Semi-implicit Euler ODE solver of order (0)1. More...
Public Member Functions | |
| TypeName ("EulerSI") | |
| Runtime type information. More... | |
| EulerSI (const ODESystem &ode, const dictionary &dict) | |
| Construct from ODE. More... | |
| scalar | solve (const scalar x0, const scalarField &y0, const scalarField &dydx0, const scalar dx, scalarField &y) const |
| Solve a single step dx and return the error. More... | |
| void | solve (scalar &x, scalarField &y, scalar &dxTry) const |
| Solve the ODE system and the update the state. More... | |
 Public Member Functions inherited from ODESolver | |
| TypeName ("ODESolver") | |
| Runtime type information. More... | |
| declareRunTimeSelectionTable (autoPtr, ODESolver, dictionary,(const ODESystem &ode, const dictionary &dict),(ode, dict)) | |
| ODESolver (const ODESystem &ode, const dictionary &dict) | |
| Construct for given ODESystem. More... | |
| ODESolver (const ODESystem &ode, const scalarField &absTol, const scalarField &relTol) | |
| Construct for given ODESystem specifying tolerances. More... | |
| virtual | ~ODESolver () |
| Destructor. More... | |
| scalarField & | absTol () |
| scalarField & | relTol () |
| virtual void | solve (scalar &x, scalarField &y, stepState &step) const |
| Solve the ODE system as far as possible upto dxTry. More... | |
| virtual void | solve (const scalar xStart, const scalar xEnd, scalarField &y, scalar &dxEst) const |
| Solve the ODE system from xStart to xEnd, update the state. More... | |
| Public Member Functions inherited from adaptiveSolver | |
| adaptiveSolver (const ODESystem &ode, const dictionary &dict) | |
| Construct from ODESystem. More... | |
| virtual | ~adaptiveSolver () |
| Destructor. More... | |
| void | solve (const ODESystem &ode, scalar &x, scalarField &y, scalar &dxTry) const |
| Solve the ODE system and the update the state. More... | |
Additional Inherited Members | |
| Static Public Member Functions inherited from ODESolver | |
| static autoPtr< ODESolver > | New (const ODESystem &ode, const dictionary &dict) |
| Select null constructed. More... | |
| Protected Member Functions inherited from ODESolver | |
| scalar | normalizeError (const scalarField &y0, const scalarField &y, const scalarField &err) const |
| Return the nomalized scalar error. More... | |
| ODESolver (const ODESolver &) | |
| Disallow default bitwise copy construct. More... | |
| void | operator= (const ODESolver &) |
| Disallow default bitwise assignment. More... | |
| Protected Attributes inherited from ODESolver | |
| const ODESystem & | odes_ |
| Reference to ODESystem. More... | |
| label | n_ |
| Size of the ODESystem. More... | |
| scalarField | absTol_ |
| Absolute convergence tolerance per step. More... | |
| scalarField | relTol_ |
| Relative convergence tolerance per step. More... | |
| label | maxSteps_ |
| The maximum number of sub-steps allowed for the integration step. More... | |
Semi-implicit Euler ODE solver of order (0)1.
The method calculates the new state from:
![\[ y_{n+1} = y_n + \delta_x\left[I - \delta_x\frac{\partial f}{\partial y}\right]^{-1} \cdot \left[f(y_n) + \delta_x\frac{\partial f}{\partial x}\right] \]](form_138.png)
The error is estimated directly from the change in the solution, i.e. the difference between the 0th and 1st order solutions:
![\[ err_{n+1} = y_{n+1} - y_n \]](form_137.png)
| EulerSI | ( | const ODESystem & | ode, |
| const dictionary & | dict | ||
| ) |
Construct from ODE.
Definition at line 40 of file EulerSI.C.
References EulerSI::solve().
| TypeName | ( | "EulerSI" | ) |
Runtime type information.
|
virtual |
Solve a single step dx and return the error.
Implements adaptiveSolver.
Definition at line 56 of file EulerSI.C.
References forAll, ODESystem::jacobian(), Foam::LUBacksubstitute(), Foam::LUDecompose(), ODESolver::n_, ODESolver::normalizeError(), and ODESolver::odes_.
Referenced by EulerSI::EulerSI().
|
virtual |
Solve the ODE system and the update the state.
Reimplemented from ODESolver.
Definition at line 96 of file EulerSI.C.
References ODESolver::odes_, and adaptiveSolver::solve().
1.8.11
