time_integrator.hpp

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/*
 * Copyright (c) 2014-2020:  G-CSC, Goethe University Frankfurt
 * Author: Arne Naegel, Andreas Kreienbuehl
 *
 * This file is part of UG4.
 *
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 *
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 *
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 *
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU Lesser General Public License for more details.
 */
 
#ifndef TIME_INTEGRATOR_HPP_
#define TIME_INTEGRATOR_HPP_
 
#if __cplusplus >= 201103L
#define OVERRIDE override
#else
#define OVERRIDE
#endif
 
// std headers.
#include <string>
 
// UG4 headers.
#include "lib_algebra/operator/interface/operator.h"
#include "lib_algebra/operator/interface/operator_inverse.h"
#include "lib_algebra/operator/linear_solver/linear_solver.h"
#include "lib_disc/function_spaces/grid_function.h"
#include "lib_disc/assemble_interface.h" // TODO: missing IAssemble in following file:
#include "lib_disc/operator/linear_operator/assembled_linear_operator.h"
#include "lib_disc/operator/non_linear_operator/assembled_non_linear_operator.h"
#include "lib_disc/spatial_disc/domain_disc.h"
#include "lib_disc/time_disc/time_disc_interface.h"
#include "lib_disc/time_disc/theta_time_step.h"
#include "lib_disc/time_disc/solution_time_series.h"
#include "lib_disc/time_disc/time_integrator_subject.hpp"
#include "lib_disc/time_disc/time_integrator_observers/time_integrator_observer_interface.h"
#include "lib_disc/function_spaces/grid_function_util.h" // SaveVectorForConnectionViewer
#include "lib_disc/function_spaces/interpolate.h" //Interpolate
#include "lib_disc/function_spaces/integrate.h" //Integral
#include "lib_disc/function_spaces/grid_function.h" //GridFunction
#include "lib_disc/io/vtkoutput.h"
 
 
 
// My headers.
#include "time_extrapolation.h"
#include "../limex_tools.h"
 
namespace ug {
 
 
template<class TDomain, class TAlgebra>
class VTKOutputObserver
: public ITimeIntegratorObserver<TDomain, TAlgebra>,
  public ITimeIntegratorStageObserver_start<TDomain, TAlgebra>,
  public ITimeIntegratorStageObserver_finalize<TDomain, TAlgebra>,
  public ITimeIntegratorStageObserver_end<TDomain, TAlgebra>
{
public:
  typedef ITimeIntegratorObserver<TDomain, TAlgebra> base_type;
  typedef GridFunction<TDomain, TAlgebra> grid_function_type;
  typedef VTKOutput<TDomain::dim> vtk_type;
 
  VTKOutputObserver()
  :  m_sp_vtk(SPNULL), m_filename("0000"), m_startTime(0.0), m_plotStep(0.0) {}
 
  VTKOutputObserver(const char *filename, SmartPtr<vtk_type> vtk)
  : m_sp_vtk(vtk), m_filename(filename), m_startTime(0.0), m_plotStep(0.0) {}
 
  VTKOutputObserver(const char *filename, SmartPtr<vtk_type> vtk, number plotStep)
  : m_sp_vtk(vtk), m_filename(filename), m_startTime(0.0), m_plotStep(plotStep) {}
 
  virtual ~VTKOutputObserver()
  { m_sp_vtk = SPNULL; }
 
 
  void set_output_scales(const std::vector<number>& vScales)
  {
    m_vOutputScales = vScales;
  }
 
 
  bool step_process(SmartPtr<grid_function_type> uNew, int step, number time, number dt) OVERRIDE
  {
    return true;
  }
 
 
  bool start_action(SmartPtr<grid_function_type> u, int step, number time, number dt) OVERRIDE
  {
    if (!m_sp_vtk.valid())
      return false;
 
    writeToFile(u, step, time);
 
    m_startTime = time;
    m_uOld = u->clone();
 
    return true;
  }
 
 
  bool finalize_action(SmartPtr<grid_function_type> uNew, int step, number time, number dt) OVERRIDE
  {
    if (!m_sp_vtk.valid())
      return false;
 
    if (m_plotStep == 0.0)
    {
      writeToFile(uNew, step, time);
      return true;
    }
 
    // otherwise, only plot data at multiples of given time step (interpolate if necessary)
    number rem = fmod(time - dt - m_startTime, m_plotStep);
    number nextPlotTimePt = time - dt - rem + m_plotStep;
    int nextStep = (int) ((nextPlotTimePt - m_startTime + 0.5 * m_plotStep) / m_plotStep);
 
    if (nextPlotTimePt > time)
    {
      m_uOld = uNew->clone();
      return true;
    }
 
