Tempus_BDF2_FSA.hpp

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//@HEADER
// *****************************************************************************
//          Tempus: Time Integration and Sensitivity Analysis Package
//
// Copyright 2017 NTESS and the Tempus contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
//@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_IntegratorForwardSensitivity.hpp"

#include "Thyra_VectorStdOps.hpp"
#include "Thyra_MultiVectorStdOps.hpp"

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

#include "Thyra_DefaultMultiVectorProductVector.hpp"

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

namespace Tempus_Test {

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

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

// ************************************************************
// ************************************************************
void test_sincos_fsa(const bool use_combined_method,
                     const bool use_dfdp_as_tangent, Teuchos::FancyOStream& out,
                     bool& success)
{
  std::vector<double> StepSize;
  std::vector<double> ErrorNorm;
  const int nTimeStepSizes = 7;
  double dt                = 0.2;
  double order             = 0.0;
  Teuchos::RCP<const Teuchos::Comm<int> > comm =
      Teuchos::DefaultComm<int>::getComm();
  for (int n = 0; n < nTimeStepSizes; n++) {
    // Read params from .xml file
    RCP<ParameterList> pList =
        getParametersFromXmlFile("Tempus_BDF2_SinCos_SA.xml");

    // Setup the SinCosModel
    RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
    scm_pl->set("Use DfDp as Tangent", use_dfdp_as_tangent);
    RCP<SinCosModel<double> > model =
        Teuchos::rcp(new SinCosModel<double>(scm_pl));

    dt /= 2;

    // Setup sensitivities
    RCP<ParameterList> pl  = sublist(pList, "Tempus", true);
    ParameterList& sens_pl = pl->sublist("Sensitivities");
    if (use_combined_method)
      sens_pl.set("Sensitivity Method", "Combined");
    else {
      sens_pl.set("Sensitivity Method", "Staggered");
      // sens_pl.set("Reuse State Linear Solver", true);
    }
    sens_pl.set("Use DfDp as Tangent", use_dfdp_as_tangent);
    ParameterList& interp_pl = pl->sublist("Default Integrator")
                                   .sublist("Solution History")
                                   .sublist("Interpolator");
    interp_pl.set("Interpolator Type", "Lagrange");
    interp_pl.set("Order", 1);

    // Setup the Integrator and reset initial time step
    pl->sublist("Default Integrator")
        .sublist("Time Step Control")
        .set("Initial Time Step", dt);
    RCP<Tempus::IntegratorForwardSensitivity<double> > integrator =
        Tempus::createIntegratorForwardSensitivity<double>(pl, model);
    order = integrator->getStepper()->getOrder();

    // Initial Conditions
    double t0 = pl->sublist("Default Integrator")
                    .sublist("Time Step Control")
                    .get<double>("Initial Time");
    RCP<const Thyra::VectorBase<double> > x0 =
        model->getExactSolution(t0).get_x();
    const int num_param = model->get_p_space(0)->dim();
    RCP<Thyra::MultiVectorBase<double> > DxDp0 =
        Thyra::createMembers(model->get_x_space(), num_param);
    for (int i = 0; i < num_param; ++i)
      Thyra::assign(DxDp0->col(i).ptr(),
                    *(model->getExactSensSolution(i, t0).get_x()));
    integrator->initializeSolutionHistory(t0, x0, Teuchos::null, Teuchos::null,
                                          DxDp0, Teuchos::null, Teuchos::null);

    // 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<const Thyra::VectorBase<double> > x         = integrator->getX();
    RCP<const Thyra::MultiVectorBase<double> > DxDp = integrator->getDxDp();
    RCP<const Thyra::VectorBase<double> > x_exact =
        model->getExactSolution(time).get_x();
    RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
        Thyra::createMembers(model->get_x_space(), num_param);
    for (int i = 0; i < num_param; ++i)
      Thyra::assign(DxDp_exact->col(i).ptr(),
                    *(model->getExactSensSolution(i, time).get_x()));

    // Plot sample solution and exact solution
    if (comm->getRank() == 0 && n == nTimeStepSizes - 1) {
      typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;

      std::ofstream ftmp("Tempus_BDF2_SinCos_Sens.dat");
      RCP<const SolutionHistory<double> > solutionHistory =
          integrator->getSolutionHistory();
      RCP<Thyra::MultiVectorBase<double> > DxDp_exact_plot =
          Thyra::createMembers(model->get_x_space(), num_param);
      for (int i = 0; i < solutionHistory->getNumStates(); i++) {
        RCP<const SolutionState<double> > solutionState = (*solutionHistory)[i];
        double time_i                                   = solutionState->getTime();
        RCP<const DMVPV> x_prod_plot =
            Teuchos::rcp_dynamic_cast<const DMVPV>(solutionState->getX());
        RCP<const Thyra::VectorBase<double> > x_plot =
            x_prod_plot->getMultiVector()->col(0);
        RCP<const Thyra::MultiVectorBase<double> > DxDp_plot =
            x_prod_plot->getMultiVector()->subView(
                Teuchos::Range1D(1, num_param));
        RCP<const Thyra::VectorBase<double> > x_exact_plot =
            model->getExactSolution(time_i).get_x();
        for (int j = 0; j < num_param; ++j)
          Thyra::assign(DxDp_exact_plot->col(j).ptr(),
                        *(model->getExactSensSolution(j, time_i).get_x()));
        ftmp << std::fixed << std::setprecision(7) << time_i << std::setw(11)
             << get_ele(*(x_plot), 0) << std::setw(11) << get_ele(*(x_plot), 1);
        for (int j = 0; j < num_param; ++j)
          ftmp << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 0)
               << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 1);
        ftmp << std::setw(11) << get_ele(*(x_exact_plot), 0) << std::setw(11)
             << get_ele(*(x_exact_plot), 1);
        for (int j = 0; j < num_param; ++j)
          ftmp << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 0)
               << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 1);
        ftmp << std::endl;
      }
      ftmp.close();
    }

    // Calculate the error
    RCP<Thyra::VectorBase<double> > xdiff         = x->clone_v();
    RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
    Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
    Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
    StepSize.push_back(dt);
    double L2norm = Thyra::norm_2(*xdiff);
    L2norm *= L2norm;
    Teuchos::Array<double> L2norm_DxDp(num_param);
    Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
    for (int i = 0; i < num_param; ++i)
      L2norm += L2norm_DxDp[i] * L2norm_DxDp[i];
    L2norm = std::sqrt(L2norm);
    ErrorNorm.push_back(L2norm);

    out << " n = " << n << " dt = " << dt << " error = " << L2norm << std::endl;
  }

  // Check the order and intercept
  double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
  out << "  Stepper = BDF2" << std::endl;
  out << "  =========================" << std::endl;
  out << "  Expected order: " << order << std::endl;
  out << "  Observed order: " << slope << std::endl;
  out << "  =========================" << std::endl;
  TEST_FLOATING_EQUALITY(slope, 1.94162, 0.015);
  TEST_FLOATING_EQUALITY(ErrorNorm[0], 0.0143743, 1.0e-4);

  if (comm->getRank() == 0) {
    std::ofstream ftmp("Tempus_BDF2_SinCos_Sens-Error.dat");
    double error0 = 0.8 * ErrorNorm[0];
    for (int n = 0; n < nTimeStepSizes; n++) {
      ftmp << StepSize[n] << "   " << ErrorNorm[n] << "   "
           << error0 * (StepSize[n] / StepSize[0]) << std::endl;
    }
    ftmp.close();
  }
}

}  // namespace Tempus_Test