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// $Id$
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/****************************************************************************
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 *   Copyright (C) 2008-2010 by Andreas Lauser                               *
 *   Copyright (C) 2008-2010 by Bernd Flemisch                               *
 *   Institute of Hydraulic Engineering                                      *
 *   University of Stuttgart, Germany                                        *
 *   email: <givenname>.<name>@iws.uni-stuttgart.de                          *
 *                                                                           *
 *   This program 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 2 of the License, or       *
 *   (at your option) any later version, as long as this copyright notice    *
 *   is included in its original form.                                       *
 *                                                                           *
 *   This program is distributed WITHOUT ANY WARRANTY.                       *
 *****************************************************************************/
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/*!
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 * \file
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 * \brief Reference implementation of a controller class for the Newton solver.
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 *
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 * Usually this controller should be sufficient.
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 */
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#ifndef DUMUX_NEWTON_CONTROLLER_HH
#define DUMUX_NEWTON_CONTROLLER_HH

#include <dumux/common/exceptions.hh>

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#include <queue> // for std::priority_queue
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#include <dumux/common/pardiso.hh>

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#include <dumux/io/vtkmultiwriter.hh>
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#include <dumux/common/pdelabpreconditioner.hh>
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namespace Dumux
{
namespace Properties
{
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//! Specifies the implementation of the Newton controller
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NEW_PROP_TAG(NewtonController);

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//! Specifies the type of the actual Newton method
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NEW_PROP_TAG(NewtonMethod);

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//! Specifies the type of a solution
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NEW_PROP_TAG(SolutionVector);

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//! Specifies the type of a vector of primary variables at a degree of freedom
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NEW_PROP_TAG(PrimaryVariables);

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//! Specifies the type of a global Jacobian matrix
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NEW_PROP_TAG(JacobianMatrix);

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//! Specifies the type of the Jacobian matrix assembler
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NEW_PROP_TAG(JacobianAssembler);

//! specifies the type of the time manager
NEW_PROP_TAG(TimeManager);

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/*!
 * \brief Specifies the verbosity of the linear solver
 *
 * By default it is 0, i.e. it doesn't print anything. Setting this
 * property to 1 prints aggregated convergence rates, 2 prints the
 * convergence rate of every iteration of the scheme.
 */
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NEW_PROP_TAG(NewtonLinearSolverVerbosity);

//! specifies whether the convergence rate and the global residual
//! gets written out to disk for every newton iteration (default is false)
NEW_PROP_TAG(NewtonWriteConvergence);

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//! Specifies whether time step size should be increased during the
//! Newton methods first few iterations
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NEW_PROP_TAG(EnableTimeStepRampUp);

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//! Specifies whether the Jacobian matrix should only be reassembled
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//! if the current solution deviates too much from the evaluation point
NEW_PROP_TAG(EnablePartialReassemble);

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/*!
 * \brief Specifies whether the update should be done using the line search
 *        method instead of the plain Newton method. 
 *
 * Whether this property has any effect depends on wether the line
 * search method is implemented for the actual model's Newton
 * controller's update() method. By default line search is not used.
 */
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NEW_PROP_TAG(NewtonUseLineSearch);

SET_PROP_DEFAULT(NewtonLinearSolverVerbosity)
{public:
    static const int value = 0;
};

SET_PROP_DEFAULT(NewtonWriteConvergence)
{public:
    static const bool value = false;
};

SET_PROP_DEFAULT(NewtonUseLineSearch)
{public:
    static const bool value = false;
};
};

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/*!
 * \internal
 * \brief Writes the intermediate solutions during 
 *        the Newton scheme
 */
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template <class TypeTag, bool enable>
struct NewtonConvergenceWriter
{
    typedef typename GET_PROP_TYPE(TypeTag, PTAG(GridView)) GridView;
    typedef typename GET_PROP_TYPE(TypeTag, PTAG(NewtonController)) NewtonController;

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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(SolutionVector)) SolutionVector;
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    typedef Dumux::VtkMultiWriter<GridView>  VtkMultiWriter;

