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Tempus::StepperIMEX_RK< Scalar > Class Template Reference

Implicit-Explicit Runge-Kutta (IMEX-RK) time stepper. More...

#include <Tempus_StepperIMEX_RK_decl.hpp>

Inheritance diagram for Tempus::StepperIMEX_RK< Scalar >:
Tempus::StepperImplicit< Scalar > Tempus::Stepper< Scalar >

Public Member Functions

 StepperIMEX_RK ()
 Default constructor. More...
 
 StepperIMEX_RK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, Teuchos::RCP< Teuchos::ParameterList > pList)
 Constructor to specialize Stepper parameters. More...
 
 StepperIMEX_RK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, std::string stepperType="IMEX RK SSP2")
 Constructor to use default Stepper parameters. More...
 
 StepperIMEX_RK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &models, std::string stepperType, Teuchos::RCP< Teuchos::ParameterList > pList)
 Constructor for StepperFactory. More...
 
virtual Scalar getAlpha (const Scalar dt) const
 Return alpha = d(xDot)/dx. More...
 
virtual Scalar getBeta (const Scalar) const
 Return beta = d(x)/dx. More...
 
void evalImplicitModelExplicitly (const Teuchos::RCP< const Thyra::VectorBase< Scalar > > &X, Scalar time, Scalar stepSize, Scalar stageNumber, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &G) const
 
void evalExplicitModel (const Teuchos::RCP< const Thyra::VectorBase< Scalar > > &X, Scalar time, Scalar stepSize, Scalar stageNumber, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &F) const
 
Basic stepper methods
virtual void setTableaus (Teuchos::RCP< Teuchos::ParameterList > pList, std::string stepperType="")
 Set both the explicit and implicit tableau from ParameterList. More...
 
virtual void setExplicitTableau (std::string stepperType, Teuchos::RCP< Teuchos::ParameterList > pList)
 Set the explicit tableau from ParameterList. More...
 
virtual void setExplicitTableau (Teuchos::RCP< const RKButcherTableau< Scalar > > explicitTableau)
 Set the explicit tableau from tableau. More...
 
virtual void setImplicitTableau (std::string stepperType, Teuchos::RCP< Teuchos::ParameterList > pList)
 Set the implicit tableau from ParameterList. More...
 
virtual void setImplicitTableau (Teuchos::RCP< const RKButcherTableau< Scalar > > implicitTableau)
 Set the implicit tableau from tableau. More...
 
virtual void setModel (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel)
 
virtual Teuchos::RCP< const
Thyra::ModelEvaluator< Scalar > > 		getModel ()
 
virtual void setModelPair (const Teuchos::RCP< WrapperModelEvaluatorPairIMEX_Basic< Scalar > > &mePair)
 Create WrapperModelPairIMEX from user-supplied ModelEvaluator pair. More...
 
virtual void setModelPair (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &explicitModel, const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &implicitModel)
 Create WrapperModelPairIMEX from explicit/implicit ModelEvaluators. More...
 
virtual void setObserver (Teuchos::RCP< StepperObserver< Scalar > > obs=Teuchos::null)
 Set Observer. More...
 
virtual void initialize ()
 Initialize during construction and after changing input parameters. More...
 
virtual void setInitialConditions (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
 Set the initial conditions and make them consistent. More...
 
virtual void takeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
 Take the specified timestep, dt, and return true if successful. More...
 
virtual Teuchos::RCP
< Tempus::StepperState< Scalar > > 		getDefaultStepperState ()
 Provide a StepperState to the SolutionState. This Stepper does not have any special state data, so just provide the base class StepperState with the Stepper description. This can be checked to ensure that the input StepperState can be used by this Stepper. More...
 
virtual Scalar getOrder () const
 
virtual Scalar getOrderMin () const
 
virtual Scalar getOrderMax () const
 
virtual bool isExplicit () const
 
virtual bool isImplicit () const
 
virtual bool isExplicitImplicit () const
 
virtual bool isOneStepMethod () const
 
virtual bool isMultiStepMethod () const
 
virtual OrderODE getOrderODE () const
 
ParameterList methods
void setParameterList (const Teuchos::RCP< Teuchos::ParameterList > &pl)
 
