Here are the classes, structs, unions and interfaces with brief descriptions:

[detail level 12]

Tempus
AdjointAuxSensitivityModelEvaluator	ModelEvaluator for forming adjoint sensitivity equations
AdjointSensitivityModelEvaluator	ModelEvaluator for forming adjoint sensitivity equations
AuxiliaryIntegralModelEvaluator	ModelEvaluator for integrating auxiliary equations
CombinedForwardSensitivityModelEvaluator	Transform a ModelEvaluator's sensitivity equations to its residual
Stepper	Thyra Base interface for time steppers
SolutionHistory	SolutionHistory is basically a container of SolutionStates. SolutionHistory maintains a collection of SolutionStates for later retrival and reuse, such as checkpointing, restart, and undo operations
TimeStepControl	TimeStepControl manages the time step size. There several mechanicisms that effect the time step size and handled with this class:
Integrator	Thyra Base interface for time integrators. Time integrators are designed to advance the solution from an initial time, , to a final time,
IntegratorAdjointSensitivity	Time integrator suitable for adjoint sensitivity analysis
IntegratorBasic	Basic time integrator
IntegratorForwardSensitivity	Time integrator implementing forward sensitivity analysis
IntegratorObserver	IntegratorObserver class for time integrators
IntegratorObserverBasic	IntegratorObserverBasic class for time integrators. This basic class has simple no-op functions, as all basic functionality should be handled through other methods
IntegratorObserverComposite	This observer is a composite observer,
IntegratorObserverLogging	This observer logs calls to observer functions. This observer simply logs and counts the calls to each of the observer functions. This is useful in monirtoring and debugging the time integration
IntegratorPseudoTransientAdjointSensitivity	Time integrator suitable for pseudotransient adjoint sensitivity analysis
IntegratorPseudoTransientForwardSensitivity	Time integrator suitable for pseudotransient forward sensitivity analysis
Interpolator	Base strategy class for interpolation functionality
InterpolatorFactory	Interpolator factory
InterpolatorLagrange	Concrete implemenation of `Interpolator` that does simple lagrange interpolation
PhysicsState	PhysicsState is a simple class to hold information about the physics
RKButcherTableau	Runge-Kutta methods
General_RKButcherTableau
GeneralExplicit_RKBT	General Explicit Runge-Kutta Butcher Tableau
BackwardEuler_RKBT	Backward Euler Runge-Kutta Butcher Tableau
ForwardEuler_RKBT	Forward Euler Runge-Kutta Butcher Tableau
Explicit4Stage4thOrder_RKBT	Runge-Kutta 4th order Butcher Tableau
ExplicitBogackiShampine32_RKBT	Explicit RK Bogacki-Shampine Butcher Tableau
ExplicitMerson45_RKBT	Explicit RK Merson Butcher Tableau
Explicit3_8Rule_RKBT	Explicit RK 3/8th Rule Butcher Tableau
Explicit4Stage3rdOrderRunge_RKBT	RK Explicit 4 Stage 3rd order by Runge
Explicit5Stage3rdOrderKandG_RKBT	RK Explicit 5 Stage 3rd order by Kinnmark and Gray
Explicit3Stage3rdOrder_RKBT	RK Explicit 3 Stage 3rd order
Explicit3Stage3rdOrderTVD_RKBT	RK Explicit 3 Stage 3rd order TVD
Explicit3Stage3rdOrderHeun_RKBT	RK Explicit 3 Stage 3rd order by Heun
Explicit2Stage2ndOrderRunge_RKBT	RK Explicit 2 Stage 2nd order by Runge
ExplicitTrapezoidal_RKBT	RK Explicit Trapezoidal
GeneralDIRK_RKBT	General Implicit Runge-Kutta Butcher Tableau
SDIRK1Stage1stOrder_RKBT	SDIRK 1 Stage 1st order
SDIRK2Stage2ndOrder_RKBT	SDIRK 2 Stage 2nd order
SDIRK2Stage3rdOrder_RKBT	SDIRK 2 Stage 3rd order
EDIRK2Stage3rdOrder_RKBT	EDIRK 2 Stage 3rd order
Implicit3Stage6thOrderKuntzmannButcher_RKBT
Implicit4Stage8thOrderKuntzmannButcher_RKBT
Implicit2Stage4thOrderHammerHollingsworth_RKBT
IRK1StageTheta_RKBT
EDIRK2StageTheta_RKBT
Implicit1Stage2ndOrderGauss_RKBT
Implicit2Stage4thOrderGauss_RKBT
Implicit3Stage6thOrderGauss_RKBT
