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Tempus_BDF2_FSA.hpp
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3 // Tempus: Copyright (2017) Sandia Corporation
4 //
5 // Distributed under BSD 3-clause license (See accompanying file Copyright.txt)
6 // ****************************************************************************
7 // @HEADER
8 
9 #include "Teuchos_UnitTestHarness.hpp"
10 #include "Teuchos_XMLParameterListHelpers.hpp"
11 #include "Teuchos_TimeMonitor.hpp"
12 #include "Teuchos_DefaultComm.hpp"
13 
14 #include "Tempus_config.hpp"
15 #include "Tempus_IntegratorBasic.hpp"
16 #include "Tempus_IntegratorForwardSensitivity.hpp"
17 
18 #include "Thyra_VectorStdOps.hpp"
19 #include "Thyra_MultiVectorStdOps.hpp"
20 
21 #include "../TestModels/SinCosModel.hpp"
22 #include "../TestUtils/Tempus_ConvergenceTestUtils.hpp"
23 
24 #include "Stratimikos_DefaultLinearSolverBuilder.hpp"
25 #include "Thyra_LinearOpWithSolveFactoryHelpers.hpp"
26 #include "Thyra_DefaultMultiVectorProductVector.hpp"
27 
28 #include <fstream>
29 #include <limits>
30 #include <sstream>
31 #include <vector>
32 
33 namespace Tempus_Test {
34 
35 using Teuchos::RCP;
36 using Teuchos::ParameterList;
37 using Teuchos::sublist;
38 using Teuchos::getParametersFromXmlFile;
39 
43 
44 // ************************************************************
45 // ************************************************************
46 void test_sincos_fsa(const bool use_combined_method,
47  const bool use_dfdp_as_tangent,
48  Teuchos::FancyOStream &out, bool &success)
49 {
50  std::vector<double> StepSize;
51  std::vector<double> ErrorNorm;
52  const int nTimeStepSizes = 7;
53  double dt = 0.2;
54  double order = 0.0;
55  Teuchos::RCP<const Teuchos::Comm<int> > comm =
56  Teuchos::DefaultComm<int>::getComm();
57  Teuchos::RCP<Teuchos::FancyOStream> my_out =
58  Teuchos::fancyOStream(Teuchos::rcpFromRef(std::cout));
59  my_out->setProcRankAndSize(comm->getRank(), comm->getSize());
60  my_out->setOutputToRootOnly(0);
61  for (int n=0; n<nTimeStepSizes; n++) {
62 
63  // Read params from .xml file
64  RCP<ParameterList> pList =
65  getParametersFromXmlFile("Tempus_BDF2_SinCos_SA.xml");
66 
67  // Setup the SinCosModel
68  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
69  scm_pl->set("Use DfDp as Tangent", use_dfdp_as_tangent);
70  RCP<SinCosModel<double> > model =
71  Teuchos::rcp(new SinCosModel<double>(scm_pl));
72 
73  dt /= 2;
74 
75  // Setup sensitivities
76  RCP<ParameterList> pl = sublist(pList, "Tempus", true);
77  ParameterList& sens_pl = pl->sublist("Sensitivities");
78  if (use_combined_method)
79  sens_pl.set("Sensitivity Method", "Combined");
80  else {
81  sens_pl.set("Sensitivity Method", "Staggered");
82  //sens_pl.set("Reuse State Linear Solver", true);
83  }
84  sens_pl.set("Use DfDp as Tangent", use_dfdp_as_tangent);
85  ParameterList& interp_pl =
86  pl->sublist("Default Integrator").sublist("Solution History").sublist("Interpolator");
87  interp_pl.set("Interpolator Type", "Lagrange");
88  interp_pl.set("Order", 1);
89 
90  // Setup the Integrator and reset initial time step
91  pl->sublist("Default Integrator")
92  .sublist("Time Step Control").set("Initial Time Step", dt);
93  RCP<Tempus::IntegratorForwardSensitivity<double> > integrator =
94  Tempus::integratorForwardSensitivity<double>(pl, model);
95  order = integrator->getStepper()->getOrder();
96 
97  // Initial Conditions
98  double t0 = pl->sublist("Default Integrator")
99  .sublist("Time Step Control").get<double>("Initial Time");
100  RCP<const Thyra::VectorBase<double> > x0 =
101  model->getExactSolution(t0).get_x();
102  const int num_param = model->get_p_space(0)->dim();
103  RCP<Thyra::MultiVectorBase<double> > DxDp0 =
104  Thyra::createMembers(model->get_x_space(), num_param);
105  for (int i=0; i<num_param; ++i)
106  Thyra::assign(DxDp0->col(i).ptr(),
107  *(model->getExactSensSolution(i, t0).get_x()));
108  integrator->initializeSolutionHistory(t0, x0, Teuchos::null, Teuchos::null,
109  DxDp0, Teuchos::null, Teuchos::null);
110 
111  // Integrate to timeMax
112  bool integratorStatus = integrator->advanceTime();
113  TEST_ASSERT(integratorStatus)
114 
115  // Test if at 'Final Time'
116  double time = integrator->getTime();
117  double timeFinal =pl->sublist("Default Integrator")
118  .sublist("Time Step Control").get<double>("Final Time");
119  TEST_FLOATING_EQUALITY(time, timeFinal, 1.0e-14);
120 
121  // Time-integrated solution and the exact solution