    NewtonConvergenceWriter(NewtonController &ctl)
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        : ctl_(ctl)
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    {
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        timeStepIndex_ = 0;
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        iteration_ = 0;
        vtkMultiWriter_ = new VtkMultiWriter("convergence");
    }

    ~NewtonConvergenceWriter()
    { delete vtkMultiWriter_; };

    void beginTimestep()
    {
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        ++timeStepIndex_;
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        iteration_ = 0;
    };

    void beginIteration(const GridView &gv)
    {
        ++ iteration_;
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        vtkMultiWriter_->beginTimestep(timeStepIndex_ + iteration_ / 100.0,
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                                       gv);
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    };

    void writeFields(const SolutionVector &uOld,
                     const SolutionVector &deltaU)
    {
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        ctl_.method().model().addConvergenceVtkFields(*vtkMultiWriter_, uOld, deltaU);
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    };

    void endIteration()
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    { vtkMultiWriter_->endTimestep(); };
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    void endTimestep()
    {
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        ++timeStepIndex_;
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        iteration_ = 0;
    };

private:
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    int timeStepIndex_;
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    int iteration_;
    VtkMultiWriter *vtkMultiWriter_;
    NewtonController &ctl_;
};

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/*!
 * \internal
 * \brief Writes the intermediate solutions during 
 *        the Newton scheme. 
 *
 * This is the dummy specialization for the case where we don't want
 * to do anything.
 */
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template <class TypeTag>
struct NewtonConvergenceWriter<TypeTag, false>
{
    typedef typename GET_PROP_TYPE(TypeTag, PTAG(GridView)) GridView;
    typedef typename GET_PROP_TYPE(TypeTag, PTAG(NewtonController)) NewtonController;
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(SolutionVector)) SolutionVector;
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    typedef Dumux::VtkMultiWriter<GridView>  VtkMultiWriter;

    NewtonConvergenceWriter(NewtonController &ctl)
    {};

    void beginTimestep()
    { };

    void beginIteration(const GridView &gv)
    { };

    void writeFields(const SolutionVector &uOld,
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                     const SolutionVector &deltaU)
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    { };

    void endIteration()
    { };

    void endTimestep()
    { };
};

/*!
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 * \brief A reference implementation of a newton controller specific
 *        for the box scheme.
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 *
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 * If you want to specialize only some methods but are happy with the
 * defaults of the reference controller, derive your controller from
 * this class and simply overload the required methods.
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 */
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template <class TypeTag>
class NewtonController
{
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(Scalar)) Scalar;
    typedef typename GET_PROP_TYPE(TypeTag, PTAG(NewtonController)) Implementation;
    typedef typename GET_PROP_TYPE(TypeTag, PTAG(GridView)) GridView;
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(Problem)) Problem;
    typedef typename GET_PROP_TYPE(TypeTag, PTAG(Model)) Model;
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(NewtonMethod)) NewtonMethod;
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(JacobianMatrix)) JacobianMatrix;
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(TimeManager)) TimeManager;
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(JacobianAssembler)) JacobianAssembler;
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(SolutionVector)) SolutionVector;
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    typedef typename GET_PROP_TYPE(TypeTag, PTAG(PrimaryVariables)) PrimaryVariables;
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    typedef NewtonConvergenceWriter<TypeTag, GET_PROP_VALUE(TypeTag, PTAG(NewtonWriteConvergence))>  ConvergenceWriter;

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    enum { enableTimeStepRampUp = GET_PROP_VALUE(TypeTag, PTAG(EnableTimeStepRampUp)) };
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    enum { enablePartialReassemble = GET_PROP_VALUE(TypeTag, PTAG(EnablePartialReassemble)) };

