Implicit midpoint rule time integration scheme. More...

#include <timestepper.hpp>

Inheritance diagram for ImplMidpoint:

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Collaboration diagram for ImplMidpoint:

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Public Member Functions
	ImplMidpoint (MasterEq mastereq_, int ntime_, double total_time_, LinearSolverType linsolve_type_, int linsolve_maxiter_, Output output_, bool storeFWD_)
	Constructor for implicit midpoint scheme.

	~ImplMidpoint ()

virtual void	evolveFWD (const double tstart, const double tstop, Vec x)
	Evolves state forward using implicit midpoint rule.

virtual void	evolveBWD (const double tstart, const double tstop, const Vec x_stop, Vec x_adj, Vec grad, bool compute_gradient)
	Evolves adjoint backward using implicit midpoint rule and adds to reduced gradient.

int	NeumannSolve (Mat A, Vec b, Vec x, double alpha, bool transpose)
	Solves (I - alphaA) x = b using Neumann iterations.

Public Member Functions inherited from TimeStepper
	TimeStepper ()

	TimeStepper (MasterEq mastereq_, int ntime_, double total_time_, Output output_, bool storeFWD_)
	Constructor for time stepper.

virtual	~TimeStepper ()

Vec	getState (size_t tindex)
	Retrieves stored state at a specific time index.

void	setEvalLeakage (bool flag)

void	setEvalWeightedCost (bool flag, double width)

void	setEvalDPDM (bool flag)

void	setEvalEnergy (bool flag)

double	getLeakageIntegral ()

double	getWeightedCostIntegral ()

double	getEnergyIntegral ()

double	getDPDMIntegral ()

Vec	solveODE (int initid, Vec rho_t0)
	Solves the ODE forward in time.

void	solveAdjointODE (Vec rho_t0_bar, Vec finalstate, double Jbar_leakage, double Jbar_weightedcost, double Jbar_dpdm, double Jbar_energy)
	Solves the adjoint ODE backward in time.

double	evalLeakage (const Vec x)
	Evaluates leakage into guard levels.

void	evalLeakage_diff (const Vec x, Vec xbar, double Jbar)
	Computes derivative of leakage term.

double	evalWeightedCost (double time, const Vec x)
	Evaluates the weighted cost function term.

void	evalWeightedCost_diff (double time, const Vec x, Vec xbar, double Jbar)
	Computes derivative of weighted cost function term.

double	evalDpDm (Vec x, Vec xm1, Vec xm2)
	Evaluates second-order derivative variation for the state.

void	evalDpDm_diff (int n, Vec xbar, double Jbar)
	Computes derivative of second-order derivative variation term.

double	evalEnergy (double time)
	Evaluates energy integral term.

void	evalEnergy_diff (double time, double Jbar, Vec redgrad)
	Computes derivative of energy integral.

Protected Attributes
Vec	stage

Vec	stage_adj
	Intermediate stage vectors for forward and adjoint.

Vec	rhs

Vec	rhs_adj
	Right-hand side vectors for forward and adjoint.

KSP	ksp
	PETSc's linear solver context for GMRES.

PC	preconditioner
	Preconditioner for linear solver.

LinearSolverType	linsolve_type
	Linear solver type (GMRES or NEUMANN)

int	linsolve_maxiter
	Maximum number of linear solver iterations.

double	linsolve_abstol
	Absolute tolerance for linear solver.

double	linsolve_reltol
	Relative tolerance for linear solver.

int	linsolve_iterstaken_avg
	Average number of linear solver iterations.

double	linsolve_error_avg
	Average error of linear solver.

int	linsolve_counter
	Counter for linear solve calls.

Vec	tmp

Vec	err
	Auxiliary vectors for Neumann iterations.

Protected Attributes inherited from TimeStepper
Vec	x
	Auxiliary vector for forward time stepping.

Vec	xadj
	Auxiliary vector needed for adjoint (backward) time stepping.

Vec	xprimal
	Auxiliary vector for backward time stepping.

std::vector< Vec >	store_states
	Storage for primal states during forward evolution.

std::vector< Vec >	dpdm_states
	Storage for states needed for second-order derivative penalty.

int	mpirank_world
	MPI rank in global communicator.

int	mpisize_petsc
	MPI size in Petsc communicator.

int	mpirank_petsc
	MPI rank in Petsc communicator.

PetscInt	localsize_u
	Size of local sub vector u or v in state x=[u,v].

PetscInt	ilow
	First index of the local sub vector u,v.

PetscInt	iupp
	Last index (+1) of the local sub vector u,v.

bool	eval_leakage
	Flag to compute leakage integral term.

bool	eval_energy
	Flag to compute energy integral term.

bool	eval_dpdm
	Flag to compute second-order derivative integral term.

bool	eval_weightedcost
	Flag to compute weighted cost integral term.

double	leakage_integral
	Sums the integral over leakage.

double	energy_integral
	Sums the energy term.

double	dpdm_integral
	Sums second-order derivative variation value.

double	weightedcost_integral
	Sums the integral over weighted cost function.

double	weightedcost_width
	Width parameter for weighted cost function.

Additional Inherited Members
Public Attributes inherited from TimeStepper
MasterEq *	mastereq
	Pointer to master equation solver.

int	ntime
	Number of time steps.

double	total_time
	Final evolution time.

double	dt
	Time step size.

bool	writeTrajectoryDataFiles
	Flag to determine whether or not trajectory data will be written to files during forward simulation *‍/.

