Tempus_TrapezoidalTest.cpp

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// @HEADER
// ****************************************************************************
//                Tempus: Copyright (2017) Sandia Corporation
//
// Distributed under BSD 3-clause license (See accompanying file Copyright.txt)
// ****************************************************************************
// @HEADER

#include "Teuchos_UnitTestHarness.hpp"
#include "Teuchos_XMLParameterListHelpers.hpp"
#include "Teuchos_TimeMonitor.hpp"
#include "Teuchos_DefaultComm.hpp"

#include "Tempus_config.hpp"
#include "Tempus_IntegratorBasic.hpp"
#include "Tempus_StepperTrapezoidal.hpp"

#include "../TestModels/SinCosModel.hpp"
#include "../TestModels/VanDerPolModel.hpp"
#include "../TestUtils/Tempus_ConvergenceTestUtils.hpp"

#include "Stratimikos_DefaultLinearSolverBuilder.hpp"
#include "Thyra_LinearOpWithSolveFactoryHelpers.hpp"

#ifdef Tempus_ENABLE_MPI
#include "Epetra_MpiComm.h"
#else
#include "Epetra_SerialComm.h"
#endif

#include <vector>
#include <fstream>
#include <sstream>
#include <limits>

namespace Tempus_Test {

using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::rcp_const_cast;
using Teuchos::ParameterList;
using Teuchos::sublist;
using Teuchos::getParametersFromXmlFile;

using Tempus::IntegratorBasic;
using Tempus::SolutionHistory;
using Tempus::SolutionState;


// ************************************************************
// ************************************************************
TEUCHOS_UNIT_TEST(Trapezoidal, ParameterList)
{
  // Read params from .xml file
  RCP<ParameterList> pList =
    getParametersFromXmlFile("Tempus_Trapezoidal_SinCos.xml");

  // Setup the SinCosModel
  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
  auto model = rcp(new SinCosModel<double> (scm_pl));

  RCP<ParameterList> tempusPL  = sublist(pList, "Tempus", true);

  // Test constructor IntegratorBasic(tempusPL, model)
  {
    RCP<Tempus::IntegratorBasic<double> > integrator =
      Tempus::integratorBasic<double>(tempusPL, model);

    RCP<ParameterList> stepperPL = sublist(tempusPL, "Default Stepper", true);

    RCP<const ParameterList> defaultPL =
      integrator->getStepper()->getValidParameters();
    bool pass = haveSameValues(*stepperPL, *defaultPL, true);
    if (!pass) {
      std::cout << std::endl;
      std::cout << "stepperPL -------------- \n" << *stepperPL << std::endl;
      std::cout << "defaultPL -------------- \n" << *defaultPL << std::endl;
    }
    TEST_ASSERT(pass)
  }

  // Test constructor IntegratorBasic(model, stepperType)
  {
    RCP<Tempus::IntegratorBasic<double> > integrator =
      Tempus::integratorBasic<double>(model, "Trapezoidal Method");

    RCP<ParameterList> stepperPL = sublist(tempusPL, "Default Stepper", true);
    RCP<const ParameterList> defaultPL =
      integrator->getStepper()->getValidParameters();

    bool pass = haveSameValues(*stepperPL, *defaultPL, true);
    if (!pass) {
      std::cout << std::endl;
      std::cout << "stepperPL -------------- \n" << *stepperPL << std::endl;
      std::cout << "defaultPL -------------- \n" << *defaultPL << std::endl;
    }
    TEST_ASSERT(pass)
  }
}


// ************************************************************
// ************************************************************
TEUCHOS_UNIT_TEST(Trapezoidal, ConstructingFromDefaults)
{
  double dt = 0.1;

  // Read params from .xml file
  RCP<ParameterList> pList =
    getParametersFromXmlFile("Tempus_Trapezoidal_SinCos.xml");
  RCP<ParameterList> pl = sublist(pList, "Tempus", true);

  // Setup the SinCosModel
  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
  //RCP<SinCosModel<double> > model = sineCosineModel(scm_pl);
  auto model = rcp(new SinCosModel<double>(scm_pl));

