EulerSI.H

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License
    This file is part of OpenFOAM.

    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

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Class
    Foam::EulerSI

Description
    Semi-implicit Euler ODE solver of order (0)1.

    The method calculates the new state from:
    \f[
        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]
    \f]
    The error is estimated directly from the change in the solution,
    i.e. the difference between the 0th and 1st order solutions:
    \f[
        err_{n+1} = y_{n+1} - y_n
    \f]

SourceFiles
    EulerSI.C

\*---------------------------------------------------------------------------*/

#ifndef EulerSI_H
#define EulerSI_H

#include "ODESolver.H"
#include "adaptiveSolver.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

/*---------------------------------------------------------------------------*\
                           Class EulerSI Declaration
\*---------------------------------------------------------------------------*/

class EulerSI
:
    public ODESolver,
    public adaptiveSolver
{
    // Private Data

        mutable scalarField err_;
        mutable scalarField dydx_;
        mutable scalarField dfdx_;
        mutable scalarSquareMatrix dfdy_;
        mutable scalarSquareMatrix a_;
        mutable labelList pivotIndices_;


public:

    //- Runtime type information
    TypeName("EulerSI");


    // Constructors

        //- Construct from ODESystem
        EulerSI(const ODESystem& ode, const dictionary& dict);


    //- Destructor
    virtual ~EulerSI()
    {}


    // Member Functions

        //- Inherit solve from ODESolver
        using ODESolver::solve;

        //- Resize the ODE solver
        virtual bool resize();

        //- Solve a single step dx and return the error
        virtual scalar solve
        (
            const scalar x0,
            const scalarField& y0,
            const label li,
            const scalarField& dydx0,
            const scalar dx,
            scalarField& y
        ) const;

        //- Solve the ODE system and the update the state
        virtual void solve
        (
            scalar& x,
            scalarField& y,
            const label li,
            scalar& dxTry
        ) const;
};


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

#endif

// ************************************************************************* //