMEXOp>
class ARK4DenseOutput< Soln, Rhs, IMEXOp >

This is a more flexible, reduced memory version 4th-order additive Runge-Kutta algorithm, that also includes dense output coefficients This templated class encapsulates the fourth-order additive Runge-Kutta method "ARK4(3)6L[2]SA" by Kennedy and Carpenter 2003 Appl. Numer. Math. 44: 139-181

See also section 3 of Zhang, Johansen, and Colella, SIAM J. Sci. Comput. 34, pp. B179-B201.

Public Member Functions

ARK4DenseOutput ()

void define (const Soln &a_state, Real a_dt, bool a_denseOutput=false)

void advance (Real a_time, Soln &a_state)

void denseOutputCoefs (Vector< Rhs * > &a_interpCoefs)

void resetDt (Real a_dt)

void start0end1 (bool a_start0, bool a_end1)

IMEXOp & getImExOp ()

bool isDefined () const

bool hasDenseOutput () const

Static Public Attributes

static const int s_nStages = 6

Runge-Kutta coefficients.

static const Real s_aIdiag = 0.25

static const Real s_c [s_nStages] = { 0.0, 0.5, 0.332, 0.62, 0.85, 1.0 }

static const Real s_aE [s_nStages][s_nStages]

static const Real s_aI [s_nStages][s_nStages]

static const Real s_b [s_nStages]

static const int s_nDenseCoefs = 3

static const Real s_bstar [s_nDenseCoefs][s_nStages]

Protected Attributes

bool m_isDefined

bool m_denseOutput

bool m_hasDenseOutput

Real m_dt

Real m_time

Soln m_phi [s_nStages]

Rhs m_rhs

Rhs m_denseCoefs [s_nDenseCoefs]

Rhs m_kE

Rhs m_kI

IMEXOp m_opImEx

Constructor & Destructor Documentation

template<class Soln, class Rhs, class IMEXOp>

ARK4DenseOutput< Soln, Rhs, IMEXOp >::ARK4DenseOutput ( ) [inline]

Member Function Documentation

template<class Soln, class Rhs, class IMEXOp>

void ARK4DenseOutput< Soln, Rhs, IMEXOp >::define	(	const Soln &	a_state,
		Real	a_dt,
		bool	a_denseOutput = `false`
	)			`[inline]`

References CH_TIMERS, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_denseCoefs, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_denseOutput, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_dt, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_hasDenseOutput, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_isDefined, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_kE, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_kI, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_opImEx, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_phi, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_rhs, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_aIdiag, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_nDenseCoefs, and ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_nStages.

template<class Soln, class Rhs, class IMEXOp>

void ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance	(	Real	a_time,
		Soln &	a_state
	)			`[inline]`

References CH_assert, CH_START, CH_STOP, CH_TIMER, CH_TIMERS, ARK4DenseOutput< Soln, Rhs, IMEXOp >::isDefined(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_denseCoefs, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_denseOutput, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_dt, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_hasDenseOutput, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_kE, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_kI, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_opImEx, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_phi, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_rhs, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_time, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_aE, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_aI, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_b, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_bstar, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_c, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_nDenseCoefs, and ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_nStages.

template<class Soln, class Rhs, class IMEXOp>

void ARK4DenseOutput< Soln, Rhs, IMEXOp >::denseOutputCoefs ( Vector< Rhs * > & a_interpCoefs ) [inline]

References CH_assert, CH_TIMERS, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_denseCoefs, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_hasDenseOutput, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_phi, ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_nDenseCoefs, and Vector< T >::size().

template<class Soln, class Rhs, class IMEXOp>

void ARK4DenseOutput< Soln, Rhs, IMEXOp >::resetDt ( Real a_dt ) [inline]

References Abs(), CH_assert, ARK4DenseOutput< Soln, Rhs, IMEXOp >::isDefined(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_dt, ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_hasDenseOutput, and ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_opImEx.

template<class Soln, class Rhs, class IMEXOp>

void ARK4DenseOutput< Soln, Rhs, IMEXOp >::start0end1	(	bool	a_start0,
		bool	a_end1
	)			`[inline]`

References CH_assert, ARK4DenseOutput< Soln, Rhs, IMEXOp >::isDefined(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_opImEx, and ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_nStages.

template<class Soln, class Rhs, class IMEXOp>

IMEXOp & ARK4DenseOutput< Soln, Rhs, IMEXOp >::getImExOp ( ) [inline]

References ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_opImEx.

template<class Soln, class Rhs, class IMEXOp>

bool ARK4DenseOutput< Soln, Rhs, IMEXOp >::isDefined ( ) const [inline]

References ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_isDefined.

