Solver for the adjoint jumps of an index-1 DAE. More...

#include <Tempus_AdjointDAEJumpSolver.hpp>

Public Types
typedef Thyra::VectorBase< Scalar >	Vector
typedef Thyra::MultiVectorBase< Scalar >	MultiVector
typedef Teuchos::ScalarTraits< Scalar >::magnitudeType	Mag

Public Member Functions
	AdjointDAEJumpSolver (const Teuchos::RCP< const DAEStructure< Scalar > > &dae, const Teuchos::RCP< const Teuchos::ParameterList > &pl=Teuchos::null)
	Constructor. pl (optional) is the "Algebraic Jump Solver" sublist.
bool	solve (const Thyra::ModelEvaluator< Scalar > &adjoint_model, const Thyra::ModelEvaluatorBase::InArgs< Scalar > &inArgs, const Scalar dt, const MultiVector &b, MultiVector &z) const
	Solve C^T z = b for each column of b.

Static Public Member Functions
static const std::string &	sublistName ()
	Name of the "Sensitivities" sublist with the options of this solver.
static Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters ()

Private Member Functions
Mag	residual (const Thyra::LinearOpBase< Scalar > &ET, const Thyra::LinearOpBase< Scalar > &AT, const MultiVector &b, const MultiVector &z, const Teuchos::Array< Mag > &b_norms, MultiVector &r) const

Private Attributes
Teuchos::RCP< const DAEStructure< Scalar > >	dae_
double	rel_tol_
int	max_iters_
double	alpha_factor_
double	alpha_growth_
int	max_alpha_increases_
double	min_reduction_
bool	verbose_

Detailed Description

template<class Scalar>
class Tempus::AdjointDAEJumpSolver< Scalar >

Solver for the adjoint jumps of an index-1 DAE.

For a "Final Time" or "Sum Over Times" response g, the adjoint of an index-1 DAE jumps at each response time t_k by the differential components of the solution z of C^T z = dg/dx^T, C = P_a A + P_d E, with E = df/dx_dot, A = df/dx at the forward state at t_k, and P_a, P_d the masks of the algebraic and differential equations (see DAEStructure), while its algebraic components give the term -df/dp^T (P_a z) of the sensitivity (see IntegratorAdjointSensitivity).

C is not assembled. The solver uses only evaluations of the adjoint model, which returns the transposed operators: E^T = W(1,0), A^T = W(0,1), and W(alpha,1) = (alpha E + A)^T. With D_alpha = P_a + P_d/alpha, W(alpha,1) D_alpha = C^T + A^T P_d / alpha, since the algebraic rows of E are zero. Hence P = W(alpha,1) D_alpha is a preconditioner of C^T, exact as alpha -> infinity (C is the limit of the row-scaled step matrix of backward Euler as the time step goes to zero), and the solver performs the preconditioned Richardson iterations z <- z + D_alpha^{-1} W(alpha,1)^{-1} (b - C^T z), with the linear solver of the adjoint model, starting from alpha = "Initial Alpha Factor" / dt, where dt is the time step size at t_k. The iteration matrix is P^{-1} A^T P_d / alpha: whenever an iteration reduces the residual by a factor larger than "Minimum Residual Reduction", alpha is multiplied by "Alpha Growth Factor" (and the solver of W(alpha,1) is rebuilt).

Options (sublist "Algebraic Jump Solver" of "Sensitivities"):

"Relative Tolerance" (default: 1e-10) on max_j |r_j|/|b_j| over the columns j.
"Maximum Iterations Per Alpha" (default: 20)
"Initial Alpha Factor" (default: 1.0)
"Alpha Growth Factor" (default: 10.0)
"Maximum Alpha Increases" (default: 8)
"Minimum Residual Reduction" (default: 0.5)
"Verbose" (default: false) Print the residual at each iteration.

Definition at line 72 of file Tempus_AdjointDAEJumpSolver.hpp.

Member Typedef Documentation

◆ Vector

template<class Scalar>

typedef Thyra::VectorBase<Scalar> Tempus::AdjointDAEJumpSolver< Scalar >::Vector

Definition at line 74 of file Tempus_AdjointDAEJumpSolver.hpp.

◆ MultiVector

template<class Scalar>

typedef Thyra::MultiVectorBase<Scalar> Tempus::AdjointDAEJumpSolver< Scalar >::MultiVector

Definition at line 75 of file Tempus_AdjointDAEJumpSolver.hpp.

◆ Mag

template<class Scalar>

typedef Teuchos::ScalarTraits<Scalar>::magnitudeType Tempus::AdjointDAEJumpSolver< Scalar >::Mag

Definition at line 76 of file Tempus_AdjointDAEJumpSolver.hpp.

Constructor & Destructor Documentation

◆ AdjointDAEJumpSolver()

template<class Scalar>

Tempus::AdjointDAEJumpSolver< Scalar >::AdjointDAEJumpSolver	(	const Teuchos::RCP< const DAEStructure< Scalar > > &	dae,
		const Teuchos::RCP< const Teuchos::ParameterList > &	pl = Teuchos::null )

inline

Constructor. pl (optional) is the "Algebraic Jump Solver" sublist.

Definition at line 101 of file Tempus_AdjointDAEJumpSolver.hpp.

Member Function Documentation

◆ sublistName()

template<class Scalar>

const std::string & Tempus::AdjointDAEJumpSolver< Scalar >::sublistName ( )

inlinestatic

Name of the "Sensitivities" sublist with the options of this solver.

Definition at line 79 of file Tempus_AdjointDAEJumpSolver.hpp.

◆ getValidParameters()

template<class Scalar>

Teuchos::RCP< const Teuchos::ParameterList > Tempus::AdjointDAEJumpSolver< Scalar >::getValidParameters ( )

inlinestatic

Definition at line 85 of file Tempus_AdjointDAEJumpSolver.hpp.

◆ solve()

template<class Scalar>

bool Tempus::AdjointDAEJumpSolver< Scalar >::solve	(	const Thyra::ModelEvaluator< Scalar > &	adjoint_model,
		const Thyra::ModelEvaluatorBase::InArgs< Scalar > &	inArgs,
		const Scalar	dt,
		const MultiVector &	b,
		MultiVector &	z ) const

inline

Solve C^T z = b for each column of b.

Parameters

adjoint_model	The adjoint model (W_op returns the transpose)
inArgs	Forward state at the response time (x, x_dot, t)
dt	Time step size at the response time
b	Right-hand side, dg/dx^T (x space)
z	Solution (residual space), overwritten

Returns true if the iterations converged.

Definition at line 140 of file Tempus_AdjointDAEJumpSolver.hpp.

◆ residual()

template<class Scalar>

Mag Tempus::AdjointDAEJumpSolver< Scalar >::residual	(	const Thyra::LinearOpBase< Scalar > &	ET,
		const Thyra::LinearOpBase< Scalar > &	AT,
		const MultiVector &	b,
		const MultiVector &	z,
		const Teuchos::Array< Mag > &	b_norms,
		MultiVector &	r ) const