Teuchos::RCP
< Teuchos::ParameterList > 		getNonconstParameterList ()
 
Teuchos::RCP
< Teuchos::ParameterList > 		unsetParameterList ()
 
Teuchos::RCP< const
Teuchos::ParameterList > 		getValidParameters () const
 
Teuchos::RCP
< Teuchos::ParameterList > 		getDefaultParameters () const
 
Overridden from Teuchos::Describable
virtual std::string description () const
 
virtual void describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel) const
 
- Public Member Functions inherited from Tempus::StepperImplicit< Scalar >
virtual void setNonConstModel (const Teuchos::RCP< Thyra::ModelEvaluator< Scalar > > &appModel)
 
virtual Teuchos::RCP< const
WrapperModelEvaluator< Scalar > > 		getWrapperModel ()
 
virtual void setSolver (std::string solverName)
 Set solver via ParameterList solver name. More...
 
virtual void setSolver (Teuchos::RCP< Teuchos::ParameterList > solverPL=Teuchos::null)
 Set solver via solver ParameterList. More...
 
virtual void setSolver (Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver)
 Set solver. More...
 
virtual Teuchos::RCP
< Thyra::NonlinearSolverBase
< Scalar > > 		getSolver () const
 Get solver. More...
 
virtual std::string getStepperType () const
 
const Thyra::SolveStatus< Scalar > solveImplicitODE (const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x)
 Solve problem using x in-place. (Needs to be deprecated!) More...
 
const Thyra::SolveStatus< Scalar > solveImplicitODE (const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &xDot, const Scalar time, const Teuchos::RCP< ImplicitODEParameters< Scalar > > &p)
 Solve implicit ODE, f(x, xDot, t, p) = 0. More...
 
void evaluateImplicitODE (Teuchos::RCP< Thyra::VectorBase< Scalar > > &f, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &xDot, const Scalar time, const Teuchos::RCP< ImplicitODEParameters< Scalar > > &p)
 Evaluate implicit ODE, f(x, xDot, t, p), residual. More...
 
virtual void setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > > initial_guess)
 Pass initial guess to Newton solver (only relevant for implicit solvers) More...
 
virtual void setZeroInitialGuess (bool zIG)
 Set parameter so that the initial guess is set to zero (=True) or use last timestep (=False). More...
 
virtual bool getZeroInitialGuess () const
 
virtual Scalar getInitTimeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &) const
 
virtual bool getEmbedded () const
 
virtual void setUseFSAL (bool a)
 
virtual bool getUseFSAL () const
 
virtual void setICConsistency (std::string s)
 
virtual std::string getICConsistency () const
 
virtual void setICConsistencyCheck (bool c)
 
virtual bool getICConsistencyCheck () const
 
virtual void setStepperXDot (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDot)
 Set xDot for Stepper storage. More...
 
virtual Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		getStepperXDot (Teuchos::RCP< SolutionState< Scalar > > state)
 Get xDot from SolutionState or Stepper storage. More...
 
virtual Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		getStepperXDotDot (Teuchos::RCP< SolutionState< Scalar > > state)
 Get xDotDot from SolutionState or Stepper storage. More...
 
- Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual void modelWarning () const
 
void getValidParametersBasic (Teuchos::RCP< Teuchos::ParameterList > pl) const
 
virtual void createSubSteppers (std::vector< Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > >)
 
void validExplicitODE (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model) const
 Validate that the model supports explicit ODE evaluation, f(x,t) [=xdot]. More...
 
void validSecondOrderExplicitODE (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model) const
 Validate that the model supports explicit second order ODE evaluation, f(x,xdot,t) [=xdotdot]. More...
 
void validImplicitODE_DAE (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model) const
 Validate ME supports implicit ODE/DAE evaluation, f(xdot,x,t) [= 0]. More...
 
void validSecondOrderODE_DAE (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model) const
 Validate ME supports 2nd order implicit ODE/DAE evaluation, f(xdotdot,xdot,x,t) [= 0]. More...
 
