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Feel++ 0.111.0-preview.14
Finite Element Embedded Library in C++
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Feel++ 0.111.0-preview.14
Finite Element Embedded Library in C++
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Backward differencing formula time discretization. More...
Inheritance diagram for Feel::Bdf< SpaceType >: Collaboration diagram for Feel::Bdf< SpaceType >:Public Types | |
| typedef std::shared_ptr< bdf_type > | bdf_ptrtype |
| typedef Bdf< SpaceType > | bdf_type |
| typedef space_type::element_ptrtype | element_ptrtype |
| typedef space_type::element_type | element_type |
| typedef node< value_type >::type | node_type |
| typedef space_type::return_type | return_type |
| typedef std::shared_ptr< space_type > | space_ptrtype |
| typedef SpaceType | space_type |
| typedef super::time_iterator | time_iterator |
| typedef std::vector< element_ptrtype > | unknowns_type |
| typedef element_type::value_type | value_type |
| Public Types inherited from Feel::TSBase | |
| typedef std::vector< double >::const_iterator | time_const_iterator |
| typedef std::vector< double >::iterator | time_iterator |
| typedef std::vector< double > | time_values_map_type |
Public Member Functions | |
| void | applyRemesh (space_ptrtype const &space, std::shared_ptr< MatrixSparse< double > > const &matInterp) |
| apply a remesh by given the new functionspace and the interpolation matrix between previous and new function space | |
| Bdf (Bdf const &b) | |
| copy operator | |
| Bdf (space_ptrtype const &__space, std::string const &name, std::string const &prefix, po::variables_map const &vm, int order, double ti, double tf, double dt, bool steady, bool reverse, bool restart, std::string const &restart_path, bool restart_at_last_save, bool save, int freq, bool rank_proc_in_files_name, std::string const &format, int n_consecutive_save) | |
| Bdf (space_ptrtype const &space, std::string const &name, std::string const &prefix="", po::variables_map const &vm=Environment::vm()) | |
| Constructor. More... | |
| int | bdfOrder () const |
| return the order in time | |
| std::string | bdfPrefix () const |
| return the prefix | |
| bdf_ptrtype | deepCopy () const |
| return a deep copy of the bdf object | |
| space_ptrtype const & | functionSpace () const |
| void | initialize (element_type const &u0) |
| Initialize all the entries of the unknown vector to be derived with the vector u0 (duplicated) | |
| void | initialize (unknowns_type const &uv0) |
| Initialize all the entries of the unknown vector to be derived with a set of vectors uv0. | |
| void | loadCurrent () |
| Load current unknown in a file (hdf5, binary, ...) More... | |
| double | next () const override |
| Move to next time step (solution not shifted). More... | |
| template<typename container_type > | |
| double | next (typename space_type::template Element< value_type, container_type > const &u_curr) |
| Move to next time step with solution shift. | |
| int | numberOfConsecutiveSave () const |
| return number of consecutive save | |
| int | numberOfIterationsBetweenOrderChange () const |
| return the number of iterations between order change | |
| int | numberOfIterationsSinceOrderChange () const |
| return the number of iterations since last order change | |
| element_type const & | poly () const |
| Compute the polynomial extrapolation approximation of order n-1 of u^{n+1} defined by the n stored state vectors. | |
| double | polyCoefficient (int i) const |
| Return \( \alpha_i \). | |
| element_type const & | polyDeriv () const |
| Returns the right hand side \( \bar{p} \) of the time derivative formula. | |
| double | polyDerivCoefficient (int i) const |
| Return \( \frac{\alpha_i}{\Delta t} \). | |
| element_ptrtype const & | polyDerivPtr () const |
| Returns the right hand side \( \bar{p} \) of the time derivative formula. | |
| element_ptrtype const & | polyPtr () const |
| Compute the polynomial extrapolation approximation of order n-1 of u^{n+1} defined by the n stored state vectors. | |
| void | print () const override |
| element_type & | prior () |
| element_type const & | prior () const |
| std::map< int, double > | priorTimes () const override |
| return a vector of the times prior to timeInitial() (included) More... | |
| double | restart () |
| restart the bdf | |
| void | setNumberOfConsecutiveSave (int n) |
| set number of consecutive save | |
| void | setOrder (int order) |
| void | setTimeOrder (int order) |
| template<typename container_type > | |