    SmartPtr<grid_function_type> uCur = uNew->clone_without_values();
    while (nextPlotTimePt <= time)
    {
      number alpha = (time - nextPlotTimePt) / dt;
      VecScaleAdd(static_cast<typename TAlgebra::vector_type&>(*uCur),
        alpha, static_cast<typename TAlgebra::vector_type&>(*m_uOld),
        1.0 - alpha, static_cast<typename TAlgebra::vector_type&>(*uNew));
 
      writeToFile(uCur, nextStep, nextPlotTimePt);
 
      nextPlotTimePt = (++nextStep) * m_plotStep;
    }
 
    m_uOld = uNew->clone();
    return true;
  }
 
 
  bool end_action(SmartPtr<grid_function_type> u, int step, number time, number dt) OVERRIDE
  {
    if (!m_sp_vtk.valid())
      return false;
 
    m_sp_vtk->write_time_pvd(m_filename.c_str(), *u);
    return true;
  }
 
 
private:
  void writeToFile(SmartPtr<grid_function_type> u, int step, number time)
  {
    if (m_vOutputScales.size())
    {
      SmartPtr<grid_function_type> uTmp = u->clone_without_values();
      ScaleGF<grid_function_type>(uTmp, u, m_vOutputScales);
      m_sp_vtk->print(m_filename.c_str(), *uTmp, step, time);
    }
    else
      m_sp_vtk->print(m_filename.c_str(), *u, step, time);
  }
 
protected:
  SmartPtr<vtk_type> m_sp_vtk;
  SmartPtr<grid_function_type> m_uOld;
  std::string m_filename;
  number m_startTime;
  number m_plotStep;
  std::vector<number> m_vOutputScales;
};
 
 
 
template<class TDomain, class TAlgebra>
class ConnectionViewerOutputObserver
: public ITimeIntegratorObserver<TDomain, TAlgebra>
{
public:
  typedef ITimeIntegratorObserver<TDomain, TAlgebra> base_type;
  typedef GridFunction<TDomain, TAlgebra> grid_function_type;
 
  ConnectionViewerOutputObserver(const char *filename)
  : m_filename(filename), m_outputTime(-1.0) {}
 
  ConnectionViewerOutputObserver(const char *filename, number t_out)
  : m_filename(filename), m_outputTime(t_out) {}
 
  virtual ~ConnectionViewerOutputObserver()
  {}
 
  bool step_process(SmartPtr<grid_function_type> uNew, /*SmartPtr<grid_function_type> uOld, */int step, number time, number dt) OVERRIDE
  {
    // quit, if time does not match
    if (m_outputTime >=0.0 && time != m_outputTime) return true;
 
    SaveVectorForConnectionViewer<grid_function_type>(*uNew, m_filename.c_str());
    return true;
  }
 
protected:
  std::string m_filename;
  number m_outputTime;
 
};
 
 
#if 0
template <typename TData, typename TDataIn1, typename TDataIn2>
class LuaFunction2 // : public IFunction<TData, TDataIn1, typename TDataIn2>
{
  public:
  LuaFunction2();
    virtual ~LuaFunction2() {};
 
 
    void set_lua_callback(const char* luaCallback, size_t numArgs);
 
    virtual void operator() (TData& out, int numArgs1, int numArgs2,...);
 
  protected:
    std::string m_cbValueName;
 
    int m_cbValueRef;
 
    lua_State*  m_L;
 
    size_t m_numArgs;
};
 
 
template <typename TData, typename TDataIn1, typename TDataIn2>
LuaFunction2<TData,TDataIn1,TDataIn2>::LuaFunction2() : m_numArgs(0)
{
  m_L = ug::script::GetDefaultLuaState();
  m_cbValueRef = LUA_NOREF;
}
 
template <typename TData, typename TDataIn1, typename TDataIn2>
void LuaFunction2<TData,TDataIn1,TDataIn2>::set_lua_callback(const char* luaCallback, size_t numArgs)
{
//  store name (string) of callback
  m_cbValueName = luaCallback;
 
//  obtain a reference
  lua_getglobal(m_L, m_cbValueName.c_str());
 
//  make sure that the reference is valid
  if(lua_isnil(m_L, -1)){
    UG_THROW("LuaFunction::set_lua_callback(...):"
        "Specified lua callback does not exist: " << m_cbValueName);
  }
 
//  store reference to lua function
  m_cbValueRef = luaL_ref(m_L, LUA_REGISTRYINDEX);
 
//  remember number of arguments to be used
  m_numArgs = numArgs;
}
#endif
 
/*
SmartUserDataWrapper* CreateNewUserData(lua_State* L, const SmartPtr<void>& ptr,
                        const char* metatableName)
{
//  create the userdata
  SmartUserDataWrapper* udata = (SmartUserDataWrapper*)lua_newuserdata(L,
                      sizeof(SmartUserDataWrapper));
  new(udata) SmartUserDataWrapper;
 
//  associate the object with the userdata.
  udata->smartPtr = ptr;
  udata->type = SMART_POINTER;
 
//  associate the metatable (userdata is already on the stack)
  luaL_getmetatable(L, metatableName);
  lua_setmetatable(L, -2);
 
  return udata;
}
*/
/*
template <typename TData, typename TDataIn1, typename TDataIn2>
void LuaFunction2<TData,TDataIn1,TDataIn2>::operator() (TData& out, int numArgs1, SmartPtr<TDataIn1> valsArgs1[],
                            int numArgs2, ...)
{
  PROFILE_CALLBACK_BEGIN(operatorBracket);
 
    UG_ASSERT((numArgs1+numArgs2) == (int)m_numArgs, "Number of arguments mismatched.");
 
  //  push the callback function on the stack
    lua_rawgeti(m_L, LUA_REGISTRYINDEX, m_cbValueRef);
 