    // class to keep track of the most offending vertices in a way
    // compatible with std::priority_queue
    class VertexError
    {
    public:
        VertexError(int idx, Scalar err)
        {
            idx_ = idx;
            err_ = err;
        }
        
        int index() const
        { return idx_; }
        
        bool operator<(const VertexError &a) const
        { return a.err_ < err_; }

    private:
        int idx_;
        Scalar err_;
    };
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public:
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    /*!
     * \brief Constructor
     */
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    NewtonController()
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        : endIterMsgStream_(std::ostringstream::out),
          convergenceWriter_(asImp_())
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    {
        numSteps_ = 0;

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        this->setRelTolerance(1e-8);
        this->rampUpSteps_ = 0;

        if (enableTimeStepRampUp) {
            this->rampUpSteps_ = 9;
            
            // the ramp-up steps are not counting
            this->setTargetSteps(10);
            this->setMaxSteps(12);
        }
        else {
            this->setTargetSteps(10);
            this->setMaxSteps(18);
        }
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    };

    /*!
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     * \brief Set the maximum acceptable difference for convergence of
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     *        any primary variable between two iterations.
     *
     * \param tolerance The maximum relative error between two Newton
     *                  iterations at which the scheme is considered
     *                  finished
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     */
    void setRelTolerance(Scalar tolerance)
    { tolerance_ = tolerance; }

    /*!
     * \brief Set the number of iterations at which the Newton method
     *        should aim at.
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     *
     * This is used to control the time step size. The heuristic used
     * is to scale the last time step size by the deviation of the
     * number of iterations used from the target steps.
     *
     * \param targetSteps Number of iterations which are considered "optimal"
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     */
    void setTargetSteps(int targetSteps)
    { targetSteps_ = targetSteps; }

    /*!
     * \brief Set the number of iterations after which the Newton
     *        method gives up.
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     *
     * \param maxSteps Number of iterations after we give up
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     */
    void setMaxSteps(int maxSteps)
    { maxSteps_ = maxSteps; }
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    /*!
     * \brief Returns the number of iterations used for the time step
     *        ramp-up.
     */
    Scalar rampUpSteps() const
    { return enableTimeStepRampUp?rampUpSteps_:0; }

    /*!
     * \brief Returns whether the time-step ramp-up is still happening
     */
    bool inRampUp() const
    { return numSteps_ < rampUpSteps(); }

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    /*!
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     * \brief Returns true if another iteration should be done.
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     *
     * \param u The current solution
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     */
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    bool newtonProceed(const SolutionVector &u)
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    {
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        if (numSteps_ < rampUpSteps() + 2)
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            return true; // we always do at least two iterations
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        else if (asImp_().newtonConverged())
            return false; // we are below the desired tolerance
        else if (numSteps_ >= rampUpSteps() + maxSteps_) {
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            // we have exceeded the allowed number of steps.  if the
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            // relative error was reduced by a factor of at least 4,
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            // we proceed even if we are above the maximum number of
            // steps
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            return error_*4.0 < lastError_;
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        }

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        return true;
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    }

    /*!
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     * \brief Returns true iff the error of the solution is below the
     *        tolerance.
     */
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    bool newtonConverged() const
    {
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        return 
            error_ <= tolerance_ && 
            model_().jacobianAssembler().reassembleTolerance() <= tolerance_/2;
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    }

    /*!
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     * \brief Called before the newton method is applied to an
     *        non-linear system of equations.
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     *
     * \param method The object where the NewtonMethod is executed
     * \param u The initial solution
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     */
    void newtonBegin(NewtonMethod &method, SolutionVector &u)
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    {
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        method_ = &method;
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        numSteps_ = 0;

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        model_().jacobianAssembler().reassembleAll();
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        dtInitial_ = timeManager_().timeStepSize();
        if (enableTimeStepRampUp) {
            rampUpDelta_ = 
                timeManager_().timeStepSize() 
                /
                rampUpSteps()
                *
                2;

            // reduce initial time step size for ramp-up.
            timeManager_().setTimeStepSize(rampUpDelta_);
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        }

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        convergenceWriter_.beginTimestep();
    }

    /*!
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     * \brief Indidicates the beginning of a newton iteration.
     */
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    void newtonBeginStep()
    { lastError_ = error_; }