Teuchos::RCP
< Teuchos::ParameterList > 		defaultSolverParameters () const
 

Protected Attributes

std::string description_
 
Teuchos::RCP< const
RKButcherTableau< Scalar > > 		explicitTableau_
 
Teuchos::RCP< const
RKButcherTableau< Scalar > > 		implicitTableau_
 
Scalar order_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		stageX_
 
std::vector< Teuchos::RCP
< Thyra::VectorBase< Scalar > > > 		stageF_
 
std::vector< Teuchos::RCP
< Thyra::VectorBase< Scalar > > > 		stageG_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		xTilde_
 
Teuchos::RCP
< StepperIMEX_RKObserver
< Scalar > > 		stepperIMEX_RKObserver_
 
- Protected Attributes inherited from Tempus::StepperImplicit< Scalar >
Teuchos::RCP
< Teuchos::ParameterList > 		stepperPL_
 
Teuchos::RCP
< WrapperModelEvaluator
< Scalar > > 		wrapperModel_
 
Teuchos::RCP
< Thyra::NonlinearSolverBase
< Scalar > > 		solver_
 
Teuchos::RCP< const
Thyra::VectorBase< Scalar > > 		initial_guess_
 
Teuchos::RCP< StepperObserver
< Scalar > > 		stepperObserver_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		stepperXDot_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		stepperXDotDot_
 

Detailed Description

template<class Scalar>
class Tempus::StepperIMEX_RK< Scalar >

Implicit-Explicit Runge-Kutta (IMEX-RK) time stepper.

For the implicit ODE system, $ \mathcal{F}(\dot{x},x,t) = 0 $, we need to specialize this in order to separate the explicit, implicit, and temporal terms for the IMEX-RK time stepper,

\begin{eqnarray*} M(x,t)\, \dot{x}(x,t) + G(x,t) + F(x,t) & = & 0, \\ \mathcal{G}(\dot{x},x,t) + F(x,t) & = & 0, \end{eqnarray*}

where $\mathcal{G}(\dot{x},x,t) = M(x,t)\, \dot{x} + G(x,t)$, $M(x,t)$ is the mass matrix, $F(x,t)$ is the operator representing the "slow" physics (and is evolved explicitly), and $G(x,t)$ is the operator representing the "fast" physics (and is evolved implicitly). Additionally, we assume that the mass matrix is invertible, so that

\[ \dot{x}(x,t) + g(x,t) + f(x,t) = 0 \]

where $f(x,t) = M(x,t)^{-1}\, F(x,t)$, and $g(x,t) = M(x,t)^{-1}\, G(x,t)$. Using Butcher tableaus for the explicit terms

\[ \begin{array}{c|c} \hat{c} & \hat{A} \\ \hline & \hat{b}^T \end{array} \;\;\;\; \mbox{ and for implicit terms } \;\;\;\; \begin{array}{c|c} c & A \\ \hline & b^T \end{array}, \]

the basic IMEX-RK method for $s$-stages can be written as

\[ \begin{array}{rcll} X_i & = & x_{n-1} - \Delta t \sum_{j=1}^{i-1} \hat{a}_{ij}\, f(X_j,\hat{t}_j) - \Delta t \sum_{j=1}^i a_{ij}\, g(X_j,t_j) & \mbox{for } i=1\ldots s, \\ x_n & = & x_{n-1} - \Delta t \sum_{i=1}^s \hat{b}_{i}\, f(X_i,\hat{t}_i) - \Delta t \sum_{i=1}^s b_{i}\, g(X_i,t_i) & \end{array} \]

where $\hat{t}_i = t_{n-1}+\hat{c}_i\Delta t$ and $t_i = t_{n-1}+c_i\Delta t$. For iterative solvers, it is useful to write the stage solutions as

\[ X_i = \tilde{X} - a_{ii} \Delta t\, g(X_i,t_i) \]

where

\[ \tilde{X} = x_{n-1} - \Delta t \sum_{j=1}^{i-1} \left(\hat{a}_{ij}\, f(X_j,\hat{t}_j) + a_{ij}\, g(X_j,t_j)\right) \]

Rearranging to solve for the implicit term

\[ g(X_i,t_i) = - \frac{X_i - \tilde{X}}{a_{ii} \Delta t} \]

We can use this to determine the time derivative at each stage for the implicit solve.

