Reference documentation for deal.II version GIT relicensing-384-g4769914377 2024-04-13 09:00:02+00:00
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
Loading...
Searching...
No Matches
Public Types | Public Member Functions | Public Attributes | Private Member Functions | Private Attributes | List of all members
PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType > Class Template Reference

#include <deal.II/lac/petsc_ts.h>

Public Types

using real_type = PetscReal
 

Public Member Functions

 TimeStepper (const TimeStepperData &data=TimeStepperData(), const MPI_Comm mpi_comm=PETSC_COMM_WORLD)
 
 ~TimeStepper ()
 
 operator TS () const
 
TS petsc_ts ()
 
MPI_Comm get_mpi_communicator () const
 
void reinit ()
 
void reinit (const TimeStepperData &data)
 
void set_matrix (PMatrixType &P)
 
void set_matrices (AMatrixType &A, PMatrixType &P)
 
real_type get_time ()
 
real_type get_time_step ()
 
unsigned int get_step_number ()
 
unsigned int solve (VectorType &y)
 
unsigned int solve (VectorType &y, PMatrixType &P)
 
unsigned int solve (VectorType &y, AMatrixType &A, PMatrixType &P)
 

Public Attributes

std::function< void(const real_type t, const VectorType &y, const VectorType &y_dot, VectorType &res)> implicit_function
 
std::function< void(const real_type t, const VectorType &y, const VectorType &y_dot, const real_type alpha, AMatrixType &A, PMatrixType &P)> implicit_jacobian
 
std::function< void(const real_type t, const VectorType &y, VectorType &res)> explicit_function
 
std::function< void(const real_type t, const VectorType &y, AMatrixType &A, PMatrixType &P)> explicit_jacobian
 
std::function< void(const real_type t, const VectorType &y, const unsigned int step_number)> monitor
 
std::function< void(const real_type t, const VectorType &y, const VectorType &ydot, const real_type alpha)> setup_jacobian
 
std::function< void(const VectorType &src, VectorType &dst)> solve_with_jacobian
 
std::function< IndexSet()> algebraic_components
 
std::function< void(const real_type t, VectorType &y)> distribute
 
std::function< void(const real_type t, const unsigned int step, const VectorType &y, bool &resize)> decide_for_coarsening_and_refinement
 
std::function< void(const std::vector< VectorType > &all_in, std::vector< VectorType > &all_out)> interpolate
 

Private Member Functions

void setup_callbacks ()
 
void setup_algebraic_constraints (const VectorType &y)
 

Private Attributes

TS ts
 
SmartPointer< AMatrixType, TimeStepperA
 
SmartPointer< PMatrixType, TimeStepperP
 
PreconditionShell solve_with_jacobian_pc
 
bool restart_if_remesh
 
bool need_dae_tolerances
 
bool need_dummy_assemble
 
std::exception_ptr pending_exception
 
bool error_in_function
 

Detailed Description

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
class PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >

Interface to the PETSc TS solver for Ordinary Differential Equations and Differential-Algebraic Equations. The TS solver is described in the PETSc manual.

This class supports two kinds of formulations. The explicit formulation:

\[ \begin{cases} \dot y = G(t,y)\, , \\ y(t_0) = y_0\, , \\ \end{cases} \]

and the implicit formulation:

\[ \begin{cases} F(t,y,\dot y) = 0\, , \\ y(t_0) = y_0\, . \\ \end{cases} \]

The interface to PETSc is realized by means of std::function callbacks like in the SUNDIALS::IDA and SUNDIALS::ARKode classes.

TimeStepper supports any vector and matrix type having constructors and methods:

class VectorType : public Subscriptor
...
explicit VectorType(Vec);
...
Vec & petsc_vector();
...
class MatrixType : public Subscriptor
...
explicit MatrixType(Mat);
...
Mat & petsc_matrix();
...

In particular, the supported types are the ones that can wrap PETSc's native vector and matrix classes, that are able to modify them in place, and that can return PETSc native types when requested.

To use explicit solvers (like for example explicit Runge-Kutta methods), the user only needs to provide the implementation of \(G\) via the TimeStepper::explicit_function. For implicit solvers, users have also the alternative of providing the \(F\) function via TimeStepper::implicit_function. IMEX methods are also supported by providing both callbacks.

The default linearization procedure of an implicit solver instantiated with this class consists in using Jacobian-Free-Newton-Krylov; the action of tangent matrices inside a linear solver process are approximated via matrix-free finite-differencing of the nonlinear residual equations that are ODE-solver specific. For details, consult the PETSc manual.

Users can also provide the implementations of the Jacobians. This can be accomplished in two ways:

TimeStepper::set_matrices() must be used in case the user wants to provide the iteration matrix of the tangent system in the deal.II style approach, thus replacing the matrix-free linearization.

The correctness of the constructed Jacobians passed using TimeStepper::set_matrix() can be checked using

./myApp -snes_test_jacobian

See TimeStepper::set_matrix() and TimeStepper::set_matrices() for additional details.