    /*!
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     * \brief Returns the number of steps done since newtonBegin() was
     *        called.
     */
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    int newtonNumSteps()
    { return numSteps_; }

    /*!
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     * \brief Update the relative error of the solution compared to
     *        the previous iteration.
     *
     * The relative error can be seen as a norm of the difference
     * between the current and the next iteration.
     *
     * \param uOld The current iterative solution
     * \param deltaU The difference between the current and the next solution
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     */
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    void newtonUpdateRelError(const SolutionVector &uOld,
                              const SolutionVector &deltaU)
    {
        // calculate the relative error as the maximum relative
        // deflection in any degree of freedom.
        typedef typename SolutionVector::block_type FV;
        error_ = 0;

        int idxI = -1;
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        int aboveTol = 0;
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        for (int i = 0; i < int(uOld.size()); ++i) {
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            PrimaryVariables uNewI = uOld[i];
            uNewI -= deltaU[i];
            Scalar vertErr = 
                model_().relativeErrorVertex(i,
                                             uOld[i],
                                             uNewI);
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            if (vertErr > tolerance_)
                ++aboveTol;
            if (vertErr > error_) {
                idxI = i;
                error_ = vertErr;
            }
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        }
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        error_ = gridView_().comm().max(error_);
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    }

    /*!
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     * \brief Solve the linear system of equations \f$\mathbf{A}u - b = 0\f$.
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     *
     * Throws Dumux::NumericalProblem if the linear solver didn't
     * converge.
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     *
     * \param A The matrix of the linear system of equations
     * \param u The vector which solves the linear system
     * \param b The right hand side of the linear system
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     */
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    template <class Vector>
    void newtonSolveLinear(const JacobianMatrix &A,
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                           Vector &u,
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                           const Vector &b)
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    {
        // if the deflection of the newton method is large, we do not
        // need to solve the linear approximation accurately. Assuming
        // that the initial value for the delta vector u is quite
        // close to the final value, a reduction of 6 orders of
        // magnitude in the defect should be sufficient...
        Scalar residReduction = 1e-6;

        try {
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            solveLinear_(A, u, b, residReduction);
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            // make sure all processes converged
            int converged = 1;
            gridView_().comm().min(converged);
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            if (!converged) {
                DUNE_THROW(NumericalProblem,
                           "A process threw MatrixBlockError");
            }
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        }
        catch (Dune::MatrixBlockError e) {
            // make sure all processes converged
            int converged = 0;
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            gridView_().comm().min(converged);
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            Dumux::NumericalProblem p;
            std::string msg;
            std::ostringstream ms(msg);
            ms << e.what() << "M=" << A[e.r][e.c];
            p.message(ms.str());
            throw p;
        }
    }

    /*!
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     * \brief Update the current solution with a delta vector.
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     *
     * The error estimates required for the newtonConverged() and
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     * newtonProceed() methods should be updated inside this method.
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     *
     * Different update strategies, such as line search and chopped
     * updates can be implemented. The default behaviour is just to
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     * subtract deltaU from uOld, i.e.
     * \f[ u^{k+1} = u^k - \Delta u^k \f]
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     *
     * \param deltaU The delta as calculated from solving the linear
     *               system of equations. This parameter also stores
     *               the updated solution.
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     * \param uOld   The solution vector of the last iteration
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     */
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    void newtonUpdate(SolutionVector &deltaU, const SolutionVector &uOld)
    {
        writeConvergence_(uOld, deltaU);

        newtonUpdateRelError(uOld, deltaU);
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        deltaU *= -1;
        deltaU += uOld;

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        // compute the vertex and element colors for partial
        // reassembly
        if (enablePartialReassemble) {
            Scalar maxDelta = 0;
            for (int i = 0; i < int(uOld.size()); ++i) {
                const PrimaryVariables &uEval = this->model_().jacobianAssembler().evalPoint()[i];
                const PrimaryVariables &uSol = this->model_().curSol()[i];
                Scalar tmp = 
                    model_().relativeErrorVertex(i,
                                                 uEval,
                                                 uSol);
                maxDelta = std::max(tmp, maxDelta);
            }
            