Implicit1Stage1stOrderRadauA_RKBT
Implicit2Stage3rdOrderRadauA_RKBT
Implicit3Stage5thOrderRadauA_RKBT
Implicit1Stage1stOrderRadauB_RKBT
Implicit2Stage3rdOrderRadauB_RKBT
Implicit3Stage5thOrderRadauB_RKBT
Implicit2Stage2ndOrderLobattoA_RKBT
Implicit3Stage4thOrderLobattoA_RKBT
Implicit4Stage6thOrderLobattoA_RKBT
Implicit2Stage2ndOrderLobattoB_RKBT
Implicit3Stage4thOrderLobattoB_RKBT
Implicit4Stage6thOrderLobattoB_RKBT
Implicit2Stage2ndOrderLobattoC_RKBT
Implicit3Stage4thOrderLobattoC_RKBT
Implicit4Stage6thOrderLobattoC_RKBT
SDIRK5Stage5thOrder_RKBT
SDIRK5Stage4thOrder_RKBT
SDIRK3Stage4thOrder_RKBT
SDIRK21_RKBT	SDIRK 2(1) pair
RKButcherTableauBuilder	Runge-Kutta Builder class. This factory creates RKButcherTableau objects given the description string from the RKButcherTableau object
SensitivityModelEvaluatorBase	A ModelEvaluator decorator for sensitivity analysis
SolutionState	Solution state for integrators and steppers. SolutionState contains the metadata for solutions and the solutions themselves
SolutionStateMetaData	Solution state meta data
StaggeredForwardSensitivityModelEvaluator	Transform a ModelEvaluator's sensitivity equations to its residual
StepperBackwardEuler	Backward Euler time stepper
StepperBackwardEulerTimeDerivative	Time-derivative interface for Backward Euler
StepperFactory	Stepper factory
StepperBackwardEulerObserver	StepperBackwardEulerObserver class for StepperBackwardEuler
StepperBDF2	BDF2 (Backward-Difference-Formula-2) time stepper
StepperBDF2TimeDerivative	Time-derivative interface for BDF2
StepperBDF2Observer	StepperBDF2Observer class for StepperBDF2
StepperDIRK	Diagonally Implicit Runge-Kutta (DIRK) time stepper
StepperDIRKTimeDerivative	Time-derivative interface for DIRK
StepperDIRKObserver	StepperDIRKObserver class for StepperDIRK
StepperExplicit	Thyra Base interface for implicit time steppers
StepperExplicitRK	Explicit Runge-Kutta time stepper
StepperExplicitRKObserver	StepperExplicitRKObserver class for StepperExplicitRK
StepperForwardEuler	Forward Euler time stepper
StepperForwardEulerObserver	StepperForwardEulerObserver class for StepperForwardEuler
StepperHHTAlpha	HHT-Alpha time stepper
StepperIMEX_RK	Implicit-Explicit Runge-Kutta (IMEX-RK) time stepper
StepperIMEX_RKTimeDerivative	Time-derivative interface for IMEX RK
StepperIMEX_RK_Partition	Partitioned Implicit-Explicit Runge-Kutta (IMEX-RK) time stepper
StepperIMEX_RKPartTimeDerivative	Time-derivative interface for Partitioned IMEX RK
StepperIMEX_RKObserver	StepperIMEX_RKObserver class for StepperIMEX_RK
StepperIMEX_RKPartObserver	StepperIMEX_RKPartObserver class for StepperIMEX_RK_Partition
ImplicitODEParameters
StepperImplicit	Thyra Base interface for implicit time steppers
StepperLeapfrog	Leapfrog time stepper
StepperLeapfrogObserver	StepperLeapfrogObserver class for StepperLeapfrog
StepperNewmarkExplicitAForm	Newmark Explicit time stepper
StepperNewmarkImplicitAForm	Newmark time stepper in acceleration form (a-form)
StepperNewmarkImplicitDForm	Newmark time stepper
StepperObserver	StepperObserver class for Stepper class
StepperObserverBasic	StepperObserverBasic class for Stepper class
StepperOperatorSplit	OperatorSplit stepper loops through the Stepper list
StepperOperatorSplitObserver	StepperOperatorSplitObserver class for StepperOperatorSplit
StepperOptimizationInterface	Stepper interface to support full-space optimization
StepperStaggeredForwardSensitivity	A stepper implementing staggered forward sensitivity analysis
StepperState	StepperState is a simple class to hold state information about the stepper
StepperTrapezoidal	Trapezoidal method time stepper
StepperTrapezoidalTimeDerivative	Time-derivative interface for Trapezoidal method
StepperTrapezoidalObserver	StepperTrapezoidalObserver class for StepperTrapezoidal
TimeDerivative	This interface defines the time derivative connection between an implicit Stepper and WrapperModelEvaluator