| void | setUnknown (int i, typename space_type::template Element< value_type, container_type > const &e) |
| template<typename container_type > | |
| void | shiftRight (typename space_type::template Element< value_type, container_type > const &u_curr) |
| Update the vectors of the previous time steps by shifting on the right the old values. More... | |
| void | showMe (std::ostream &__out=std::cout) const |
| double | start () |
| start the bdf | |
| double | start (element_type const &u0) |
| double | start (unknowns_type const &uv0) |
| int | timeOrder () const |
| return the curent order used at current time time | |
| element_type & | unknown (int i) |
| Return the previous element at previous time i-1. | |
| element_ptrtype | unknownPtr (int i) |
| Return the previous element at previous time i-1. | |
| unknowns_type & | unknowns () |
| Return a vector with the last n state vectors. | |
| unknowns_type const & | unknowns () const |
| Return a vector with the last n state vectors. | |
| void | updateDerivative (element_type &u, int i=0) const |
| update field \u with derivative at previous time indexed by \i (i.e. curent_time - i - 1) | |
| Public Member Functions inherited from Feel::TSBase | |
| bool | doRestartAtLastSave () const |
| return value of do restart at last save | |
| std::string | fileFormat () const |
| return file format saved and loaded : binary or hdf5 | |
| bool | isFinished () const |
| return true if Bdf is finished, false otherwise | |
| bool | isRestart () const |
| return the value of the bool restart | |
| bool | isReverse () const |
| return the reverse time loop state. | |
| bool | isReverseLoad () const |
| return the reverse time loop state. | |
| bool | isRunning () const |
| bool | isSteady () const |
| bool | isStopped () const |
| int | iteration () const |
| return the current iteration | |
| const int | iterationNumber () const |
| return the number of iteration | |
| virtual double | next () const |
| advance in time More... | |
| int | nRestart () const |
| return the number of restarts | |
| TSBase & | operator= (TSBase const &b) |
| fs::path | path () |
| return the relative path where the bdf data is stored | |
| std::string const & | prefix () const |
| virtual void | print () const |
| virtual std::map< int, double > | priorTimes () const |
| bool | rankProcInNameOfFiles () const |
| double | realTimePerIteration () const |
| return the real time in seconds spent in the iteration | |
| void | reloadMetaData () |
| reload metadata to get all time step already done | |
| double | restart () |
| restart the bdf | |
| fs::path | restartPath () |
| int | restartStepBeforeLastSave () const |
| return the step index before the last used to restart | |
| int | saveFreq () const |
| bool | saveInFile () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
| save/load Bdf metadata | |
| void | setfileFormat (std::string s) |
| void | setPathSave (std::string s) |
| void | setRankProcInNameOfFiles (bool b) |
| void | setRestart (bool doRestart) |
| void | setRestartAtLastSave (bool b) |
| void | setRestartPath (std::string const &s) |
| void | setReverse (bool reverse=false) |
| Reverse time (iteration always start at 0!) | |
| void | setReverseLoad (bool reverseLoad=false) |
| Load saved unknown beginning from last iteration. In bdf, solutions are saved from Ti (iter 0) ->Tf (iter N) in hdf5 files indexed by the iteration. If we reverse bdf, it runs from Tf (iter 0) -> Ti (iter N). To read hdf5 solution from files, we have to load the file N at Ti. Therefore reversing iteration index to load the correct file. Note: it is not required if the solution has to be saved. | |
| void | setSaveFreq (int v) |
| void | setSaveInFile (bool b) |
| void | setSteady (bool steady=true) |
| void | setTimeFinal (double T) |
| void | setTimeInitial (double ti) |
| void | setTimeStep (double dt) |
| virtual void | shiftRight () |
| double | start () |
| start the bdf | |
| TSState | state () const |
| return the state of the BDF | |
| TSStragegy | strategy () const |
| double | time () const |
| return the current time | |
| double | timeFinal () const |
| return the final time | |
| double | timeInitial () const |
| return the initial time | |
| double | timeStep () const |
| return the final step | |
| time_values_map_type | timeValues () const |
| return vector of time | |
| TSBase (std::string name, std::string const &prefix, WorldComm const &worldComm, po::variables_map const &vm, double ti, double tf, double dt, bool steady, bool reverse, bool restart, std::string const &restart_path, bool restart_at_last_save, bool save, int freq, bool rank_proc_in_files_name, std::string const &format) | |