  //  get list of arguments
    va_list ap;
    va_start(ap, numArgs2);
 
  //  read all arguments and push them to the lua stack
    for(int i = 0; i < numArgs1; ++i)
    {
 
      CreateNewUserData(m_L, &valArgs1[i], "");
 
    }
    for(int i = 0; i < numArgs2; ++i)
    {
      TDataIn2 val = va_arg(ap, TDataIn2);
      lua_traits<TDataIn2>::push(m_L, val);
    }
 
 
  //  end read in of parameters
    va_end(ap);
 
  //  compute total args size
    size_t argSize = lua_traits<TDataIn1>::size * numArgs1;
    argSize += lua_traits<TDataIn2>::size * numArgs2;
 
  //  compute total return size
    size_t retSize = lua_traits<TData>::size;
 
  //  call lua function
    if(lua_pcall(m_L, argSize, retSize, 0) != 0)
      UG_THROW("LuaFunction::operator(...): Error while "
            "running callback '" << m_cbValueName << "',"
            " lua message: "<< lua_tostring(m_L, -1));
 
    try{
    //  read return value
      lua_traits<TData>::read(m_L, out);
      UG_COND_THROW(IsFiniteAndNotTooBig(out)==false, out);
    }
    UG_CATCH_THROW("LuaFunction::operator(...): Error while running "
            "callback '" << m_cbValueName << "'");
 
  //  pop values
    lua_pop(m_L, retSize);
 
      PROFILE_CALLBACK_END();
}
*/
 
template<class TDomain, class TAlgebra>
class PlotRefOutputObserver
: public ITimeIntegratorObserver<TDomain, TAlgebra>
{
public:
  typedef ITimeIntegratorObserver<TDomain, TAlgebra> base_type;
  typedef GridFunction<TDomain, TAlgebra> grid_function_type;
  typedef VTKOutput<TDomain::dim> vtk_type;
 
  PlotRefOutputObserver(SmartPtr<UserData<number, grid_function_type::dim> > spExactSol)
  { m_spReference = spExactSol; }
 
#ifdef UG_FOR_LUA
  PlotRefOutputObserver(const char *ExactSol)
  : m_sp_vtk(SPNULL)
  { m_spReference = make_sp(new LuaUserData<number, grid_function_type::dim>(ExactSol)); }
 
  PlotRefOutputObserver(const char *ExactSol, SmartPtr<vtk_type> vtk)
  : m_sp_vtk(vtk)
  { m_spReference = make_sp(new LuaUserData<number, grid_function_type::dim>(ExactSol)); }
 
#endif
 
  virtual ~PlotRefOutputObserver()
  {}
 
  // TODO: replace by call 'func (SmartPtr<G> u, int step, number dt, number t)'
  bool step_process(SmartPtr<grid_function_type> uNew, /* SmartPtr<grid_function_type> uOld, */ int step, number time, number dt) OVERRIDE
  {
    UG_LOG("L2Error(\t"<< time << "\t) = \t" << L2Error(m_spReference, uNew, "c", time, 4) << std::endl);
    if (m_sp_vtk.valid())
    {
      SmartPtr<grid_function_type> ref = uNew->clone();
      Interpolate<grid_function_type> (m_spReference, ref, "c", time);
      m_sp_vtk->print("MyReference", *ref, step, time);
      return true;
    }
 
    return false;
 
  }
 
protected:
  // TODO: replace by appropriate call-back
  SmartPtr<UserData<number, grid_function_type::dim> > m_spReference;
  SmartPtr<vtk_type> m_sp_vtk;
};
 
 
template<class TDomain, class TAlgebra>
class IntegrationOutputObserver
: public ITimeIntegratorObserver<TDomain, TAlgebra>
{
public:
  typedef ITimeIntegratorObserver<TDomain, TAlgebra> base_type;
  typedef GridFunction<TDomain, TAlgebra> grid_function_type;
  typedef VTKOutput<TDomain::dim> vtk_type;
protected:
  struct IntegralSpecs
  {
    IntegralSpecs(const char* cmp, const char* subsets, int quadOrder, const char *idString) :
      m_cmp(cmp), m_subsets(subsets), m_quadOrder(quadOrder), m_idString(idString)
    {};
    std::string m_cmp;
    std::string m_subsets;
    int m_quadOrder;
    std::string m_idString;
  };
 
public:
  IntegrationOutputObserver() : m_vIntegralData()
  {}
 
  virtual ~IntegrationOutputObserver()
  {}
 
  // TODO: replace by call 'func (SmartPtr<G> u, int step, number dt, number t)'
  bool step_process(SmartPtr<grid_function_type> uNew, /*SmartPtr<grid_function_type> uOld,*/ int step, number time, number dt) OVERRIDE
  {
 
    for (typename std::vector<IntegralSpecs>::iterator it = m_vIntegralData.begin();
       it!=m_vIntegralData.end(); ++it)
    {
      number value=Integral(uNew, it->m_cmp.c_str(), it->m_subsets.c_str(), it->m_quadOrder);
      UG_LOG("Integral(\t"<< it->m_idString << "\t"<< time << "\t)=\t" << value << std::endl);
    }
 
    return true;
 