The deal.II style approach still allows command line customization, like for example,

./myApp -snes_type newtontr -ksp_type cg

in case the user wants to change the default nonlinear solver to a trust region solver and iterate on the tangent system with CG, still using TimeStepper::solve_with_jacobian as a preconditioner.

The PETSc style approach has instead the advantage that only the matrix assembly procedure has to be implemented, thus allowing quicker implementations and faster turnaround for experimenting with linear solver preconditioning configurations via command line customizations, like for example,

./myApp -ksp_type cg -pc_type gamg
Note
This class, function, or variable is a template, and it can only be instantiated if the following condition is true: If your compiler supports the C++20 standard, then this constraint will be enforced by a C++20 requires clause.

Definition at line 334 of file petsc_ts.h.

Member Typedef Documentation

◆ real_type

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
using PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::real_type = PetscReal

Type that holds real-valued numbers.

Used to represent time and norms tolerances.

Definition at line 342 of file petsc_ts.h.

Constructor & Destructor Documentation

◆ TimeStepper()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::TimeStepper ( const TimeStepperData data = TimeStepperData(),
const MPI_Comm  mpi_comm = PETSC_COMM_WORLD 
)

Constructor.

◆ ~TimeStepper()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::~TimeStepper ( )

Destructor.

Member Function Documentation

◆ operator TS()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::operator TS ( ) const

Conversion operator to gain access to the underlying PETSc type. If you do this, you cut this class off some information it may need, so this conversion operator should only be used if you know what you do.

◆ petsc_ts()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
TS PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::petsc_ts ( )

Return the PETSc TS object.

◆ get_mpi_communicator()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
MPI_Comm PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::get_mpi_communicator ( ) const

Return the underlying MPI communicator.

◆ reinit() [1/2]

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
void PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::reinit ( )

Reset the solver, it does not change the customization.

◆ reinit() [2/2]

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
void PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::reinit ( const TimeStepperData data)

Reset solver. Change customization according to data.

◆ set_matrix()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
void PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::set_matrix ( PMatrixType &  P)

Set the preconditioning matrix only.

When used with TimeStepper::setup_jacobian and TimeStepper::solve_with_jacobian, PETSc will approximate the linear system matrix-vector product using an internal matrix-free representation.

When used with TimeStepper::implicit_jacobian or TimeStepper::explicit_jacobian, PETSc will use the same matrix for both preconditioning and matrix-vector products.

◆ set_matrices()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
void PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::set_matrices ( AMatrixType &  A,
PMatrixType &  P 
)

Set both the linear system matrix and the preconditioning matrix that PETSc will use (can be the same matrix). In this case, the Jacobian-Free-Newton-Krylov approach will not be used.

◆ get_time()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
real_type PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::get_time ( )

Return current time.

◆ get_time_step()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
real_type PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::get_time_step ( )

Return current time step.

◆ get_step_number()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
unsigned int PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::get_step_number ( )

Return current step number.

◆ solve() [1/3]

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
unsigned int PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::solve ( VectorType &  y)

Integrate the differential-algebraic equations starting from y.

This function returns the final number of computed steps. Upon returning, the y vector contains the solution of the DAE at the end time.

◆ solve() [2/3]

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
unsigned int PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::solve ( VectorType &  y,
PMatrixType &  P 
)

Integrate the differential-algebraic equations starting from y.

This function returns the final number of computed steps. Upon returning, the y vector contains the solution of the DAE at the end time.

Here we also set the matrix to precondition the tangent system.

◆ solve() [3/3]

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
unsigned int PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::solve ( VectorType &  y,
AMatrixType &  A,
PMatrixType &  P 
)

Integrate the differential-algebraic equations starting from y.

This function returns the final number of computed steps. Upon returning, the y vector contains the solution of the DAE at the end time.

Here we also set the matrices to describe and precondition the tangent system.

◆ setup_callbacks()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
void PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::setup_callbacks ( )
private

Setup callbacks.

This function is called inside TimeStepper::solve routines and does not need to be called by the user. It is used to reinitialize the solver if mesh adaption has been performed.

◆ setup_algebraic_constraints()

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
void PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::setup_algebraic_constraints ( const VectorType &  y)
private

Setup algebraic constraints.

This function is called inside TimeStepper::solve routines and does not need to be called by the user. It is used to reinitialize the solver if mesh adaption has been performed.

Member Data Documentation

◆ implicit_function

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const real_type t, const VectorType &y, const VectorType &y_dot, VectorType &res)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::implicit_function

Callback for the computation of the implicit residual \(F(t, y, \dot y)\).

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 475 of file petsc_ts.h.

◆ implicit_jacobian

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const real_type t, const VectorType &y, const VectorType &y_dot, const real_type alpha, AMatrixType &A, PMatrixType &P)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::implicit_jacobian

Callback for the computation of the implicit Jacobian \(\dfrac{\partial F}{\partial y} + \alpha \dfrac{\partial F}{\partial \dot y}\).