            Scalar reassembleTol = std::max(maxDelta/10, this->tolerance_/5);
            if (error_ < 10*tolerance_)
                reassembleTol = tolerance_/5;
            this->model_().jacobianAssembler().computeColors(reassembleTol);
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        }
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    }
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    /*!
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     * \brief Indicates that one newton iteration was finished.
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     *
     * \param u The solution after the current iteration
     * \param uOld The solution at the beginning of the current iteration
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     */
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    void newtonEndStep(SolutionVector &u, SolutionVector &uOld)
    {
        ++numSteps_;
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        Scalar realError = error_;
        if (inRampUp() && error_ < 1.0) {
            // change time step size
            Scalar dt = timeManager_().timeStepSize();
            dt += rampUpDelta_;
            timeManager_().setTimeStepSize(dt);

            endIterMsg() << ", dt=" << timeManager_().timeStepSize() << ", ddt=" << rampUpDelta_;
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        }
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        if (verbose())
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            std::cout << "\rNewton iteration " << numSteps_ << " done: "
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                      << "error=" << realError << endIterMsg().str() << "\n";
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        endIterMsgStream_.str("");
    }

    /*!
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     * \brief Indicates that we're done solving the non-linear system
     *        of equations.
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     */
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    void newtonEnd()
    {
        convergenceWriter_.endTimestep();
    }

    /*!
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     * \brief Called if the newton method broke down.
     *
     * This method is called _after_ newtonEnd()
     */
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    void newtonFail()
    {
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        timeManager_().setTimeStepSize(dtInitial_);
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        numSteps_ = targetSteps_*2;
    }

    /*!
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     * \brief Called when the newton method was sucessful.
     *
     * This method is called _after_ newtonEnd()
     */
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    void newtonSucceed()
    { }

    /*!
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     * \brief Suggest a new time stepsize based on the old time step
     *        size.
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     *
     * The default behaviour is to suggest the old time step size
     * scaled by the ratio between the target iterations and the
     * iterations required to actually solve the last time step.
     */
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    Scalar suggestTimeStepSize(Scalar oldTimeStep) const
    {
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        if (enableTimeStepRampUp)
            return oldTimeStep; 

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        Scalar n = numSteps_;
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        n -= rampUpSteps();

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        // be agressive reducing the timestep size but
        // conservative when increasing it. the rationale is
        // that we want to avoid failing in the next newton
        // iteration which would require another linearization
        // of the problem.
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        if (n > targetSteps_) {
            Scalar percent = (n - targetSteps_)/targetSteps_;
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            return oldTimeStep/(1.0 + percent);
        }
        else {
            /*Scalar percent = (Scalar(1))/targetSteps_;
              return oldTimeStep*(1 + percent);
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            */
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            Scalar percent = (targetSteps_ - n)/targetSteps_;
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            return oldTimeStep*(1.0 + percent/1.2);
        }
    }

    /*!
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     * \brief Returns a reference to the current newton method
     *        which is controlled by this controller.
     */
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    NewtonMethod &method()
    { return *method_; }

    /*!
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     * \brief Returns a reference to the current newton method
     *        which is controlled by this controller.
     */
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    const NewtonMethod &method() const
    { return *method_; }

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    std::ostringstream &endIterMsg()
    { return endIterMsgStream_; }

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    /*!
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     * \brief Returns true iff the newton method ought to be chatty.
     */
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    bool verbose() const
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    { return gridView_().comm().rank() == 0; }
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protected:
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    /*!
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     * \brief Returns a reference to the grid view.
     */
    const GridView &gridView_() const
    { return problem_().gridView(); }
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    /*!
     * \brief Returns a reference to the problem.
     */
    Problem &problem_()
    { return method_->problem(); }

    /*!
     * \brief Returns a reference to the problem.
     */
    const Problem &problem_() const
    { return method_->problem(); }