 
  }
 
 
  void add_integral_specs(const char* cmp, const char* subsets, int quadOrder, const char* idString)
  {
    m_vIntegralData.push_back(IntegralSpecs(cmp, subsets, quadOrder, idString));
  }
 
protected:
 
  std::vector<IntegralSpecs> m_vIntegralData;
  //const char* cmp,
  //                const char* subsets,
  // int quadOrder
};
 
 
 
template<class TDomain, class TAlgebra>
class ITimeIntegrator
    : public IOperator< GridFunction<TDomain, TAlgebra> >,
      public TimeIntegratorSubject<TDomain, TAlgebra>
{
  public:
 
    typedef TAlgebra algebra_type;
    typedef typename TAlgebra::vector_type vector_type;
    typedef typename TAlgebra::matrix_type matrix_type;
 
 
    typedef TDomain domain_type;
    typedef GridFunction<TDomain, TAlgebra> grid_function_type;
 
  protected:
    double m_dt;
    double m_lower_tim;
    double m_upper_tim;
 
    double m_precisionBound;
 
    bool m_bNoLogOut;
 
 
  public:
    // constructor
    ITimeIntegrator()
    : m_dt(1.0), m_lower_tim(0.0), m_upper_tim(0.0), m_precisionBound(1e-10), m_bNoLogOut(false)
     {}
 
    virtual ~ITimeIntegrator() {};
 
 
   virtual void init(grid_function_type const& u)
   {
   // UG_ASSERT(m_spDomainDisc.valid(), "TimeIntegrator<TDomain, TAlgebra>::init: m_spDomainDisc invalid.");
   // m_spTimeDisc = make_sp(new time_disc_type(m_spDomainDisc, m_theta));
   }
 
 
 
    void init()
    { UG_THROW("Please init with grid function!"); }
 
 
  /*  This method is used to prepare the in- and output vector used later in apply.
   * It can be called, after the init method has been called at least once.
   * The prepare method is e.g. used to set dirichlet values.
   */
  void prepare(grid_function_type& u) {}
 
 
  void apply(grid_function_type& u1, const grid_function_type& u0)
  { UG_THROW("Fix interfaces!"); }
 
    virtual bool apply(SmartPtr<grid_function_type> u1, number t1, ConstSmartPtr<grid_function_type> u0, number t0) = 0;
 
  void set_time_step(double dt)
  { m_dt = dt; }
 
  double get_time_step()
  { return m_dt; }
 
  void set_precision_bound(double precisionBound)
  { m_precisionBound = precisionBound; return; }
 
  void set_no_log_out(bool bNoLogOut)
  { m_bNoLogOut = bNoLogOut; return; }
 
 
 
};
 
 
 
template<class TDomain, class TAlgebra>
class ILinearTimeIntegrator : public ITimeIntegrator<TDomain, TAlgebra>
{
 
public:
  typedef ITimeIntegrator<TDomain, TAlgebra> base_type;
  typedef typename base_type::vector_type vector_type;
  typedef ILinearOperatorInverse<vector_type> linear_solver_type;
  typedef AssembledLinearOperator<TAlgebra> assembled_operator_type;
 
  // forward constructor
  ILinearTimeIntegrator()
  : base_type() {}
 
  ILinearTimeIntegrator(SmartPtr<linear_solver_type> lSolver)
  : base_type(),  m_spLinearSolver(lSolver)
  {}
 
 
  void set_linear_solver(SmartPtr<linear_solver_type> lSolver)
  { m_spLinearSolver=lSolver;}
 
protected:
  SmartPtr<linear_solver_type> m_spLinearSolver;
 
};
 
 
template<class TAlgebra>
class ITimeDiscDependentObject
{
public:
  typedef ITimeDiscretization<TAlgebra> time_disc_type;
 
  ITimeDiscDependentObject(SmartPtr<time_disc_type> spTimeDisc) :
    m_spTimeDisc(spTimeDisc)
  {}
 
  SmartPtr<time_disc_type> get_time_disc() {return m_spTimeDisc;}
protected:
  SmartPtr<time_disc_type> m_spTimeDisc;
};
 
 
template<class TDomain, class TAlgebra>
class LinearTimeIntegrator :
  public ILinearTimeIntegrator<TDomain, TAlgebra>,
  public ITimeDiscDependentObject<TAlgebra>
 
{
private:
 
protected:
  typedef ITimeDiscDependentObject<TAlgebra> tdisc_dep_type;
public:
  typedef ILinearTimeIntegrator<TDomain, TAlgebra> base_type;
  typedef ITimeDiscretization<TAlgebra> time_disc_type;
  typedef typename base_type::grid_function_type grid_function_type;
  typedef VectorTimeSeries<typename base_type::vector_type> vector_time_series_type;
 
  // constructor
  LinearTimeIntegrator (SmartPtr< time_disc_type> tDisc)
  : base_type(), ITimeDiscDependentObject<TAlgebra>(tDisc) {}
 
  LinearTimeIntegrator (SmartPtr< time_disc_type> tDisc,  SmartPtr<typename base_type::linear_solver_type> lSolver)
  : base_type(lSolver), ITimeDiscDependentObject<TAlgebra>(tDisc) {}
 
  bool apply(SmartPtr<grid_function_type> u1, number t1, ConstSmartPtr<grid_function_type> u0, number t0);
};
 
