Tempus  Version of the Day
Time Integration
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Macros Pages
Tempus_ExplicitRK_FSA.hpp
Go to the documentation of this file.
1 // @HEADER
2 // ****************************************************************************
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 "Thyra_VectorStdOps.hpp"
15 #include "Thyra_MultiVectorStdOps.hpp"
16 
17 #include "Tempus_IntegratorBasic.hpp"
18 #include "Tempus_IntegratorForwardSensitivity.hpp"
19 
20 #include "Thyra_DefaultMultiVectorProductVector.hpp"
21 #include "Thyra_DefaultProductVector.hpp"
22 
23 #include "../TestModels/SinCosModel.hpp"
24 #include "../TestUtils/Tempus_ConvergenceTestUtils.hpp"
25 
26 #include <fstream>
27 #include <vector>
28 
29 namespace Tempus_Test {
30 
31 using Teuchos::RCP;
32 using Teuchos::ParameterList;
33 using Teuchos::sublist;
34 using Teuchos::getParametersFromXmlFile;
35 
36 using Tempus::IntegratorBasic;
37 using Tempus::SolutionHistory;
38 using Tempus::SolutionState;
39 
40 // ************************************************************
41 // ************************************************************
42 void test_sincos_fsa(const std::string& method_name,
43  const bool use_combined_method,
44  const bool use_dfdp_as_tangent,
45  Teuchos::FancyOStream &out, bool &success)
46 {
47  std::vector<std::string> RKMethods;
48  RKMethods.push_back("RK Forward Euler");
49  RKMethods.push_back("RK Explicit 4 Stage");
50  RKMethods.push_back("RK Explicit 3/8 Rule");
51  RKMethods.push_back("RK Explicit 4 Stage 3rd order by Runge");
52  RKMethods.push_back("RK Explicit 5 Stage 3rd order by Kinnmark and Gray");
53  RKMethods.push_back("RK Explicit 3 Stage 3rd order");
54  RKMethods.push_back("RK Explicit 3 Stage 3rd order TVD");
55  RKMethods.push_back("RK Explicit 3 Stage 3rd order by Heun");
56  RKMethods.push_back("RK Explicit 2 Stage 2nd order by Runge");
57  RKMethods.push_back("RK Explicit Trapezoidal");
58  RKMethods.push_back("General ERK");
59 
60  // Check that method_name is valid
61  if (method_name != "") {
62  auto it = std::find(RKMethods.begin(), RKMethods.end(), method_name);
63  TEUCHOS_TEST_FOR_EXCEPTION(it == RKMethods.end(), std::logic_error,
64  "Invalid RK method name " << method_name);
65  }
66 
67  std::vector<double> RKMethodErrors;
68  if (use_combined_method) {
69  RKMethodErrors.push_back(0.183799);
70  RKMethodErrors.push_back(6.88637e-06);
71  RKMethodErrors.push_back(6.88637e-06);
72  RKMethodErrors.push_back(0.000264154);
73  RKMethodErrors.push_back(5.22798e-05);
74  RKMethodErrors.push_back(0.000261896);
75  RKMethodErrors.push_back(0.000261896);
76  RKMethodErrors.push_back(0.000261896);
77  RKMethodErrors.push_back(0.00934377);
78  RKMethodErrors.push_back(0.00934377);
79  RKMethodErrors.push_back(6.88637e-06);
80  }
81  else {
82  RKMethodErrors.push_back(0.183799);
83  RKMethodErrors.push_back(2.1915e-05);
84  RKMethodErrors.push_back(2.23367e-05);
85  RKMethodErrors.push_back(0.000205051);
86  RKMethodErrors.push_back(2.85141e-05);
87  RKMethodErrors.push_back(0.000126478);
88  RKMethodErrors.push_back(9.64964e-05);
89  RKMethodErrors.push_back(0.000144616);
90  RKMethodErrors.push_back(0.00826159);
91  RKMethodErrors.push_back(0.00710492);
92  RKMethodErrors.push_back(2.1915e-05);
93  }
94  Teuchos::RCP<const Teuchos::Comm<int> > comm =
95  Teuchos::DefaultComm<int>::getComm();
96  Teuchos::RCP<Teuchos::FancyOStream> my_out =
97  Teuchos::fancyOStream(Teuchos::rcpFromRef(std::cout));
98  my_out->setProcRankAndSize(comm->getRank(), comm->getSize());
99  my_out->setOutputToRootOnly(0);
100 
101  for(std::vector<std::string>::size_type m = 0; m != RKMethods.size(); m++) {
102 
103  // If we were given a method to run, skip this method if it doesn't match
104  if (method_name != "" && RKMethods[m] != method_name)
105  continue;
106 
107  std::string RKMethod_ = RKMethods[m];
108  std::replace(RKMethod_.begin(), RKMethod_.end(), ' ', '_');