\[ \dot{X}_i(X_i,t_i) + g(X_i,t_i) + f(X_i,t_i) = 0 \]

Note that the explicit term, $f(X_i,t_i)$, is evaluated at the implicit stage time, $t_i$. We can form the time derivative

\begin{eqnarray*} \dot{X}(X_i,t_i) & = & - g(X_i,t_i) - f(X_i,t_i) \\ \dot{X}(X_i,t_i) & = & \frac{X_i - \tilde{X}}{a_{ii} \Delta t} - f(X_i,t_i) \\ \dot{X}(X_i,t_i) & = & \frac{X_i - \tilde{X}}{a_{ii} \Delta t} -M(X_i, t_i)^{-1}\, F(X_i,t_i)\\ \end{eqnarray*}

Returning to the governing equation

\begin{eqnarray*} M(X_i,t_i)\, \dot{X}(X_i,t_i) + G(X_i,t_i) + F(X_i,t_i) & = & 0 \\ M(X_i,t_i)\, \left[ \frac{X_i - \tilde{X}}{a_{ii} \Delta t} - M(X_i, t_i)^{-1}\, F(X_i,t_i) \right] + G(X_i,t_i) + F(X_i,t_i) & = & 0 \\ M(X_i,t_i)\, \left[ \frac{X_i - \tilde{X}}{a_{ii} \Delta t} \right] + G(X_i,t_i) & = & 0 \\ \end{eqnarray*}

Recall $\mathcal{G}(\dot{x},x,t) = M(x,t)\, \dot{x} + G(x,t)$ and if we define a pseudo time derivative,

\[ \tilde{\dot{X}} = \frac{X_i - \tilde{X}}{a_{ii} \Delta t} = - g(X_i,t_i), \]

we can write

\[ \mathcal{G}(\tilde{\dot{X}},X_i,t_i) = M(X_i,t_i)\, \tilde{\dot{X}} + G(X_i,t_i) = 0 \]

For the case when $a_{ii}=0$, we need the time derivative for the plain explicit case. Thus the stage solution is

\[ X_i = x_{n-1} - \Delta t\,\sum_{j=1}^{i-1} \left( \hat{a}_{ij}\, f_j + a_{ij}\, g_j \right) = \tilde{X} \]

and we can simply evaluate

\begin{eqnarray*} f_i & = & M(X_i,\hat{t}_i)^{-1}\, F(X_i,\hat{t}_i) \\ g_i & = & M(X_i, t_i)^{-1}\, G(X_i, t_i) \end{eqnarray*}

We can then form the time derivative as

\[ \dot{X}_i(X_i,t_i) = - g(X_i,t_i) - f(X_i,t_i) \]

but again note that the explicit term, $f(X_i,t_i)$, is evaluated at the implicit stage time, $t_i$.

IMEX-RK Algorithm

The single-timestep algorithm for IMEX-RK using the real time derivative, $\dot{X}(X_i,t_i)$, is

  • $X_1 \leftarrow x_{n-1}$
  • for $i = 1 \ldots s$ do
    • $\tilde{X} \leftarrow x_{n-1} - \Delta t\,\sum_{j=1}^{i-1} \left( \hat{a}_{ij}\, f_j + a_{ij}\, g_j \right) $
    • if $a_{ii} = 0$
      • $X_i \leftarrow \tilde{X}$
      • $g_i \leftarrow M(X_i, t_i)^{-1}\, G(X_i, t_i)$
    • else
      • Define $\dot{X}(X_i,t_i) = \frac{X_i-\tilde{X}}{a_{ii} \Delta t} - M(X_i,t_i)^{-1}\, F(X_i,t_i) $
      • Solve $\mathcal{G}\left(\dot{X}(X_i,t_i),X_i,t_i\right) + F(X_i,t_i) = 0$ for $X_i$
      • $g_i \leftarrow - \frac{X_i-\tilde{X}}{a_{ii} \Delta t}$
    • $f_i \leftarrow M(X_i,\hat{t}_i)^{-1}\, F(X_i,\hat{t}_i)$
  • end for
  • $x_n \leftarrow x_{n-1} - \Delta t\,\sum_{i=1}^{s}\hat{b}_i\,f_i - \Delta t\,\sum_{i=1}^{s} b_i\,g_i$