Vec	redgrad
	Reduced gradient vector for optimization.

OptimTarget *	optim_target
	Pointer to optimization target specification.

Output *	output
	Pointer to output handler.

bool	storeFWD
	Flag to store primal states during forward evaluation.

Detailed Description

Implicit midpoint rule time integration scheme.

Second-order implicit method with symplectic properties. This is the default and recommended time integration, due to its stability and energy conservation properties.

Runge-Kutta tableau:

1/2 | 1/2
----------
    |  1

Constructor & Destructor Documentation

◆ ImplMidpoint()

ImplMidpoint::ImplMidpoint	(	MasterEq *	mastereq_,
		int	ntime_,
		double	total_time_,
		LinearSolverType	linsolve_type_,
		int	linsolve_maxiter_,
		Output *	output_,
		bool	storeFWD_
	)

Constructor for implicit midpoint scheme.

Parameters

mastereq_	Pointer to master equation solver
ntime_	Number of time steps
total_time_	Final evolution time
linsolve_type_	Linear solver type (GMRES or NEUMANN)
linsolve_maxiter_	Maximum linear solver iterations
output_	Pointer to output handler
storeFWD_	Flag to store forward states

◆ ~ImplMidpoint()

ImplMidpoint::~ImplMidpoint ( )

Member Function Documentation

◆ evolveBWD()

void ImplMidpoint::evolveBWD	(	const double	tstart,
		const double	tstop,
		const Vec	x_stop,
		Vec	x_adj,
		Vec	grad,
		bool	compute_gradient
	)

virtual

Evolves adjoint backward using implicit midpoint rule and adds to reduced gradient.

Parameters

tstart	Start time (backward evolution)
tstop	Stop time (backward evolution)
x_stop	State at stop time
x_adj	Adjoint state vector
grad	Gradient vector to update
compute_gradient	Flag to compute gradient

Reimplemented from TimeStepper.

Reimplemented in CompositionalImplMidpoint.

◆ evolveFWD()

void ImplMidpoint::evolveFWD	(	const double	tstart,
		const double	tstop,
		Vec	x
	)

virtual

Evolves state forward using implicit midpoint rule.

Parameters

tstart	Start time
tstop	Stop time
x	State vector to evolve

Implements TimeStepper.

Reimplemented in CompositionalImplMidpoint.

◆ NeumannSolve()

int ImplMidpoint::NeumannSolve	(	Mat	A,
		Vec	b,
		Vec	x,
		double	alpha,
		bool	transpose
	)

Solves (I - alpha*A) * x = b using Neumann iterations.

Parameters

A	Matrix A
b	Right-hand side vector
x	Solution vector
alpha	Scaling parameter
transpose	Flag to solve transposed system (I - alphaA^T)x = b

Returns: int Number of iterations taken

Member Data Documentation

◆ err

Vec ImplMidpoint::err

protected

Auxiliary vectors for Neumann iterations.

◆ ksp

KSP ImplMidpoint::ksp

protected

PETSc's linear solver context for GMRES.

◆ linsolve_abstol

double ImplMidpoint::linsolve_abstol

protected

Absolute tolerance for linear solver.

◆ linsolve_counter

int ImplMidpoint::linsolve_counter

protected

Counter for linear solve calls.

◆ linsolve_error_avg

double ImplMidpoint::linsolve_error_avg

protected

Average error of linear solver.

◆ linsolve_iterstaken_avg

int ImplMidpoint::linsolve_iterstaken_avg

protected

Average number of linear solver iterations.

◆ linsolve_maxiter

int ImplMidpoint::linsolve_maxiter

protected

Maximum number of linear solver iterations.

◆ linsolve_reltol

double ImplMidpoint::linsolve_reltol

protected

Relative tolerance for linear solver.

◆ linsolve_type

LinearSolverType ImplMidpoint::linsolve_type

protected

Linear solver type (GMRES or NEUMANN)

◆ preconditioner

PC ImplMidpoint::preconditioner

protected

Preconditioner for linear solver.

◆ rhs

Vec ImplMidpoint::rhs

protected

◆ rhs_adj

Vec ImplMidpoint::rhs_adj

protected

Right-hand side vectors for forward and adjoint.

◆ stage

Vec ImplMidpoint::stage

protected

◆ stage_adj

Vec ImplMidpoint::stage_adj

protected

Intermediate stage vectors for forward and adjoint.

◆ tmp

Vec ImplMidpoint::tmp

protected

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

/home/runner/work/quandary/quandary/include/timestepper.hpp
/home/runner/work/quandary/quandary/src/timestepper.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ImplMidpoint()

◆ ~ImplMidpoint()

Member Function Documentation

◆ evolveBWD()

◆ evolveFWD()

◆ NeumannSolve()

Member Data Documentation

◆ err

◆ ksp

◆ linsolve_abstol

◆ linsolve_counter

◆ linsolve_error_avg

◆ linsolve_iterstaken_avg

◆ linsolve_maxiter

◆ linsolve_reltol

◆ linsolve_type

◆ preconditioner

◆ rhs

◆ rhs_adj

◆ stage

◆ stage_adj

◆ tmp