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    /*!
     * \brief Returns a reference to the time manager.
     */
    TimeManager &timeManager_()
    { return problem_().timeManager(); }

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    /*!
     * \brief Returns a reference to the time manager.
     */
    const TimeManager &timeManager_() const
    { return problem_().timeManager(); }

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    /*!
     * \brief Returns a reference to the problem.
     */
    Model &model_()
    { return problem_().model(); }

    /*!
     * \brief Returns a reference to the problem.
     */
    const Model &model_() const
    { return problem_().model(); }
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    // returns the actual implementation for the cotroller we do
    // it this way in order to allow "poor man's virtual methods",
    // i.e. methods of subclasses which can be called by the base
    // class.
    Implementation &asImp_()
    { return *static_cast<Implementation*>(this); }
    const Implementation &asImp_() const
    { return *static_cast<const Implementation*>(this); }

    void writeConvergence_(const SolutionVector &uOld,
                           const SolutionVector &deltaU)
    {
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        convergenceWriter_.beginIteration(this->gridView_());
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        convergenceWriter_.writeFields(uOld, deltaU);
        convergenceWriter_.endIteration();
    };

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    /*!
     * \brief Actually invoke the linear solver 
     *
     * Usually we use the solvers from DUNE-ISTL.
     */
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    template <class Vector>
    void solveLinear_(const JacobianMatrix &A,
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                      Vector &x,
                      const Vector &b,
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                      Scalar residReduction)
    {
        int verbosity = GET_PROP_VALUE(TypeTag, PTAG(NewtonLinearSolverVerbosity));
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        if (gridView_().comm().rank() != 0)
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            verbosity = 0;

#if HAVE_PARDISO
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        typedef Dumux::PDELab::ISTLBackend_NoOverlap_Loop_Pardiso<TypeTag> Solver;
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        Solver solver(problem_(), 500, verbosity);
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#else // !HAVE_PARDISO
#if HAVE_MPI
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//        typedef Dune::PDELab::ISTLBackend_NOVLP_BCGS_NOPREC<GridFunctionSpace> Solver;
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//        Solver solver(model_().jacobianAssembler().gridFunctionSpace(), 50000, verbosity);
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        typedef Dumux::PDELab::ISTLBackend_NoOverlap_BCGS_ILU<TypeTag> Solver;
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        Solver solver(problem_(), 500, verbosity);
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#else
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        typedef Dune::PDELab::ISTLBackend_SEQ_BCGS_SSOR Solver;
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        Solver solver(500, verbosity);
#endif // HAVE_MPI
#endif // HAVE_PARDISO

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        //    Solver solver(model_().jacobianAssembler().gridFunctionSpace(), 500, verbosity);
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        Vector bTmp(b);
        solver.apply(A, x, bTmp, residReduction);
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        if (!solver.result().converged)
            DUNE_THROW(Dumux::NumericalProblem,
                       "Solving the linear system of equations did not converge.");

        // make sure the solver didn't produce a nan or an inf
        // somewhere. this should never happen but for some strange
        // reason it happens anyway.
        Scalar xNorm2 = x.two_norm2();
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        gridView_().comm().sum(xNorm2);
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        if (std::isnan(xNorm2) || !std::isfinite(xNorm2))
            DUNE_THROW(Dumux::NumericalProblem,
                       "The linear solver produced a NaN or inf somewhere.");
    }

    std::ostringstream endIterMsgStream_;

    NewtonMethod *method_;

    ConvergenceWriter convergenceWriter_;

    Scalar error_;
    Scalar lastError_;
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    Scalar tolerance_;
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    // number of iterations for the time-step ramp-up
    Scalar rampUpSteps_;
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    // the increase of the time step size during the rampup
    Scalar rampUpDelta_;

    Scalar dtInitial_; // initial time step size
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    // optimal number of iterations we want to achive
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    int targetSteps_;
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    // maximum number of iterations we do before giving up
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    int maxSteps_;
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    // actual number of steps done so far
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    int numSteps_;
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};
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} // namespace Dumux
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#endif