marian::ImplicitScheme Class Reference
Class implements implicit schemes. More...
#include <implicitScheme.hpp>
Inheritance diagram for marian::ImplicitScheme:
Public Member Functions | |
| ImplicitScheme () | |
| defualt constructor | |
| ImplicitScheme (SmartPointer< TridiagonalSolver > solver) | |
| constructor | |
| void | setSolver (const SmartPointer< TridiagonalSolver > &solver) override |
| Provides a solver used in implicit scheme. | |
| std::vector< double > | solve (std::vector< double > f, const std::vector< SmartPointer< BoundaryCondition > > &bcs, const std::vector< double > &time_grid, const TridiagonalOperator &L) override |
| Solves PDE defined by provided linear operator L and initial and boundary conditions. More... | |
| std::vector< double > | solveAndSave (std::vector< double > f, const std::vector< SmartPointer< BoundaryCondition > > &bcs, const std::vector< double > &spatial_grid, const std::vector< double > &time_grid, const TridiagonalOperator &L, const std::string file_name) override |
| Solves PDE defined by provided linear operator L and initial and boundary conditions. Additionally saves solution to CSV file. More... | |
| std::string | info () const override |
| Returns scheme name. | |
 Public Member Functions inherited from marian::DCFDScheme< ImplicitScheme > | |
| virtual FDScheme * | clone () const |
| Virtual copy constructor. | |
| Public Member Functions inherited from marian::FDScheme | |
| virtual | ~FDScheme () |
| Deconstructor. | |
Private Attributes | |
| SmartPointer< TridiagonalSolver > | solver_ |
| Sovler used in implicit step. | |
Detailed Description
When we solve following parabolic PDE:
![\[\frac{df(x,t)}{dt} = L f(x,t)\]](form_19.png)
where L is linear operator, we can use different time discretization scheme, for example:
![\[ \begin{aligned} \text{in case of Forward Equation: }\frac{f(x_i,t_{j+1})-f(x_i,t_{j})}{t_{j+1}-t_{j}} & = \hat{L} f(x_i,t_{j+1}) \Rightarrow f(x_i,t_{j})= (I + (t_{j+1}-t_{j})\hat{L}) f(x_i,t_{j+1}) \\ \text{in case of Backward Equation: }\frac{f(x_i,t_{j+1})-f(x_i,t_{j})}{t_{j+1}-t_{j}} & = \hat{L} f(x_i,t_{j}) \Rightarrow f(x_i,t_{j+1})= (I - (t_{j+1}-t_{j})\hat{L}) f(x_i,t_{j}) \end{aligned} \]](form_24.png)
For more information see [2] [5] [10] .
- Examples:
- convergenceExample.cpp.
Member Function Documentation
|
overridevirtual |
- Parameters
-
f Initial condition bcs Boundary conditions time_grid Time grid used in L Linear operator defining PDE
- Returns
- Solution in form of std::vector
Implements marian::FDScheme.
|
overridevirtual |
- Parameters
-
f Initial condition bcs Boundary conditions spatial_grid Spatial grid corresponding to initial conditions (used only to save the solution to CSV file) time_grid Time grid used for time dimension of FDM L Linear operator defining PDE file_name Name of CSV file
- Returns
- Solution in form of std::vector
Implements marian::FDScheme.
The documentation for this class was generated from the following files:
- C:/Unix/home/OEM/fdm/src/FDM/schemes/implicitScheme.hpp
- C:/Unix/home/OEM/fdm/src/FDM/schemes/implicitScheme.cpp
