timestepping::Euler Class Reference
Timestep strategy for the explicit Euler algorithm to solve first order problems in time. More...
#include <euler.hh>
Public Member Functions | |
| Euler (concepts::SolverFabric< Real > &fabric, concepts::Operator< Real > &D1, concepts::Operator< Real > &D0, timestepping::TimeVector &trhs, const concepts::Vector< Real > &Y0, Real dt) | |
| Constructor. More... | |
| virtual | ~Euler () |
Protected Member Functions | |
| virtual std::ostream & | info (std::ostream &os) const |
| Returns information in an output stream. More... | |
| virtual void | next () |
| The overloaded member function next() has to calculate the new right hand side and to release the solution vector. More... | |
Protected Attributes | |
| Real | dt_ |
| Time step size. More... | |
| concepts::Operator< Real > * | liCo_ |
| Operator of the linear equation system which is solved by the friend class TimeStepping. More... | |
| concepts::Vector< Real > | rhs_ |
| The right hand side vector of the linear equation system which is solved by the friend class TimeStepping. More... | |
| concepts::Vector< Real > | sol_ |
| The solution vector of the linear equation system which is solved by the friend class TimeStepping. More... | |
| std::unique_ptr< concepts::Operator< Real > > | solver_ |
| Solver for the linear system. More... | |
| Real | t_ |
| Time of the actual solution. More... | |
Private Attributes | |
| concepts::Operator< Real > & | D0_ |
| Space operator. More... | |
| TimeVector & | trhs_ |
| External driver function. More... | |
| TimeVector | Yn1_ |
| Store the latest timestep. More... | |
Detailed Description
Timestep strategy for the explicit Euler algorithm to solve first order problems in time.
![\[ [ D_1 \partial_t + D_0 ] y(x,t) = f(x,t) \]](form_773.png)
The scheme has convergence order 1. Please notice that this algorithm is not absolutely stable and may not converge if the stability condition is not fullfilled.
- See also
- H. R. Schwarz Numerische Mathematik, Teubner, 1997
Constructor & Destructor Documentation
◆ Euler()
| timestepping::Euler::Euler | ( | concepts::SolverFabric< Real > & | fabric, |
| concepts::Operator< Real > & | D1, | ||
| concepts::Operator< Real > & | D0, | ||
| timestepping::TimeVector & | trhs, | ||
| const concepts::Vector< Real > & | Y0, | ||
| Real | dt | ||
| ) |
Constructor.
- Parameters
-
D1 Space operator D1 D0 Space operator D0 trhs Timedependent external driver f(x,t) Y0 Initial condition y(x,0) dt Time step size
◆ ~Euler()
|
virtual |
Member Function Documentation
◆ info()
|
protectedvirtual |
Returns information in an output stream.
Reimplemented from concepts::OutputOperator.
◆ next()
|
protectedvirtual |
The overloaded member function next() has to calculate the new right hand side and to release the solution vector.
Then the Timestepping solver can set the new solution.
Implements timestepping::TimeStepStrategy.
Member Data Documentation
◆ D0_
|
private |
◆ dt_
|
protectedinherited |
Time step size.
Definition at line 77 of file strategy.hh.
◆ liCo_
|
protectedinherited |
Operator of the linear equation system which is solved by the friend class TimeStepping.
It can be stored as a linear combination of two operators. The exact form depends on the specific scheme.
- See also
- TimeStepping
Definition at line 65 of file strategy.hh.
◆ rhs_
|
protectedinherited |
The right hand side vector of the linear equation system which is solved by the friend class TimeStepping.
- See also
- TimeStepping
Definition at line 75 of file strategy.hh.
◆ sol_
|
protectedinherited |
The solution vector of the linear equation system which is solved by the friend class TimeStepping.
- See also
- TimeStepping
Definition at line 70 of file strategy.hh.
◆ solver_
|
protectedinherited |
Solver for the linear system.
Definition at line 59 of file strategy.hh.
◆ t_
|
protectedinherited |
Time of the actual solution.
Definition at line 79 of file strategy.hh.
◆ trhs_
|
private |
◆ Yn1_
|
private |
The documentation for this class was generated from the following file:
- timestepping/euler.hh