 
 
template<typename TDomain, typename TAlgebra>
bool LinearTimeIntegrator<TDomain, TAlgebra>::apply(SmartPtr<grid_function_type> u1, number t1, ConstSmartPtr<grid_function_type> u0, number t0)
{
 
  LIMEX_PROFILE_FUNC()
  UG_COND_THROW(!base_type::m_spLinearSolver.valid(), "Linear solver invalid");
 
  // short-cuts
  GridLevel const &gl = u0->grid_level();
  time_disc_type &tdisc = *tdisc_dep_type::m_spTimeDisc;
 
  // create solution vector & right hand side
  SmartPtr<typename base_type::vector_type> uold= u0->clone();
  SmartPtr<typename base_type::vector_type> b= u0->clone_without_values();
 
  // solution time series
  SmartPtr<vector_time_series_type> m_spSolTimeSeries;
  m_spSolTimeSeries=make_sp(new vector_time_series_type());
  m_spSolTimeSeries->clear();
  m_spSolTimeSeries->push(uold, t0);
 
  // create matrix operator
  SmartPtr<typename base_type::assembled_operator_type> spAssOp=make_sp(new typename base_type::assembled_operator_type(tdisc_dep_type::m_spTimeDisc, gl));
 
  // integrate
  if(!base_type::m_bNoLogOut)
    UG_LOG("+++ Integrating: ["<< t0 <<", "<< t1 <<"]\n");
 
  double t = t0;
  number dt_assembled = -1.0;   // invalid
  int step = 1;
 
  number currdt = base_type::m_dt;
 
  while((t < t1) && (t1-t > base_type::m_precisionBound))
  {
 
    if(!base_type::m_bNoLogOut)
    { UG_LOG("+++ Timestep +++" << step << "\n"); }
 
    // determine step size
    number dt = std::min(currdt, t1-t);
 
    // prepare step
    tdisc.prepare_step(m_spSolTimeSeries, dt);
    if (fabs(dt-dt_assembled) > base_type::m_precisionBound)
    {
      // re-assemble operator
      if(!base_type::m_bNoLogOut)
        UG_LOG("+++ Reassemble (t=" << t << ", dt=" << dt <<")\n");
 
      tdisc.assemble_linear(*spAssOp, *b, gl);
      (base_type::m_spLinearSolver)->init(spAssOp, *u1);
      dt_assembled = dt;
    }
    else
    {
      // keep old operator
      tdisc.assemble_rhs(*b, gl);
    }
 
    // execute step
    if (base_type::m_spLinearSolver->apply(*u1, *b))
    {
      // ACCEPTING:
      // push updated solution into time series
      t += dt;
      SmartPtr<typename base_type::vector_type> tmp = m_spSolTimeSeries->oldest();
      VecAssign(*tmp, *u1.template cast_dynamic<typename base_type::vector_type>());
      m_spSolTimeSeries->push_discard_oldest(tmp, t);
 
      this->notify_finalize_step(u1, step++, t+dt, dt);
    }
    else
    {
      // DISCARDING
      currdt *= 0.5;
    }
 
  }
 
  this->notify_end(u1, step, t1, currdt);
 
  return true;
};
 
 
template<class TDomain, class TAlgebra>
class ConstStepLinearTimeIntegrator :
  public ILinearTimeIntegrator<TDomain, TAlgebra>,
  public ITimeDiscDependentObject<TAlgebra>
{
protected:
  typedef ITimeDiscDependentObject<TAlgebra> tdisc_dep_type;
public:
  typedef ILinearTimeIntegrator<TDomain, TAlgebra> base_type;
  typedef ITimeDiscretization<TAlgebra> time_disc_type;
  typedef typename base_type::linear_solver_type linear_solver_type;
  typedef typename base_type::grid_function_type grid_function_type;
  typedef VectorTimeSeries<typename base_type::vector_type> vector_time_series_type;
 
private:
 
protected:
 
  int m_numSteps;
public:
 
  // constructor
  ConstStepLinearTimeIntegrator (SmartPtr<time_disc_type> tDisc)
  : base_type(), ITimeDiscDependentObject<TAlgebra>(tDisc), m_numSteps(1) {}
 
  ConstStepLinearTimeIntegrator (SmartPtr<time_disc_type> tDisc, SmartPtr<typename base_type::linear_solver_type> lSolver)
  : base_type(lSolver), ITimeDiscDependentObject<TAlgebra>(tDisc), m_numSteps(1) {}
 
  void set_num_steps(int steps) {m_numSteps = steps;}
 
  bool apply(SmartPtr<grid_function_type> u1, number t1, ConstSmartPtr<grid_function_type> u0, number t0);
};
 
 
 
template<typename TDomain, typename TAlgebra>
bool ConstStepLinearTimeIntegrator<TDomain, TAlgebra>::apply(SmartPtr<grid_function_type> u1, number t1, ConstSmartPtr<grid_function_type> u0, number t0)
{
  LIMEX_PROFILE_FUNC()
  UG_COND_THROW(!base_type::m_spLinearSolver.valid(), "Linear solver invalid");
 