| TSBase (std::string name, std::string const &prefix, WorldComm const &worldComm, po::variables_map const &vm=Environment::vm()) | |
| TSBase (std::string name, WorldComm const &worldComm) | |
| TSBase (TSBase const &b) | |
| virtual void | update () |
| WorldComm const & | worldComm () const |
Friends | |
| class | boost::serialization::access |
Additional Inherited Members | |
| Protected Member Functions inherited from Feel::TSBase | |
| void | init () |
| Protected Attributes inherited from Feel::TSBase | |
| bool | M_displayStats |
| indicates if display stat is enabled | |
| double | M_dt |
| timestep | |
| std::string | M_fileFormat |
| file format saved and loaded : binary or hdf5 | |
| int | M_iteration |
| iteration | |
| int | M_n_restart |
| restart | |
| std::string | M_name |
| name of the file holding the bdf data | |
| fs::path | M_path_save |
| path to the directory to store the functions | |
| std::string | M_prefix |
| bool | M_rankProcInNameOfFiles |
| put the rank of the processor in generated files | |
| double | M_real_time_per_iteration |
| real time spent per iteration (in seconds) | |
| bool | M_restart |
| do a restart | |
| bool | M_restartAtLastSave |
| do restart with ti the last save | |
| fs::path | M_restartPath |
| restart path | |
| int | M_restartStepBeforeLastSave |
| do restart with the ieme step before the last save | |
| bool | M_reverse |
| is reversed | |
| bool | M_reverseLoad |
| is file load from reverse | |
| int | M_saveFreq |
| frequence of save solutions | |
| bool | M_saveInFile |
| Save solutions in file after each step. | |
| TSState | M_state |
| state of the time stepping algorithm | |
| bool | M_steady |
| is steady | |
| double | M_Tf |
| final time | |
| double | M_Ti |
| initial time to start | |
| double | M_time |
| time | |
| time_values_map_type | M_time_values_map |
| vector that holds the time order at each bdf step More... | |
| Feel::Timer | M_timer |
| timer for real time per iteration | |
| WorldComm | M_worldComm |
| mpi communicator tool | |
Backward differencing formula time discretization.
A differential equation of the form
\( M u' = A u + f \)
is discretized in time as
\( M p'(t_{k+1}) = A u_{k+1} + f_{k+1} \)
where p denotes the polynomial of order n in t that interpolates \( (t_i,u_i) \) for \( i = k-n+1,...,k+1\).
The approximative time derivative \( p'(t_{k+1}) \) is a linear combination of state vectors \(u_i\):
\( p'(t_{k+1}) = \frac{1}{\Delta t} (\alpha_0 u_{k+1} - \sum_{i=0}^n \alpha_i u_{k+1-i} )\)
Thus we have
\( \frac{\alpha_0}{\Delta t} M u_{k+1} = A u_{k+1} + f + M \bar{p} \)
with
\( \bar{p} = \frac{1}{\Delta t} \sum_{i=1}^n \alpha_i u_{k+1-i} \)
This class stores the n last state vectors in order to be able to calculate \( \bar{p} \). It also provides \( \alpha_i \) and can extrapolate the new state from the n last states with a polynomial of order n-1:
\( u_{k+1} \approx \sum_{i=0}^{n-1} \beta_i u_{k-i} \)
| Feel::Bdf< SpaceType >::Bdf | ( | space_ptrtype const & | space, |
| std::string const & | name, | ||
| std::string const & | prefix = "", |
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| po::variables_map const & | vm = Environment::vm() |
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| ) |
Constructor.
| space | approximation space |
| name | name of the BDF |
| space_ptrtype const & Feel::Bdf< SpaceType >::functionSpace | ( | ) | const |
| void Feel::Bdf< SpaceType >::loadCurrent |
Load current unknown in a file (hdf5, binary, ...)
Load current unknown in a file (hdf5, binary, ...) The filename depends on the bdf name and the time iteration.
Notes:
setReverse(true), the iteration 0 will be loaded.setReverseLoad(true) to load existing unknowns from last iteration! It is require after a restart if time loop sense changed.
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overridevirtual |
Move to next time step (solution not shifted).
Reimplemented from Feel::TSBase.
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overridevirtual |
Reimplemented from Feel::TSBase.
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overridevirtual |
return a vector of the times prior to timeInitial() (included)
Reimplemented from Feel::TSBase.
| void Feel::Bdf< SpaceType >::shiftRight | ( | typename space_type::template Element< value_type, container_type > const & | u_curr | ) |
Update the vectors of the previous time steps by shifting on the right the old values.
| u_curr | current (new) value of the state vector |
Referenced by Feel::Bdf< SpaceType >::polyCoefficient().
1.9.3