TimeStepControlStrategy	StepControlStrategy class for TimeStepControl
TimeStepControlStrategyBasicVS	StepControlStrategy class for TimeStepControl
TimeStepControlStrategyComposite	StepControlStrategy class for TimeStepControl
TimeStepControlStrategyConstant	StepControlStrategy class for TimeStepControl
TimeStepControlStrategyIntegralController	StepControlStrategy class for TimeStepControl
TimeStepControlStrategyPID	StepControlStrategy class for TimeStepControl
WrapperModelEvaluator	A ModelEvaluator which wraps the application ModelEvaluator
WrapperModelEvaluatorBasic	A ModelEvaluator for residual evaluations given a state. This ModelEvaluator takes a state, x, and determines its residual, , which is suitable for a nonlinear solve. This is accomplished by computing the time derivative of the state, x_dot, (through Lambda functions), supplying the current time, and calling the application application ModelEvaluator, $f(x,\dot{x},t)$
WrapperModelEvaluatorPairIMEX	ModelEvaluator pair for implicit and explicit (IMEX) evaluations
WrapperModelEvaluatorPairIMEX_Basic	ModelEvaluator pair for implicit and explicit (IMEX) evaulations
WrapperModelEvaluatorPairIMEX_CombinedFSA	Specialization of IMEX ME for "combined" FSA method
WrapperModelEvaluatorPairIMEX_StaggeredFSA	Specialization of IMEX ME for "staggered" FSA method
WrapperModelEvaluatorPairPartIMEX_Basic	ModelEvaluator pair for implicit and explicit (IMEX) evaulations
WrapperModelEvaluatorPairPartIMEX_CombinedFSA	Specialization of IMEX-Part ME for "combined" FSA method
WrapperModelEvaluatorPairPartIMEX_StaggeredFSA	Specialization of IMEX-Part ME for "combined" FSA method
WrapperModelEvaluatorSecondOrder	A ModelEvaluator for residual evaluations given a state. This ModelEvaluator takes a state, x, and determines its residual, , which is suitable for a nonlinear solve. This is accomplished by computing the time derivative of the state, x_dot, (through Lambda functions), supplying the current time, and calling the application application ModelEvaluator, $f(\dot{x},x,t)$
Tempus_Test
PhysicsStateCounter	PhysicsStateCounter is a simple PhysicsState that counts steps
PhysicsStateTest_StepperForwardEuler	This is a Forward Euler time stepper to test the PhysicsState
ModelEvaluator1DFEM
CDR_Model	1D CGFEM model for convection/diffusion/reaction
Basis
HarmonicOscillatorModel	Consider the ODE: $m\ddot{x} + c\dot{x} + kx=f$ where $k \geq 0$ is a constant, is a constant damping parameter, is a constant forcing parameter, and is a constant mass parameter, with initial conditions are: $\begin{eqnarray} x(0) & = & 0\\ \dot{x}(0) & = & 1 \end{eqnarray}$ It is straight-forward to show that the exact solution to this ODE is: $\begin{eqnarray} x(t) & = & t(1+0.5\tilde{f}t), \hspace{3.6cm} if \hspace{0.2cm} k = c = 0 \\ & = & \frac{(\tilde{c}-\tilde{f})}{\tilde{c}^2}(1-e^{-\tilde{c}t}) + \frac{f}{c}t, \hspace{1.9cm} if \hspace{0.2cm} k = 0, c\neq 0 \\ & = & \frac{1}{\sqrt{\tilde{k}}}\sin(\sqrt{\tilde{k}}t) + \frac{f}{k}\left(1-\cos(\sqrt{\tilde{k}}t) \right), \hspace{0.2cm} if \hspace{0.2cm} k > 0, c = 0 \end{eqnarray}$ where $\tilde{c}\equiv c/m$ , $\tilde{k}\equiv k/m$ and $\tilde{f}\equiv f/m$ . While it is possible to derive the solution to this ODE for the case when and $c \neq 0$ , we do not consider that case here. When , , and , our ODE simplies to a canonical differential equation model of a ball thrown up in the air, with a parabolic trajectory solution, namely $x(t) = t(1-0.5t)$ where $t\in [0,2]$ . An EpetraExt version of this simplified version of the test is implemented in Piro::MockModelEval_B (see Trilinos/packages/piro/test), where it is used to test the Piro (EpetraExt) Newmark-Beta scheme (see input_Solver_NB.xml input file). When and , this test is equivalent to the SinCos model.