  // short-cuts
  GridLevel const &gl = u0->grid_level();
  time_disc_type &tdisc = *tdisc_dep_type::m_spTimeDisc;
 
  // create solution vector & right hand side
  SmartPtr<typename base_type::vector_type> uold= u0->clone();
  SmartPtr<typename base_type::vector_type> b= u0->clone_without_values();
  
  // solution time series
  SmartPtr<vector_time_series_type> m_spSolTimeSeries;
  m_spSolTimeSeries=make_sp(new vector_time_series_type());
  m_spSolTimeSeries->push(uold, t0);
 
  SmartPtr<typename base_type::assembled_operator_type> spAssOp = SPNULL;
 
  // select number of steps
   double t = t0;
   int numSteps = round((t1-t0) / base_type::m_dt);
   number currdt = (t1-t0) / numSteps;
  
 
 
   //std::cerr << "+++ Integrating: ["<< t0 <<", "<< t1 <<"] with dt=" << currdt << "("<< numSteps<< " iters)\n";
  if(!base_type::m_bNoLogOut)
  {
    UG_LOG("+++ Integrating: [\t"<< t0 <<"\t, \t"<< t1 <<"\t] with dt=\t" << currdt << "("<< numSteps<< " iters)" << std::endl);
  }
   
   // integrate
   for(int step = 1; step<=numSteps; ++step)
   {
       // determine step size
       // number dt = std::min(currdt, t1-t);
     const number dt = currdt;
 
    if(!base_type::m_bNoLogOut)
    {
      UG_LOG("+++ Const timestep +++" << step<< "(t=" << t << ", dt=" << dt << ")"<< std::endl);
    }
    this->notify_init_step(u1, step, t, dt);
    
    // prepare step
     tdisc.prepare_step(m_spSolTimeSeries, dt);
     if (spAssOp==SPNULL)
     {
       // Assemble operator.
      if(!base_type::m_bNoLogOut) UG_LOG("+++ Assemble (t=" << t << ", dt=" << dt <<")" << std::endl);
 
       spAssOp=make_sp(new typename base_type::assembled_operator_type(tdisc_dep_type::m_spTimeDisc, gl));
       tdisc.assemble_linear(*spAssOp, *b, gl);
       (base_type::m_spLinearSolver)->init(spAssOp, *u1);
     }
     else
     {
       // Recycle existing operator.
       // std::cerr << "Recycling timestep " << step << "\n";
       tdisc.assemble_rhs(*b, gl);
     }
 
     // execute step
     if (base_type::m_spLinearSolver->apply(*u1, *b))
     {
       // ACCEPTING: push updated solution into time series
       t += dt;
       SmartPtr<typename base_type::vector_type> tmp = m_spSolTimeSeries->oldest();
       VecAssign(*tmp,  *u1.template cast_dynamic<typename base_type::vector_type>());
       m_spSolTimeSeries->push_discard_oldest(tmp, t);
       this->notify_finalize_step(u1, step, t, dt);  // t updated already!
     }
     else
     {
      UG_THROW("ConstStepLinearTimeIntegrator::apply failed!!!");
      this->notify_rewind_step(u1, step, t+dt, dt);
     }
 
   }
 
   this->notify_end(u1, numSteps, t1, currdt);
 
   return true;
};
 
 
 
template<class TDomain, class TAlgebra>
class TimeIntegratorLinearAdaptive :
  public ILinearTimeIntegrator<TDomain, TAlgebra>,
  public ITimeDiscDependentObject<TAlgebra>
{
protected:
  typedef ITimeDiscDependentObject<TAlgebra> tdisc_dep_type;
public:
  typedef ILinearTimeIntegrator<TDomain, TAlgebra> base_type;
  typedef ITimeDiscretization<TAlgebra> time_disc_type;
  typedef typename base_type::grid_function_type grid_function_type;
  typedef VectorTimeSeries<typename base_type::vector_type> vector_time_series_type;
 
private:
 
 
protected:
 
  SmartPtr<time_disc_type> m_spTimeDisc2;        // set during init
 
  double m_tol, m_dtmin, m_dtmax;
 
 
public:
  TimeIntegratorLinearAdaptive (SmartPtr<time_disc_type> tDisc1, SmartPtr<time_disc_type> tDisc2)
  : base_type(), ITimeDiscDependentObject<TAlgebra>(tDisc1), m_tol(1e-2), m_dtmin(-1.0), m_dtmax(-1.0)
  {
    m_spTimeDisc2 = tDisc2;
  }
 
  void init(grid_function_type const& u);
  bool apply(SmartPtr<grid_function_type> u1, number t1, ConstSmartPtr<grid_function_type> u0, number t0);
 
    void set_tol(double tol) {m_tol = tol;}
    void set_time_step_min(number dt) {m_dtmin = dt;}
    void set_time_step_max(number dt) {m_dtmax = dt;}
};
 
 
template<typename TDomain, typename TAlgebra>
void TimeIntegratorLinearAdaptive<TDomain, TAlgebra>::init(grid_function_type const& u)
{
  // call base
  base_type::init(u);
  //m_spTimeDisc2 = make_sp(new typename base_type::time_disc_type(base_type::m_spDomainDisc, base_type::m_theta));
}
 
template<typename TDomain, typename TAlgebra>
bool TimeIntegratorLinearAdaptive<TDomain, TAlgebra>::apply(SmartPtr<grid_function_type> u1, number t1, ConstSmartPtr<grid_function_type> u0, number t0)
{
  // short-cuts
  GridLevel const &gl = u0->grid_level();
  time_disc_type &tdisc = *tdisc_dep_type::m_spTimeDisc;
  time_disc_type &tdisc2 = *m_spTimeDisc2;
 