109  std::replace(RKMethod_.begin(), RKMethod_.end(), '/', '.');
110  std::vector<double> StepSize;
111  std::vector<double> ErrorNorm;
112  const int nTimeStepSizes = 7;
113  double dt = 0.2;
114  double order = 0.0;
115  for (int n=0; n<nTimeStepSizes; n++) {
116 
117  // Read params from .xml file
118  RCP<ParameterList> pList =
119  getParametersFromXmlFile("Tempus_ExplicitRK_SinCos.xml");
120 
121  // Setup the SinCosModel
122  RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
123  scm_pl->set("Use DfDp as Tangent", use_dfdp_as_tangent);
124  RCP<SinCosModel<double> > model =
125  Teuchos::rcp(new SinCosModel<double>(scm_pl));
126 
127  // Set the Stepper
128  RCP<ParameterList> pl = sublist(pList, "Tempus", true);
129  if (RKMethods[m] == "General ERK") {
130  pl->sublist("Demo Integrator").set("Stepper Name", "Demo Stepper 2");
131  } else {
132  pl->sublist("Demo Stepper").set("Stepper Type", RKMethods[m]);
133  }
134 
135 
136  dt /= 2;
137 
138  // Setup sensitivities
139  ParameterList& sens_pl = pl->sublist("Sensitivities");
140  if (use_combined_method)
141  sens_pl.set("Sensitivity Method", "Combined");
142  else
143  sens_pl.set("Sensitivity Method", "Staggered");
144  sens_pl.set("Use DfDp as Tangent", use_dfdp_as_tangent);
145  ParameterList& interp_pl =
146  pl->sublist("Demo Integrator").sublist("Solution History").sublist("Interpolator");
147  interp_pl.set("Interpolator Type", "Lagrange");
148  interp_pl.set("Order", 3); // All RK methods here are at most 4th order
149 
150  // Setup the Integrator and reset initial time step
151  pl->sublist("Demo Integrator")
152  .sublist("Time Step Control").set("Initial Time Step", dt);
153  RCP<Tempus::IntegratorForwardSensitivity<double> > integrator =
154  Tempus::integratorForwardSensitivity<double>(pl, model);
155  order = integrator->getStepper()->getOrder();
156 
157  // Initial Conditions
158  double t0 = pl->sublist("Demo Integrator")
159  .sublist("Time Step Control").get<double>("Initial Time");
160  // RCP<const Thyra::VectorBase<double> > x0 =
161  // model->getExactSolution(t0).get_x()->clone_v();
162  RCP<Thyra::VectorBase<double> > x0 =
163  model->getNominalValues().get_x()->clone_v();
164  const int num_param = model->get_p_space(0)->dim();
165  RCP<Thyra::MultiVectorBase<double> > DxDp0 =
166  Thyra::createMembers(model->get_x_space(), num_param);
167  for (int i=0; i<num_param; ++i)
168  Thyra::assign(DxDp0->col(i).ptr(),
169  *(model->getExactSensSolution(i, t0).get_x()));
170  integrator->initializeSolutionHistory(t0, x0, Teuchos::null, Teuchos::null,
171  DxDp0, Teuchos::null, Teuchos::null);
172 
173  // Integrate to timeMax
174  bool integratorStatus = integrator->advanceTime();
175  TEST_ASSERT(integratorStatus)
176 
177  // Test if at 'Final Time'
178  double time = integrator->getTime();
179  double timeFinal = pl->sublist("Demo Integrator")
180  .sublist("Time Step Control").get<double>("Final Time");
181  TEST_FLOATING_EQUALITY(time, timeFinal, 1.0e-14);
182 
183  // Time-integrated solution and the exact solution
184  RCP<const Thyra::VectorBase<double> > x = integrator->getX();
185  RCP<const Thyra::MultiVectorBase<double> > DxDp = integrator->getDxDp();
186  RCP<const Thyra::VectorBase<double> > x_exact =
187  model->getExactSolution(time).get_x();
188  RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
189  Thyra::createMembers(model->get_x_space(), num_param);
190  for (int i=0; i<num_param; ++i)
191  Thyra::assign(DxDp_exact->col(i).ptr(),
192  *(model->getExactSensSolution(i, time).get_x()));
193 
194  // Plot sample solution and exact solution
195  if (comm->getRank() == 0 && n == nTimeStepSizes-1) {
196  typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
197 
198  std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_Sens.dat");
199  RCP<const SolutionHistory<double> > solutionHistory =
200  integrator->getSolutionHistory();
201  RCP< Thyra::MultiVectorBase<double> > DxDp_exact_plot =
202  Thyra::createMembers(model->get_x_space(), num_param);