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::resetDt(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::start0end1().

template<class Soln, class Rhs, class IMEXOp>

bool ARK4DenseOutput< Soln, Rhs, IMEXOp >::hasDenseOutput ( ) const [inline]

References ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_hasDenseOutput.

Member Data Documentation

template<class Soln, class Rhs, class IMEXOp>

const int ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_nStages = 6 [static]

Runge-Kutta coefficients.

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::define(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::start0end1().

template<class Soln, class Rhs, class IMEXOp>

const Real ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_aIdiag = 0.25 [inline, static]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::define().

template<class Soln, class Rhs, class IMEXOp>

const Real ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_c = { 0.0, 0.5, 0.332, 0.62, 0.85, 1.0 } [inline, static]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance().

template<class Soln, class Rhs, class IMEXOp>

const Real ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_aE [inline, static]

Initial value:

 {
  {0., 0., 0., 0., 0., 0.},
  {0.5, 0., 0., 0., 0., 0.},
  {0.221776, 0.110224, 0., 0., 0., 0.},
  {-0.04884659515311857, -0.17772065232640102, 0.8465672474795197, 0., 0., 0.},
  {-0.15541685842491548, -0.3567050098221991, 1.0587258798684427, 0.30339598837867193, 0., 0.},
  { 0.2014243506726763, 0.008742057842904185, 0.15993995707168115, 0.4038290605220775, 0.22606457389066084, 0.}
}

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance().

template<class Soln, class Rhs, class IMEXOp>

const Real ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_aI [inline, static]

Initial value:

 {
  {0., 0., 0., 0., 0., 0.},
  {0.25, 0.25, 0., 0., 0., 0.},
  {0.137776, -0.055776, 0.25, 0., 0., 0.},
  {0.14463686602698217, -0.22393190761334475, 0.4492950415863626, 0.25, 0., 0.},
  {0.09825878328356477, -0.5915442428196704, 0.8101210538282996, 0.283164405707806, 0.25, 0.},
  {0.15791629516167136, 0., 0.18675894052400077, 0.6805652953093346, -0.27524053099500667, 0.25}
}

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance().

template<class Soln, class Rhs, class IMEXOp>

const Real ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_b [inline, static]

Initial value:

  {0.15791629516167136, 0., 0.18675894052400077, 0.6805652953093346, -0.27524053099500667, 0.25}

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance().

template<class Soln, class Rhs, class IMEXOp>

const int ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_nDenseCoefs = 3 [static]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::define(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::denseOutputCoefs().

template<class Soln, class Rhs, class IMEXOp>

const Real ARK4DenseOutput< Soln, Rhs, IMEXOp >::s_bstar [inline, static]

Initial value:

 {
  {0.961753400252887, 0., 0.787405595186356, -2.74544192086633, 3.70351728061223, -1.70723435518514},
  {-1.76418754019038, 0., -0.774504669155511, 9.64023584441292, -12.544886411271, 5.44334277620397},
  {0.960350435099165, 0., 0.173858014493155, -6.21422862823726, 8.56612859966376, -3.48610842101883}
}

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance().

template<class Soln, class Rhs, class IMEXOp>

bool ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_isDefined [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::define(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::isDefined().

template<class Soln, class Rhs, class IMEXOp>

bool ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_denseOutput [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::define().

template<class Soln, class Rhs, class IMEXOp>

bool ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_hasDenseOutput [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::define(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::denseOutputCoefs(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::hasDenseOutput(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::resetDt().

template<class Soln, class Rhs, class IMEXOp>

Real ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_dt [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::define(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::resetDt().

template<class Soln, class Rhs, class IMEXOp>

Real ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_time [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance().

template<class Soln, class Rhs, class IMEXOp>

Soln ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_phi[s_nStages] [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::define(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::denseOutputCoefs().

template<class Soln, class Rhs, class IMEXOp>

Rhs ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_rhs [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::define().

template<class Soln, class Rhs, class IMEXOp>

Rhs ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_denseCoefs[s_nDenseCoefs] [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::define(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::denseOutputCoefs().

template<class Soln, class Rhs, class IMEXOp>

Rhs ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_kE [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::define().

template<class Soln, class Rhs, class IMEXOp>

Rhs ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_kI [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::define().

template<class Soln, class Rhs, class IMEXOp>

IMEXOp ARK4DenseOutput< Soln, Rhs, IMEXOp >::m_opImEx [protected]

Referenced by ARK4DenseOutput< Soln, Rhs, IMEXOp >::advance(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::define(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::getImExOp(), ARK4DenseOutput< Soln, Rhs, IMEXOp >::resetDt(), and ARK4DenseOutput< Soln, Rhs, IMEXOp >::start0end1().

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

ARK4DenseOutput.H

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