  // create solution vector & right hand side
  SmartPtr<typename base_type::vector_type> uold= u0->clone();
  SmartPtr<typename base_type::vector_type> b= u0->clone_without_values();
 
  // create matrix operator
  SmartPtr<typename base_type::assembled_operator_type> spAssOp=make_sp(new typename base_type::assembled_operator_type(tdisc_dep_type::m_spTimeDisc, gl));
 
  // create additional solutions
  SmartPtr<typename base_type::grid_function_type>  u2old = u0->clone();
  SmartPtr<typename base_type::grid_function_type>  u2 = u0->clone();
 
  // solution time series
  SmartPtr<vector_time_series_type> m_spSolTimeSeries;
  m_spSolTimeSeries=make_sp(new vector_time_series_type());
  m_spSolTimeSeries->push(uold, t0);
 
  SmartPtr<vector_time_series_type> m_spSolTimeSeries2;
  m_spSolTimeSeries2=make_sp(new vector_time_series_type());
  m_spSolTimeSeries2->push(u2old, t0);
  
  // automatic selection of min/max time step
  if (m_dtmin <= 0.0) { m_dtmin = (t1 - t0)/1.0e+5; }
  if (m_dtmax <= 0.0) { m_dtmax = (t1 - t0)/10.0; }
 
  // Aitken Neville extrapolation
  const size_t tsteps[2] = {1,2};
  std::vector<size_t> vsteps (tsteps, tsteps+2);
  AitkenNevilleTimex<typename base_type::vector_type> timex(vsteps);
 
  // integrate
  if(!base_type::m_bNoLogOut)
    UG_LOG("+++ Integrating: ["<< t0 <<", "<< t1 <<"]\n");
 
   double t = t0;
   int step = 0;
 
   number dt = base_type::m_dt;
   while((t < t1) && (t1-t > base_type::m_precisionBound))
   {
     // step: t -> t+dt
     bool bSuccess = false;
     while (!bSuccess){
    
       // determine step size
       if (dt<m_dtmin){
        if(!base_type::m_bNoLogOut)
         UG_LOG("Step size below minimum")
     }
     dt = std::min(dt, t1-t);
     
     // basic step
      if(!base_type::m_bNoLogOut)
       UG_LOG("+++ Timestep: " << ++step << "\n");
 
     tdisc.prepare_step(m_spSolTimeSeries, dt);
     tdisc.assemble_linear(*spAssOp, *b, gl);
     base_type::m_spLinearSolver->init(spAssOp, *u1);
     base_type::m_spLinearSolver->apply(*u1, *b);
     
     
     // control 1/2
      if(!base_type::m_bNoLogOut)
       UG_LOG("+++ Control: " << step << "\n");
 
     tdisc2.prepare_step(m_spSolTimeSeries, 0.5*dt);
     tdisc2.assemble_linear(*spAssOp, *b, gl);
     base_type::m_spLinearSolver->init(spAssOp, *u2);
     base_type::m_spLinearSolver->apply(*u2, *b);
     
     // push back solution
     SmartPtr<typename base_type::vector_type> tmp2 =  m_spSolTimeSeries2->oldest();
     (*tmp2)=*(u2.template cast_static<typename base_type::vector_type>());
     m_spSolTimeSeries2->push_discard_oldest(tmp2, t + 0.5*dt);
     
     // control 2/2
     tdisc2.prepare_step(m_spSolTimeSeries2, 0.5*dt);
     tdisc2.assemble_linear(*spAssOp, *b, gl);
     base_type::m_spLinearSolver->init(spAssOp, *u2);
     base_type::m_spLinearSolver->apply(*u2, *b);
 
     // obtain extrapolated solution
     timex.set_solution(u1, 0);
     timex.set_solution(u2, 1);
     timex.apply();
 
     // predict (subsequent) time step
     number eps = timex.get_error_estimates()[0];
     number lambda = std::pow(0.8* m_tol/eps, 0.5); 
 
     number dtEst= dt*lambda; 
     dtEst = std::min(dtEst, 1.5*dt); 
     dtEst = std::min(dtEst, m_dtmax); 
     
     dt = dtEst;
     if (eps <= m_tol)
     {
       // ACCEPT STEP (and thus solution u2)
      if(!base_type::m_bNoLogOut)
       UG_LOG("ACCEPTING solution, dtnew=" << dt);
 
       bSuccess = true;
     }
     else
     {
       // DISCARD step
      if(!base_type::m_bNoLogOut)
       UG_LOG("DISCARDING solution, dtnew=" << dt);
 
       // => reset solutions
       VecAssign(*u1.template cast_dynamic<typename base_type::vector_type>(), *uold);
       