  // Setup Stepper for field solve ----------------------------
  auto stepper = rcp(new Tempus::StepperTrapezoidal<double>());
  //{
  //  // Turn on NOX output.
  //  RCP<ParameterList> sPL = stepper->getNonconstParameterList();
  //  std::string solverName = sPL->get<std::string>("Solver Name");
  //  RCP<ParameterList> solverPL = Teuchos::sublist(sPL, solverName, true);
  //  solverPL->sublist("NOX").sublist("Printing").sublist("Output Information")
  //           .set("Outer Iteration", true);
  //  solverPL->sublist("NOX").sublist("Printing").sublist("Output Information")
  //           .set("Parameters", true);
  //  solverPL->sublist("NOX").sublist("Printing").sublist("Output Information")
  //           .set("Details", true);
  //  stepper->setSolver(solverPL);
  //}
  stepper->setModel(model);
  stepper->initialize();

  // Setup TimeStepControl ------------------------------------
  auto timeStepControl = rcp(new Tempus::TimeStepControl<double>());
  ParameterList tscPL = pl->sublist("Default Integrator")
                           .sublist("Time Step Control");
  timeStepControl->setStepType (tscPL.get<std::string>("Integrator Step Type"));
  timeStepControl->setInitIndex(tscPL.get<int>   ("Initial Time Index"));
  timeStepControl->setInitTime (tscPL.get<double>("Initial Time"));
  timeStepControl->setFinalTime(tscPL.get<double>("Final Time"));
  timeStepControl->setInitTimeStep(dt);
  timeStepControl->initialize();

  // Setup initial condition SolutionState --------------------
  Thyra::ModelEvaluatorBase::InArgs<double> inArgsIC =
    stepper->getModel()->getNominalValues();
  auto icSoln = rcp_const_cast<Thyra::VectorBase<double> > (inArgsIC.get_x());
  auto icSolnDot =
    rcp_const_cast<Thyra::VectorBase<double> > (inArgsIC.get_x_dot());
  auto icState = Tempus::createSolutionStateX(icSoln,icSolnDot);
  icState->setTime    (timeStepControl->getInitTime());
  icState->setIndex   (timeStepControl->getInitIndex());
  icState->setTimeStep(0.0);
  icState->setOrder   (stepper->getOrder());
  icState->setSolutionStatus(Tempus::Status::PASSED);  // ICs are passing.

  // Setup SolutionHistory ------------------------------------
  auto solutionHistory = rcp(new Tempus::SolutionHistory<double>());
  solutionHistory->setName("Forward States");
  solutionHistory->setStorageType(Tempus::STORAGE_TYPE_STATIC);
  solutionHistory->setStorageLimit(2);
  solutionHistory->addState(icState);

  // Setup Integrator -----------------------------------------
  RCP<Tempus::IntegratorBasic<double> > integrator =
    Tempus::integratorBasic<double>();
  integrator->setStepperWStepper(stepper);
  integrator->setTimeStepControl(timeStepControl);
  integrator->setSolutionHistory(solutionHistory);
  //integrator->setObserver(...);
  integrator->initialize();


  // Integrate to timeMax
  bool integratorStatus = integrator->advanceTime();
  TEST_ASSERT(integratorStatus)


  // Test if at 'Final Time'
  double time = integrator->getTime();
  double timeFinal =pl->sublist("Default Integrator")
     .sublist("Time Step Control").get<double>("Final Time");
  TEST_FLOATING_EQUALITY(time, timeFinal, 1.0e-14);

  // Time-integrated solution and the exact solution
  RCP<Thyra::VectorBase<double> > x = integrator->getX();
  RCP<const Thyra::VectorBase<double> > x_exact =
    model->getExactSolution(time).get_x();

  // Calculate the error
  RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
  Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));

  // Check the order and intercept
  std::cout << "  Stepper = Trapezoidal" << std::endl;
  std::cout << "  =========================" << std::endl;
  std::cout << "  Exact solution   : " << get_ele(*(x_exact), 0) << "   "
                                       << get_ele(*(x_exact), 1) << std::endl;
  std::cout << "  Computed solution: " << get_ele(*(x      ), 0) << "   "
                                       << get_ele(*(x      ), 1) << std::endl;
  std::cout << "  Difference       : " << get_ele(*(xdiff  ), 0) << "   "
                                       << get_ele(*(xdiff  ), 1) << std::endl;
  std::cout << "  =========================" << std::endl;
  TEST_FLOATING_EQUALITY(get_ele(*(x), 0), 0.841021, 1.0e-4 );
  TEST_FLOATING_EQUALITY(get_ele(*(x), 1), 0.541002, 1.0e-4 );
}