203  for (int i=0; i<solutionHistory->getNumStates(); i++) {
204  RCP<const SolutionState<double> > solutionState =
205  (*solutionHistory)[i];
206  double time_i = solutionState->getTime();
207  RCP<const DMVPV> x_prod_plot =
208  Teuchos::rcp_dynamic_cast<const DMVPV>(solutionState->getX());
209  RCP<const Thyra::VectorBase<double> > x_plot =
210  x_prod_plot->getMultiVector()->col(0);
211  RCP<const Thyra::MultiVectorBase<double> > DxDp_plot =
212  x_prod_plot->getMultiVector()->subView(Teuchos::Range1D(1,num_param));
213  RCP<const Thyra::VectorBase<double> > x_exact_plot =
214  model->getExactSolution(time_i).get_x();
215  for (int j=0; j<num_param; ++j)
216  Thyra::assign(DxDp_exact_plot->col(j).ptr(),
217  *(model->getExactSensSolution(j, time_i).get_x()));
218  ftmp << std::fixed << std::setprecision(7)
219  << time_i
220  << std::setw(11) << get_ele(*(x_plot), 0)
221  << std::setw(11) << get_ele(*(x_plot), 1);
222  for (int j=0; j<num_param; ++j)
223  ftmp << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 0)
224  << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 1);
225  ftmp << std::setw(11) << get_ele(*(x_exact_plot), 0)
226  << std::setw(11) << get_ele(*(x_exact_plot), 1);
227  for (int j=0; j<num_param; ++j)
228  ftmp << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 0)
229  << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 1);
230  ftmp << std::endl;
231  }
232  ftmp.close();
233  }
234 
235  // Calculate the error
236  RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
237  RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
238  Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
239  Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
240  StepSize.push_back(dt);
241  double L2norm = Thyra::norm_2(*xdiff);
242  L2norm *= L2norm;
243  Teuchos::Array<double> L2norm_DxDp(num_param);
244  Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
245  for (int i=0; i<num_param; ++i)
246  L2norm += L2norm_DxDp[i]*L2norm_DxDp[i];
247  L2norm = std::sqrt(L2norm);
248  ErrorNorm.push_back(L2norm);
249 
250  *my_out << " n = " << n << " dt = " << dt << " error = " << L2norm
251  << std::endl;
252  }
253 
254  // Check the order and intercept
255  double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
256  *my_out << " Stepper = " << RKMethods[m] << std::endl;
257  *my_out << " =========================" << std::endl;
258  *my_out << " Expected order: " << order << std::endl;
259  *my_out << " Observed order: " << slope << std::endl;
260  *my_out << " =========================" << std::endl;
261  TEST_FLOATING_EQUALITY( slope, order, 0.04 );
262  TEST_FLOATING_EQUALITY( ErrorNorm[0], RKMethodErrors[m], 1.0e-4 );
263 
264  if (comm->getRank() == 0) {
265  std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_Sens-Error.dat");
266  double error0 = 0.8*ErrorNorm[0];
267  for (int n=0; n<nTimeStepSizes; n++) {
268  ftmp << StepSize[n] << " " << ErrorNorm[n] << " "
269  << error0*(pow(StepSize[n]/StepSize[0],order)) << std::endl;
270  }
271  ftmp.close();
272  }
273  }
274 
275  Teuchos::TimeMonitor::summarize();
276 }
277 
278 } // namespace Tempus_Test
Tempus_Test::test_sincos_fsa
void test_sincos_fsa(const bool use_combined_method, const bool use_dfdp_as_tangent, Teuchos::FancyOStream &out, bool &success)
Definition: Tempus_BackwardEuler_FSA.hpp:48
Tempus::solutionHistory
Teuchos::RCP< SolutionHistory< Scalar > > solutionHistory(Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)
Nonmember constructor.
Definition: Tempus_SolutionHistory_impl.hpp:512
Tempus::SolutionHistory
SolutionHistory is basically a container of SolutionStates. SolutionHistory maintains a collection of...
Definition: Tempus_Integrator.hpp:25
method_name
std::string method_name
Definition: Tempus_DIRK_Combined_FSA.cpp:15
Tempus::SolutionState
Solution state for integrators and steppers. SolutionState contains the metadata for solutions and th...
Definition: Tempus_SolutionState_decl.hpp:56