122  RCP<const Thyra::VectorBase<double> > x = integrator->getX();
123  RCP<const Thyra::MultiVectorBase<double> > DxDp = integrator->getDxDp();
124  RCP<const Thyra::VectorBase<double> > x_exact =
125  model->getExactSolution(time).get_x();
126  RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
127  Thyra::createMembers(model->get_x_space(), num_param);
128  for (int i=0; i<num_param; ++i)
129  Thyra::assign(DxDp_exact->col(i).ptr(),
130  *(model->getExactSensSolution(i, time).get_x()));
131 
132  // Plot sample solution and exact solution
133  if (comm->getRank() == 0 && n == nTimeStepSizes-1) {
134  typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
135 
136  std::ofstream ftmp("Tempus_BDF2_SinCos_Sens.dat");
137  RCP<const SolutionHistory<double> > solutionHistory =
138  integrator->getSolutionHistory();
139  RCP< Thyra::MultiVectorBase<double> > DxDp_exact_plot =
140  Thyra::createMembers(model->get_x_space(), num_param);
141  for (int i=0; i<solutionHistory->getNumStates(); i++) {
142  RCP<const SolutionState<double> > solutionState = (*solutionHistory)[i];
143  double time_i = solutionState->getTime();
144  RCP<const DMVPV> x_prod_plot =
145  Teuchos::rcp_dynamic_cast<const DMVPV>(solutionState->getX());
146  RCP<const Thyra::VectorBase<double> > x_plot =
147  x_prod_plot->getMultiVector()->col(0);
148  RCP<const Thyra::MultiVectorBase<double> > DxDp_plot =
149  x_prod_plot->getMultiVector()->subView(Teuchos::Range1D(1,num_param));
150  RCP<const Thyra::VectorBase<double> > x_exact_plot =
151  model->getExactSolution(time_i).get_x();
152  for (int j=0; j<num_param; ++j)
153  Thyra::assign(DxDp_exact_plot->col(j).ptr(),
154  *(model->getExactSensSolution(j, time_i).get_x()));
155  ftmp << std::fixed << std::setprecision(7)
156  << time_i
157  << std::setw(11) << get_ele(*(x_plot), 0)
158  << std::setw(11) << get_ele(*(x_plot), 1);
159  for (int j=0; j<num_param; ++j)
160  ftmp << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 0)
161  << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 1);
162  ftmp << std::setw(11) << get_ele(*(x_exact_plot), 0)
163  << std::setw(11) << get_ele(*(x_exact_plot), 1);
164  for (int j=0; j<num_param; ++j)
165  ftmp << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 0)
166  << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 1);
167  ftmp << std::endl;
168  }
169  ftmp.close();
170  }
171 
172  // Calculate the error
173  RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
174  RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
175  Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
176  Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
177  StepSize.push_back(dt);
178  double L2norm = Thyra::norm_2(*xdiff);
179  L2norm *= L2norm;
180  Teuchos::Array<double> L2norm_DxDp(num_param);
181  Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
182  for (int i=0; i<num_param; ++i)
183  L2norm += L2norm_DxDp[i]*L2norm_DxDp[i];
184  L2norm = std::sqrt(L2norm);
185  ErrorNorm.push_back(L2norm);
186 
187  *my_out << " n = " << n << " dt = " << dt << " error = " << L2norm
188  << std::endl;
189 
190  }
191 
192  // Check the order and intercept
193  double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
194  *my_out << " Stepper = BDF2" << std::endl;
195  *my_out << " =========================" << std::endl;
196  *my_out << " Expected order: " << order << std::endl;
197  *my_out << " Observed order: " << slope << std::endl;
198  *my_out << " =========================" << std::endl;
199  TEST_FLOATING_EQUALITY( slope, order, 0.015 );
200  TEST_FLOATING_EQUALITY( ErrorNorm[0], 0.0344598, 1.0e-4 );
201 
202  if (comm->getRank() == 0) {
203  std::ofstream ftmp("Tempus_BDF2_SinCos_Sens-Error.dat");
204  double error0 = 0.8*ErrorNorm[0];
205  for (int n=0; n<nTimeStepSizes; n++) {
206  ftmp << StepSize[n] << " " << ErrorNorm[n] << " "
207  << error0*(StepSize[n]/StepSize[0]) << std::endl;
208  }
209  ftmp.close();
210  }
211 
212 }
213 
214 } // namespace Tempus_Test
void test_sincos_fsa(const bool use_combined_method, const bool use_dfdp_as_tangent, Teuchos::FancyOStream &out, bool &success)
Teuchos::RCP< SolutionHistory< Scalar > > solutionHistory(Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)
Nonmember constructor.
SolutionHistory is basically a container of SolutionStates. SolutionHistory maintains a collection of...
Solution state for integrators and steppers. SolutionState contains the metadata for solutions and th...