SinCosModel	Sine-Cosine model problem from Rythmos. This is a canonical Sine-Cosine differential equation $\mathbf{\ddot{x}}=-\mathbf{x}$ with a few enhancements. We start with the exact solution to the differential equation $\begin{eqnarray} x_{0}(t) & = & a+b\sin((f/L)t+\phi)\\ x_{1}(t) & = & b(f/L)\cos((f/L)t+\phi) \end{eqnarray}$ then the form of the model is $\begin{eqnarray} \frac{d}{dt}x_{0}(t) & = & x_{1}(t)\\ \frac{d}{dt}x_{1}(t) & = & \left(\frac{f}{L}\right)^{2}(a-x_{0}(t)) \end{eqnarray}$ where the default parameter values are , , and , and the initial conditions $\begin{eqnarray} x_{0}(t_{0}=0) & = & \gamma_{0}[=0]\\ x_{1}(t_{0}=0) & = & \gamma_{1}[=1] \end{eqnarray}$ determine the remaining coefficients $\begin{eqnarray} \phi & = & \arctan(((f/L)/\gamma_{1})(\gamma_{0}-a))-(f/L)t_{0}[=0]\\ b & = & \gamma_{1}/((f/L)cos((f/L)t_{0}+\phi))[=1] \end{eqnarray*}$
SteadyQuadraticModel	Simple quadratic equation with a stable steady-state. This is a simple differential equation $\mathbf{\dot{x}}=\mathbf{x}^2 - b^2$ which has steady state solutions $\mathbf{x} = \pm b$ . The solution $\mathbf{x} = b$ is stable if and the solution $\mathbf{x} = -b$ is stable if . This model is used to test pseudo-transient sensitivity analysis methods
VanDerPol_IMEX_ExplicitModel	Van der Pol model formulated for IMEX
VanDerPol_IMEX_ImplicitModel	Van der Pol model formulated for IMEX-RK
VanDerPol_IMEXPart_ImplicitModel	Van der Pol model formulated for the partitioned IMEX-RK
VanDerPolModel	Van der Pol model problem for nonlinear electrical circuit
LinearRegression	Linear regression class. Copied and modified from Rythmos
Teuchos
Thyra
AdjointLinearOpWithSolveFactory	Create a LinearOpWithSolveFactory for an adjoint linear op
AdjointPreconditioner	Concrete `PreconditionerBase` subclass that wraps a preconditioner operator in MultiVectorLinearOp
AdjointPreconditionerFactory	Concrete `PreconditionerFactoryBase` subclass that wraps a preconditioner in AdjointPreconditioner
BlockedTriangularLinearOpWithSolveFactory	Implicit subclass that takes a blocked triangular LOWB object and turns it into a LOWSB object
MultiVectorLinearOp	Implicit concrete `LinearOpBase` subclass that takes a flattended out multi-vector and performs a multi-RHS apply with it
MultiVectorLinearOpWithSolveFactory	Create a LinearOpWithSolveFactory for a flattened-out multi-vector
MultiVectorPreconditioner	Concrete `PreconditionerBase` subclass that wraps a preconditioner operator in MultiVectorLinearOp
MultiVectorPreconditionerFactory	Concrete `PreconditionerFactoryBase` subclass that wraps a preconditioner in MultiVectorPreconditioner
ReuseLinearOpWithSolveFactory	A LinearOpWithSolveFactory that is designed to reuse an already created/initialized preconditioner
ReusePreconditionerFactory	Concrete `PreconditionerFactoryBase` subclass that just returns an already created/initialized preconditioner object
ScaledIdentityLinearOpWithSolve	Implicit concrete `LinearOpBase` subclass that takes a flattended out multi-vector and performs a multi-RHS apply with it
ScaledIdentityLinearOpWithSolveFactory	Create a LinearOpWithSolveFactory for a flattened-out multi-vector