The single-timestep algorithm for IMEX-RK using the pseudo time derivative, $\tilde{\dot{X}}$, is (which is currently implemented)

  • $X_1 \leftarrow x_{n-1}$
  • for $i = 1 \ldots s$ do
    • $\tilde{X} \leftarrow x_{n-1} - \Delta t\,\sum_{j=1}^{i-1} \left( \hat{a}_{ij}\, f_j + a_{ij}\, g_j \right) $
    • if $a_{ii} = 0$
      • $X_i \leftarrow \tilde{X}$
      • $g_i \leftarrow M(X_i, t_i)^{-1}\, G(X_i, t_i)$
    • else
      • Define $\tilde{\dot{X}} = \frac{X_i-\tilde{X}}{a_{ii} \Delta t} $
      • Solve $\mathcal{G}\left(\tilde{\dot{X}},X_i,t_i\right) = 0$ for $X_i$
      • $g_i \leftarrow - \tilde{\dot{X}}$
    • $f_i \leftarrow M(X_i,\hat{t}_i)^{-1}\, F(X_i,\hat{t}_i)$
  • end for
  • $x_n \leftarrow x_{n-1} - \Delta t\,\sum_{i=1}^{s}\hat{b}_i\,f_i - \Delta t\,\sum_{i=1}^{s} b_i\,g_i$

The following table contains the pre-coded IMEX-RK tableaus.

IMEX-RK Tableaus
Name Order Implicit Tableau Explicit Tableau
IMEX RK 1st order 1st

\[ \begin{array}{c|cc} 0 & 0 & 0 \\ 1 & 0 & 1 \\ \hline & 0 & 1 \end{array} \]

\[ \begin{array}{c|cc} 0 & 0 & 0 \\ 1 & 1 & 0 \\ \hline & 1 & 0 \end{array} \]

IMEX RK SSP2
$\gamma = 1-1/\sqrt{2}$ 		2nd

\[ \begin{array}{c|cc} \gamma & \gamma & 0 \\ 1-\gamma & 1-2\gamma & \gamma \\ \hline & 1/2 & 1/2 \end{array} \]

\[ \begin{array}{c|cc} 0 & 0 & 0 \\ 1 & 1 & 0 \\ \hline & 1/2 & 1/2 \end{array} \]

IMEX RK ARS 233
$\gamma = (3+\sqrt{3})/6$ 		3rd

\[ \begin{array}{c|ccc} 0 & 0 & 0 & 0 \\ \gamma & 0 & \gamma & 0 \\ 1-\gamma & 0 & 1-2\gamma & \gamma \\ \hline & 0 & 1/2 & 1/2 \end{array} \]

\[ \begin{array}{c|ccc} 0 & 0 & 0 & 0 \\ \gamma & \gamma & 0 & 0 \\ 1-\gamma & \gamma-1 & 2-2\gamma & 0 \\ \hline & 0 & 1/2 & 1/2 \end{array} \]

The First-Step-As-Last (FSAL) principle is not valid for IMEX RK. The default is to set useFSAL=false, and useFSAL=true will result in an error.

References

  1. Ascher, Ruuth, Spiteri, "Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations", Applied Numerical Mathematics 25 (1997) 151-167.
  2. Cyr, "IMEX Lagrangian Methods", SAND2015-3745C.
  3. Shadid, Cyr, Pawlowski, Widley, Scovazzi, Zeng, Phillips, Conde, Chuadhry, Hensinger, Fischer, Robinson, Rider, Niederhaus, Sanchez, "Towards an IMEX Monolithic ALE Method with Integrated UQ for Multiphysics Shock-hydro", SAND2016-11353, 2016, pp. 21-28.

Definition at line 228 of file Tempus_StepperIMEX_RK_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >
Tempus::StepperIMEX_RK< Scalar >::StepperIMEX_RK ( )

Default constructor.

Definition at line 28 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
Tempus::StepperIMEX_RK< Scalar >::StepperIMEX_RK ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel,
Teuchos::RCP< Teuchos::ParameterList >  pList 
)

Constructor to specialize Stepper parameters.