// ************************************************************
// ************************************************************
TEUCHOS_UNIT_TEST(Trapezoidal, SinCos)
{
  RCP<Tempus::IntegratorBasic<double> > integrator;
  std::vector<RCP<Thyra::VectorBase<double>>> solutions;
  std::vector<RCP<Thyra::VectorBase<double>>> solutionsDot;
  std::vector<double> StepSize;
  std::vector<double> xErrorNorm;
  std::vector<double> xDotErrorNorm;
  const int nTimeStepSizes = 7;
  double dt = 0.2;
  double time = 0.0;
  for (int n=0; n<nTimeStepSizes; n++) {

    // Read params from .xml file
    RCP<ParameterList> pList =
      getParametersFromXmlFile("Tempus_Trapezoidal_SinCos.xml");

    //std::ofstream ftmp("PL.txt");
    //pList->print(ftmp);
    //ftmp.close();

    // Setup the SinCosModel
    RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
    //RCP<SinCosModel<double> > model = sineCosineModel(scm_pl);
    auto model = rcp(new SinCosModel<double>(scm_pl));

    dt /= 2;

    // Setup the Integrator and reset initial time step
    RCP<ParameterList> pl = sublist(pList, "Tempus", true);
    pl->sublist("Default Integrator")
       .sublist("Time Step Control").set("Initial Time Step", dt);
    integrator = Tempus::integratorBasic<double>(pl, model);

    // Initial Conditions
    // During the Integrator construction, the initial SolutionState
    // is set by default to model->getNominalVales().get_x().  However,
    // the application can set it also by integrator->initializeSolutionHistory.
    {
      RCP<Thyra::VectorBase<double> > x0 =
        model->getNominalValues().get_x()->clone_v();
      RCP<Thyra::VectorBase<double> > xdot0 =
        model->getNominalValues().get_x_dot()->clone_v();
      integrator->initializeSolutionHistory(0.0, x0, xdot0);
    }

    // Integrate to timeMax
    bool integratorStatus = integrator->advanceTime();
    TEST_ASSERT(integratorStatus)

    // Test if at 'Final Time'
    time = integrator->getTime();
    double timeFinal =pl->sublist("Default Integrator")
       .sublist("Time Step Control").get<double>("Final Time");
    TEST_FLOATING_EQUALITY(time, timeFinal, 1.0e-14);

    // Plot sample solution and exact solution
    if (n == 0) {
      RCP<const SolutionHistory<double> > solutionHistory =
        integrator->getSolutionHistory();
      writeSolution("Tempus_Trapezoidal_SinCos.dat", solutionHistory);

      auto solnHistExact = rcp(new Tempus::SolutionHistory<double>());
      for (int i=0; i<solutionHistory->getNumStates(); i++) {
        double time_i = (*solutionHistory)[i]->getTime();
        auto state = Tempus::createSolutionStateX(
          rcp_const_cast<Thyra::VectorBase<double> > (
            model->getExactSolution(time_i).get_x()),
          rcp_const_cast<Thyra::VectorBase<double> > (
            model->getExactSolution(time_i).get_x_dot()));
        state->setTime((*solutionHistory)[i]->getTime());
        solnHistExact->addState(state);
      }
      writeSolution("Tempus_Trapezoidal_SinCos-Ref.dat", solnHistExact);
    }

    // Store off the final solution and step size
    StepSize.push_back(dt);
    auto solution = Thyra::createMember(model->get_x_space());
    Thyra::copy(*(integrator->getX()),solution.ptr());
    solutions.push_back(solution);
    auto solutionDot = Thyra::createMember(model->get_x_space());
    Thyra::copy(*(integrator->getXdot()),solutionDot.ptr());
    solutionsDot.push_back(solutionDot);
    if (n == nTimeStepSizes-1) {  // Add exact solution last in vector.
      StepSize.push_back(0.0);
      auto solutionExact = Thyra::createMember(model->get_x_space());
      Thyra::copy(*(model->getExactSolution(time).get_x()),solutionExact.ptr());
      solutions.push_back(solutionExact);
      auto solutionDotExact = Thyra::createMember(model->get_x_space());
      Thyra::copy(*(model->getExactSolution(time).get_x_dot()),
                  solutionDotExact.ptr());
      solutionsDot.push_back(solutionDotExact);
    }
  }

 double xSlope = 0.0;
  double xDotSlope = 0.0;
  RCP<Tempus::Stepper<double> > stepper = integrator->getStepper();
  double order = stepper->getOrder();
  writeOrderError("Tempus_Trapezoidal_SinCos-Error.dat",
                  stepper, StepSize,
                  solutions,    xErrorNorm,    xSlope,
                  solutionsDot, xDotErrorNorm, xDotSlope);