All implicit solvers implementations are recast to use the above linearization. The \(\alpha\) parameter is time-step and solver-type specific.

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 497 of file petsc_ts.h.

◆ explicit_function

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const real_type t, const VectorType &y, VectorType &res)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::explicit_function

Callback for the computation of the explicit residual \(G(t, y)\).

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 508 of file petsc_ts.h.

◆ explicit_jacobian

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const real_type t, const VectorType &y, AMatrixType &A, PMatrixType &P)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::explicit_jacobian

Callback for the computation of the explicit Jacobian \(\dfrac{\partial G}{\partial y}\).

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 523 of file petsc_ts.h.

◆ monitor

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const real_type t, const VectorType &y, const unsigned int step_number)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::monitor

Callback for monitoring the solution process.

This function is called by TimeStepper at the beginning of each time step.

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 539 of file petsc_ts.h.

◆ setup_jacobian

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const real_type t, const VectorType &y, const VectorType &ydot, const real_type alpha)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::setup_jacobian

Callback for the set up of the Jacobian system.

This callback gives full control to users to set up the linearized equations \(\dfrac{\partial F}{\partial y} + \alpha \dfrac{\partial F}{\partial \dot y}\).

All implicit solvers implementations are recast to use the above linearization. The \(\alpha\) parameter is time-step and solver-type specific.

Solvers must be provided via TimeStepper::solve_with_jacobian.

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 564 of file petsc_ts.h.

◆ solve_with_jacobian

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const VectorType &src, VectorType &dst)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::solve_with_jacobian

Callback for the solution of the tangent system set up with TimeStepper::setup_jacobian.

This is used as a preconditioner inside the Krylov process.

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 578 of file petsc_ts.h.

◆ algebraic_components

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<IndexSet()> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::algebraic_components

Callback to return an index set containing the algebraic components.

Implementation of this function is optional. If your equation is also algebraic (i.e., it contains algebraic constraints, or Lagrange multipliers), you should implement this function in order to return only these components of your system.

Definition at line 588 of file petsc_ts.h.

◆ distribute

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const real_type t, VectorType &y)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::distribute

Callback to distribute solution to hanging nodes.

Implementation of this function is optional. It is called at the end of each successful stage. The same functionality can be equivalently implemented in TimeStepper::solve_with_jacobian.

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 603 of file petsc_ts.h.

◆ decide_for_coarsening_and_refinement

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const real_type t, const unsigned int step, const VectorType &y, bool &resize)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::decide_for_coarsening_and_refinement

Callback to set up mesh adaption.

Implementation of this function is optional. resize must be set to true if mesh adaption is to be performed, false otherwise. The y vector contains the current solution, t the current time, @ step the step number. Solution transfer and actual mesh adaption must be performed in a separate callback, TimeStepper::interpolate

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 625 of file petsc_ts.h.

◆ interpolate

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::function<void(const std::vector<VectorType> &all_in, std::vector<VectorType> &all_out)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::interpolate

Callback to interpolate vectors and perform mesh adaption.

Implementation of this function is mandatory if TimeStepper::decide_for_coarsening_and_refinement is used. This function must perform mesh adaption and interpolate the discrete functions that are stored in all_in onto the refined and/or coarsenend grid. Output vectors must be created inside the callback.

Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions.

Definition at line 643 of file petsc_ts.h.

◆ ts

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
TS PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::ts
private

The PETSc object.

Definition at line 649 of file petsc_ts.h.

◆ A

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
SmartPointer<AMatrixType, TimeStepper> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::A
private

Pointers to the internal PETSc matrix objects.

Definition at line 654 of file petsc_ts.h.

◆ P

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
SmartPointer<PMatrixType, TimeStepper> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::P
private

Definition at line 655 of file petsc_ts.h.

◆ solve_with_jacobian_pc

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
PreconditionShell PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::solve_with_jacobian_pc
private

Object to apply solve_with_jacobian.

Definition at line 660 of file petsc_ts.h.

◆ restart_if_remesh

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
bool PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::restart_if_remesh
private

This flag is used to decide whether or not to restart the step if remeshing has been performed

Definition at line 666 of file petsc_ts.h.

◆ need_dae_tolerances

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
bool PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::need_dae_tolerances
private

This flag is set when changing the customization and used within solve.

Definition at line 671 of file petsc_ts.h.

◆ need_dummy_assemble

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
bool PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::need_dummy_assemble
private

This flag is used to support versions of PETSc older than 3.13.

Definition at line 676 of file petsc_ts.h.

◆ pending_exception

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
std::exception_ptr PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::pending_exception
mutableprivate

A pointer to any exception that may have been thrown in user-defined call-backs and that we have to deal after the KINSOL function we call has returned.

Definition at line 683 of file petsc_ts.h.

◆ error_in_function

template<typename VectorType = PETScWrappers::VectorBase, typename PMatrixType = PETScWrappers::MatrixBase, typename AMatrixType = PMatrixType>
bool PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::error_in_function
private

Internal data to handle recoverable errors.

Definition at line 688 of file petsc_ts.h.


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