Definition at line 37 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
Tempus::StepperIMEX_RK< Scalar >::StepperIMEX_RK ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel,
std::string  stepperType = "IMEX RK SSP2" 
)

Constructor to use default Stepper parameters.

Definition at line 55 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
Tempus::StepperIMEX_RK< Scalar >::StepperIMEX_RK ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  models,
std::string  stepperType,
Teuchos::RCP< Teuchos::ParameterList >  pList 
)

Constructor for StepperFactory.

Definition at line 73 of file Tempus_StepperIMEX_RK_impl.hpp.

Member Function Documentation

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::describe ( Teuchos::FancyOStream &  out,
const Teuchos::EVerbosityLevel  verbLevel 
) const
virtual

Definition at line 672 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
std::string Tempus::StepperIMEX_RK< Scalar >::description ( ) const
virtual

Definition at line 665 of file Tempus_StepperIMEX_RK_impl.hpp.

template<typename Scalar >
void Tempus::StepperIMEX_RK< Scalar >::evalExplicitModel ( const Teuchos::RCP< const Thyra::VectorBase< Scalar > > &  X,
Scalar  time,
Scalar  stepSize,
Scalar  stageNumber,
const Teuchos::RCP< Thyra::VectorBase< Scalar > > &  F 
) const

Definition at line 495 of file Tempus_StepperIMEX_RK_impl.hpp.

template<typename Scalar >
void Tempus::StepperIMEX_RK< Scalar >::evalImplicitModelExplicitly ( const Teuchos::RCP< const Thyra::VectorBase< Scalar > > &  X,
Scalar  time,
Scalar  stepSize,
Scalar  stageNumber,
const Teuchos::RCP< Thyra::VectorBase< Scalar > > &  G 
) const

Definition at line 463 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
virtual Scalar Tempus::StepperIMEX_RK< Scalar >::getAlpha ( const Scalar  dt) const
inlinevirtual

Return alpha = d(xDot)/dx.

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 321 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
virtual Scalar Tempus::StepperIMEX_RK< Scalar >::getBeta ( const Scalar  ) const
inlinevirtual

Return beta = d(x)/dx.

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 327 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperIMEX_RK< Scalar >::getDefaultParameters ( ) const
virtual

Implements Tempus::Stepper< Scalar >.

Definition at line 718 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperIMEX_RK< Scalar >::getDefaultStepperState ( )
virtual

Provide a StepperState to the SolutionState. This Stepper does not have any special state data, so just provide the base class StepperState with the Stepper description. This can be checked to ensure that the input StepperState can be used by this Stepper.

Implements Tempus::Stepper< Scalar >.

Definition at line 656 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
virtual Teuchos::RCP<const Thyra::ModelEvaluator<Scalar> > Tempus::StepperIMEX_RK< Scalar >::getModel ( )
inlinevirtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 281 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperIMEX_RK< Scalar >::getNonconstParameterList ( )

Definition at line 736 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
virtual Scalar Tempus::StepperIMEX_RK< Scalar >::getOrder ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 306 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
virtual Scalar Tempus::StepperIMEX_RK< Scalar >::getOrderMax ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 308 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
virtual Scalar Tempus::StepperIMEX_RK< Scalar >::getOrderMin ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 307 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
virtual OrderODE Tempus::StepperIMEX_RK< Scalar >::getOrderODE ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 317 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Teuchos::RCP< const Teuchos::ParameterList > Tempus::StepperIMEX_RK< Scalar >::getValidParameters ( ) const

Definition at line 702 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::initialize ( )
virtual

Initialize during construction and after changing input parameters.

Implements Tempus::Stepper< Scalar >.

Definition at line 381 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
virtual bool Tempus::StepperIMEX_RK< Scalar >::isExplicit ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 310 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
virtual bool Tempus::StepperIMEX_RK< Scalar >::isExplicitImplicit ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 312 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
virtual bool Tempus::StepperIMEX_RK< Scalar >::isImplicit ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 311 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
virtual bool Tempus::StepperIMEX_RK< Scalar >::isMultiStepMethod ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 315 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
virtual bool Tempus::StepperIMEX_RK< Scalar >::isOneStepMethod ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 314 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setExplicitTableau ( std::string  stepperType,
Teuchos::RCP< Teuchos::ParameterList >  pList 
)
virtual

Set the explicit tableau from ParameterList.