  TEST_FLOATING_EQUALITY( xSlope,                 order, 0.01   );
  TEST_FLOATING_EQUALITY( xErrorNorm[0],    0.000832086, 1.0e-4 );
  TEST_FLOATING_EQUALITY( xDotSlope,              order, 0.01   );
  TEST_FLOATING_EQUALITY( xDotErrorNorm[0], 0.000832086, 1.0e-4 );

  Teuchos::TimeMonitor::summarize();
}


// ************************************************************
// ************************************************************
TEUCHOS_UNIT_TEST(Trapezoidal, VanDerPol)
{
  RCP<Tempus::IntegratorBasic<double> > integrator;
  std::vector<RCP<Thyra::VectorBase<double>>> solutions;
  std::vector<RCP<Thyra::VectorBase<double>>> solutionsDot;
  std::vector<double> StepSize;
  std::vector<double> xErrorNorm;
  std::vector<double> xDotErrorNorm;
  const int nTimeStepSizes = 4;
  double dt = 0.05;
  double time = 0.0;
  for (int n=0; n<nTimeStepSizes; n++) {

    // Read params from .xml file
    RCP<ParameterList> pList =
      getParametersFromXmlFile("Tempus_Trapezoidal_VanDerPol.xml");

    // Setup the VanDerPolModel
    RCP<ParameterList> vdpm_pl = sublist(pList, "VanDerPolModel", true);
    auto model = rcp(new VanDerPolModel<double>(vdpm_pl));

    // Set the step size
    dt /= 2;
    if (n == nTimeStepSizes-1) dt /= 10.0;

    // Setup the Integrator and reset initial time step
    RCP<ParameterList> pl = sublist(pList, "Tempus", true);
    pl->sublist("Demo Integrator")
       .sublist("Time Step Control").set("Initial Time Step", dt);
    integrator = Tempus::integratorBasic<double>(pl, model);

    // Integrate to timeMax
    bool integratorStatus = integrator->advanceTime();
    TEST_ASSERT(integratorStatus)

    // Test if at 'Final Time'
    time = integrator->getTime();
    double timeFinal =pl->sublist("Demo Integrator")
      .sublist("Time Step Control").get<double>("Final Time");
    double tol = 100.0 * std::numeric_limits<double>::epsilon();
    TEST_FLOATING_EQUALITY(time, timeFinal, tol);

    // Store off the final solution and step size
    StepSize.push_back(dt);
    auto solution = Thyra::createMember(model->get_x_space());
    Thyra::copy(*(integrator->getX()),solution.ptr());
    solutions.push_back(solution);
    auto solutionDot = Thyra::createMember(model->get_x_space());
    Thyra::copy(*(integrator->getXdot()),solutionDot.ptr());
    solutionsDot.push_back(solutionDot);

    // Output finest temporal solution for plotting
    // This only works for ONE MPI process
    if ((n == 0) or (n == nTimeStepSizes-1)) {
      std::string fname = "Tempus_Trapezoidal_VanDerPol-Ref.dat";
      if (n == 0) fname = "Tempus_Trapezoidal_VanDerPol.dat";
      RCP<const SolutionHistory<double> > solutionHistory =
        integrator->getSolutionHistory();
      writeSolution(fname, solutionHistory);
    }
  }
  // Check the order and intercept
  double xSlope = 0.0;
  double xDotSlope = 0.0;
  RCP<Tempus::Stepper<double> > stepper = integrator->getStepper();
  double order = stepper->getOrder();
  writeOrderError("Tempus_Trapezoidal_VanDerPol-Error.dat",
                  stepper, StepSize,
                  solutions,    xErrorNorm,    xSlope,
                  solutionsDot, xDotErrorNorm, xDotSlope);

  TEST_FLOATING_EQUALITY( xSlope,            order, 0.10 );
  TEST_FLOATING_EQUALITY( xDotSlope,         order, 0.10 );//=order at samll dt
  TEST_FLOATING_EQUALITY( xErrorNorm[0],    0.00085855, 1.0e-4 );
  TEST_FLOATING_EQUALITY( xDotErrorNorm[0], 0.00120695, 1.0e-4 );

  Teuchos::TimeMonitor::summarize();
}


} // namespace Tempus_Test