       // => timeSeries2 has been updated...
       SmartPtr<typename base_type::vector_type> tmp = m_spSolTimeSeries2->oldest();
       VecAssign(*tmp, *uold);
       m_spSolTimeSeries2->push_discard_oldest(tmp, t);
 
     }
 
     } 
 
   
     // prepare next loop
     t += dt;
 
     // push updated solution into time series (and continue)
     SmartPtr<typename base_type::vector_type> tmp = m_spSolTimeSeries->oldest();
     VecAssign(*tmp, static_cast<typename base_type::vector_type> (*u2));
     m_spSolTimeSeries->push_discard_oldest(tmp, t);
 
   }
 
   return true;
};
 
class TimeStepBounds
{
public:
  TimeStepBounds()
  : m_dtMin(0.0), m_dtMax(std::numeric_limits<double>::max()),  m_redFac(1.0), m_incFac(1.0)
  {}
 
  void set_dt_min(double min) { m_dtMin = min; }
  double get_dt_min() { return m_dtMin; }
 
  void set_dt_max(double max) { m_dtMax = max; }
  double get_dt_max() { return m_dtMax; }
 
  void set_reduction_factor(double dec) { m_redFac = dec; }
  double get_reduction_factor() { return m_redFac; }
 
  void set_increase_factor(double inc) { m_incFac = inc; }
  double get_increase_factor() { return m_incFac; }
 
  void rescale(double alpha)
  { m_dtMin*= alpha; m_dtMax*= alpha;}
 
protected:
  double m_dtMin, m_dtMax;
  double m_redFac, m_incFac;
};
 
template<class TDomain, class TAlgebra>
class INonlinearTimeIntegrator
: public ITimeIntegrator<TDomain, TAlgebra>
{
public:
  typedef ITimeIntegrator<TDomain, TAlgebra> base_type;
  typedef typename base_type::vector_type vector_type;
  typedef IOperatorInverse<vector_type> solver_type;
  typedef AssembledOperator<TAlgebra> assembled_operator_type;
 
  INonlinearTimeIntegrator()
  : m_dtBounds() {}
 
  void set_solver(SmartPtr<solver_type> solver)
  { m_spSolver=solver;}
 
  ConstSmartPtr<solver_type> get_solver() const
  { return m_spSolver;}
 
  SmartPtr<solver_type> get_solver()
  { return m_spSolver;}
 
  void set_dt_min(double min) { m_dtBounds.set_dt_min(min); }
  double get_dt_min() { return m_dtBounds. get_dt_min(); }
 
  void set_dt_max(double max) { m_dtBounds.set_dt_max(max); }
  double get_dt_max() { return m_dtBounds.get_dt_max(); }
 
  void set_reduction_factor(double dec) { m_dtBounds.set_reduction_factor(dec); }
  double get_reduction_factor() { return m_dtBounds.get_reduction_factor(); }
 
  void set_increase_factor(double inc) { m_dtBounds.set_increase_factor(inc); }
  double get_increase_factor() { return m_dtBounds.get_increase_factor(); }
 
protected:
  SmartPtr<solver_type> m_spSolver;
  TimeStepBounds m_dtBounds;
 
 
};
 
 
} // ug
 
#include "simple_integrator.hpp"
 
namespace ug {
 
template<class TDomain, class TAlgebra>
class DiscontinuityIntegrator :
    public INonlinearTimeIntegrator<TDomain, TAlgebra>
{
public:
 
  typedef INonlinearTimeIntegrator<TDomain, TAlgebra> base_type;
  typedef typename base_type::grid_function_type grid_function_type;
 
  DiscontinuityIntegrator(SmartPtr<base_type> baseIntegrator) :
    base_type(), m_wrappedIntegrator(baseIntegrator), m_timePoints() {};
 
  bool apply(SmartPtr<grid_function_type> u1, number t1, ConstSmartPtr<grid_function_type> u0, number t0)
  {
    int dstep = 0;
    auto tpoint = m_timePoints.begin();
    double tcurr = (tpoint == m_timePoints.end()) ? t1 : (*tpoint);
    double eps = 1e-8;
 
    // Perform first step.
    //this->notify_init_step(u0, dstep, t0,  tcurr-t0);
    bool status = m_wrappedIntegrator->apply(u1, tcurr*(1.0-eps), u0, t0);
    this->notify_finalize_step(u1, dstep++, tcurr, tcurr-t0);
 
    // Repeat for all intermediate points.
    while (tpoint != m_timePoints.end())
    {
      tpoint++;
      double tnext = (tpoint == m_timePoints.end()) ? t1 : (*tpoint);
 
      // Perform step.
      //this->notify_init_step(u1, dstep, tcurr, tnext-tcurr);
      status = status && m_wrappedIntegrator->apply(u1, tnext*(1.0-eps), u1, tcurr);
      this->notify_finalize_step(u1, dstep++, tnext, tnext-tcurr);
 
      tcurr = tnext;
    }
    this->notify_end(u1, dstep, t1, 0.0);
    return status;
  }
 
  void insert_points (std::vector<double> points)
  {
    m_timePoints = points;
  }
protected:
  SmartPtr<base_type> m_wrappedIntegrator;
  std::vector<double> m_timePoints;
};
 
} // namespace ug
 
#endif /* TIME_INTEGRATOR_HPP_ */