Definition at line 246 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setExplicitTableau ( Teuchos::RCP< const RKButcherTableau< Scalar > >  explicitTableau)
virtual

Set the explicit tableau from tableau.

Definition at line 257 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setImplicitTableau ( std::string  stepperType,
Teuchos::RCP< Teuchos::ParameterList >  pList 
)
virtual

Set the implicit tableau from ParameterList.

Definition at line 269 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setImplicitTableau ( Teuchos::RCP< const RKButcherTableau< Scalar > >  implicitTableau)
virtual

Set the implicit tableau from tableau.

Definition at line 280 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setInitialConditions ( const Teuchos::RCP< SolutionHistory< Scalar > > &  solutionHistory)
virtual

Set the initial conditions and make them consistent.

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 416 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setModel ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel)
virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 291 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setModelPair ( const Teuchos::RCP< WrapperModelEvaluatorPairIMEX_Basic< Scalar > > &  modelPairIMEX)
virtual

Create WrapperModelPairIMEX from user-supplied ModelEvaluator pair.

The user-supplied ME pair can contain any user-specific IMEX interactions between explicit and implicit MEs.

Definition at line 318 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setModelPair ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  explicitModel,
const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  implicitModel 
)
virtual

Create WrapperModelPairIMEX from explicit/implicit ModelEvaluators.

Use the supplied explicit/implicit MEs to create a WrapperModelPairIMEX with basic IMEX interactions between explicit and implicit MEs.

Definition at line 346 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setObserver ( Teuchos::RCP< StepperObserver< Scalar > >  obs = Teuchos::null)
virtual

Set Observer.

Implements Tempus::Stepper< Scalar >.

Definition at line 359 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setParameterList ( const Teuchos::RCP< Teuchos::ParameterList > &  pl)

Definition at line 686 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::setTableaus ( Teuchos::RCP< Teuchos::ParameterList >  pList,
std::string  stepperType = "" 
)
virtual

Set both the explicit and implicit tableau from ParameterList.

Definition at line 92 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
void Tempus::StepperIMEX_RK< Scalar >::takeStep ( const Teuchos::RCP< SolutionHistory< Scalar > > &  solutionHistory)
virtual

Take the specified timestep, dt, and return true if successful.

Implements Tempus::Stepper< Scalar >.

Definition at line 530 of file Tempus_StepperIMEX_RK_impl.hpp.

template<class Scalar >
Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperIMEX_RK< Scalar >::unsetParameterList ( )

Definition at line 744 of file Tempus_StepperIMEX_RK_impl.hpp.

Member Data Documentation

template<class Scalar >
std::string Tempus::StepperIMEX_RK< Scalar >::description_
protected

Definition at line 357 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Teuchos::RCP<const RKButcherTableau<Scalar> > Tempus::StepperIMEX_RK< Scalar >::explicitTableau_
protected

Definition at line 359 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Teuchos::RCP<const RKButcherTableau<Scalar> > Tempus::StepperIMEX_RK< Scalar >::implicitTableau_
protected

Definition at line 360 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Scalar Tempus::StepperIMEX_RK< Scalar >::order_
protected

Definition at line 362 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
std::vector<Teuchos::RCP<Thyra::VectorBase<Scalar> > > Tempus::StepperIMEX_RK< Scalar >::stageF_
protected

Definition at line 365 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
std::vector<Teuchos::RCP<Thyra::VectorBase<Scalar> > > Tempus::StepperIMEX_RK< Scalar >::stageG_
protected

Definition at line 366 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperIMEX_RK< Scalar >::stageX_
protected

Definition at line 364 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Teuchos::RCP<StepperIMEX_RKObserver<Scalar> > Tempus::StepperIMEX_RK< Scalar >::stepperIMEX_RKObserver_
protected

Definition at line 370 of file Tempus_StepperIMEX_RK_decl.hpp.

template<class Scalar >
Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperIMEX_RK< Scalar >::xTilde_
protected

Definition at line 368 of file Tempus_StepperIMEX_RK_decl.hpp.

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