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Tempus_DIRK_ASA.cpp
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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_IntegratorAdjointSensitivity.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
29namespace Tempus_Test {
30
31using Teuchos::RCP;
32using Teuchos::ParameterList;
33using Teuchos::sublist;
34using Teuchos::getParametersFromXmlFile;
35
39
40// ************************************************************
41// ************************************************************
42TEUCHOS_UNIT_TEST(DIRK, SinCos_ASA)
43{
44 std::vector<std::string> RKMethods;
45 RKMethods.push_back("General DIRK");
46 RKMethods.push_back("RK Backward Euler");
47 RKMethods.push_back("DIRK 1 Stage Theta Method");
48 RKMethods.push_back("RK Implicit 1 Stage 1st order Radau IA");
49 RKMethods.push_back("SDIRK 2 Stage 2nd order");
50 RKMethods.push_back("RK Implicit 2 Stage 2nd order Lobatto IIIB");
51 RKMethods.push_back("SDIRK 2 Stage 3rd order");
52 RKMethods.push_back("EDIRK 2 Stage 3rd order");
53 RKMethods.push_back("EDIRK 2 Stage Theta Method");
54 RKMethods.push_back("SDIRK 3 Stage 4th order");
55 RKMethods.push_back("SDIRK 5 Stage 4th order");
56 RKMethods.push_back("SDIRK 5 Stage 5th order");
57
58 std::vector<double> RKMethodErrors;
59 RKMethodErrors.push_back(8.48235e-05);
60 RKMethodErrors.push_back(0.0383339);
61 RKMethodErrors.push_back(0.000221028);
62 RKMethodErrors.push_back(0.0428449);
63 RKMethodErrors.push_back(8.48235e-05);
64 RKMethodErrors.push_back(0.000297933);
65 RKMethodErrors.push_back(4.87848e-06);
66 RKMethodErrors.push_back(7.30827e-07);
67 RKMethodErrors.push_back(0.000272997);
68 RKMethodErrors.push_back(3.10132e-07);
69 RKMethodErrors.push_back(7.56838e-10);
70 RKMethodErrors.push_back(1.32374e-10);
71
72 Teuchos::RCP<const Teuchos::Comm<int> > comm =
73 Teuchos::DefaultComm<int>::getComm();
74 Teuchos::RCP<Teuchos::FancyOStream> my_out =
75 Teuchos::fancyOStream(Teuchos::rcpFromRef(std::cout));
76 my_out->setProcRankAndSize(comm->getRank(), comm->getSize());
77 my_out->setOutputToRootOnly(0);
78
79 for(std::vector<std::string>::size_type m = 0; m != RKMethods.size(); m++) {
80
81 std::string RKMethod_ = RKMethods[m];
82 std::replace(RKMethod_.begin(), RKMethod_.end(), ' ', '_');
83 std::replace(RKMethod_.begin(), RKMethod_.end(), '/', '.');
84 std::vector<double> StepSize;
85 std::vector<double> ErrorNorm;
86 const int nTimeStepSizes = 2; // 7 for error plots
87 double dt = 0.05;
88 double order = 0.0;
89 for (int n=0; n<nTimeStepSizes; n++) {
90
91 // Read params from .xml file
92 RCP<ParameterList> pList =
93 getParametersFromXmlFile("Tempus_DIRK_SinCos.xml");
94
95 // Setup the SinCosModel
96 RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
97 RCP<SinCosModel<double> > model =
98 Teuchos::rcp(new SinCosModel<double>(scm_pl));
99
100 // Set the Stepper
101 RCP<ParameterList> pl = sublist(pList, "Tempus", true);
102 pl->sublist("Default Stepper").set("Stepper Type", RKMethods[m]);
103 if (RKMethods[m] == "DIRK 1 Stage Theta Method" ||
104 RKMethods[m] == "EDIRK 2 Stage Theta Method") {
105 pl->sublist("Default Stepper").set<double>("theta", 0.5);
106 } else if (RKMethods[m] == "SDIRK 2 Stage 2nd order") {
107 pl->sublist("Default Stepper").set("gamma", 0.2928932188134524);
108 } else if (RKMethods[m] == "SDIRK 2 Stage 3rd order") {
109 pl->sublist("Default Stepper")
110 .set<std::string>("Gamma Type", "3rd Order A-stable");
111 }
112
113 dt /= 2;
114
115 // Setup sensitivities
116 ParameterList& sens_pl = pl->sublist("Sensitivities");
117 sens_pl.set("Mass Matrix Is Identity", true); // Necessary for explicit
118 ParameterList& interp_pl =
119 pl->sublist("Default Integrator").sublist("Solution History").sublist("Interpolator");
120 interp_pl.set("Interpolator Type", "Lagrange");
121 interp_pl.set("Order", 4); // All RK methods here are at most 5th order
122
123 // Setup the Integrator and reset initial time step
124 pl->sublist("Default Integrator")
125 .sublist("Time Step Control").set("Initial Time Step", dt);
126 RCP<Tempus::IntegratorAdjointSensitivity<double> > integrator =
127 Tempus::createIntegratorAdjointSensitivity<double>(pl, model);
128 order = integrator->getStepper()->getOrder();
129
130 // Initial Conditions
131 // During the Integrator construction, the initial SolutionState
132 // is set by default to model->getNominalVales().get_x(). However,
133 // the application can set it also by integrator->initializeSolutionHistory.
134 RCP<Thyra::VectorBase<double> > x0 =
135 model->getNominalValues().get_x()->clone_v();
136 const int num_param = model->get_p_space(0)->dim();
137 RCP<Thyra::MultiVectorBase<double> > DxDp0 =
138 Thyra::createMembers(model->get_x_space(), num_param);
139 for (int i=0; i<num_param; ++i)
140 Thyra::assign(DxDp0->col(i).ptr(),
141 *(model->getExactSensSolution(i, 0.0).get_x()));
142 integrator->initializeSolutionHistory(0.0, x0, Teuchos::null, Teuchos::null,
143 DxDp0, Teuchos::null, Teuchos::null);
144
145 // Integrate to timeMax
146 bool integratorStatus = integrator->advanceTime();
147 TEST_ASSERT(integratorStatus)
148
149 // Test if at 'Final Time'
150 double time = integrator->getTime();
151 double timeFinal = pl->sublist("Default Integrator")
152 .sublist("Time Step Control").get<double>("Final Time");
153 double tol = 100.0 * std::numeric_limits<double>::epsilon();
154 TEST_FLOATING_EQUALITY(time, timeFinal, tol);
155
156 // Time-integrated solution and the exact solution along with
157 // sensitivities (relying on response g(x) = x). Note we must transpose
158 // dg/dp since the integrator returns it in gradient form.
159 RCP<const Thyra::VectorBase<double> > x = integrator->getX();
160 RCP<const Thyra::MultiVectorBase<double> > DgDp = integrator->getDgDp();
161 RCP<Thyra::MultiVectorBase<double> > DxDp =
162 Thyra::createMembers(model->get_x_space(), num_param);
163 {
164 Thyra::ConstDetachedMultiVectorView<double> dgdp_view(*DgDp);
165 Thyra::DetachedMultiVectorView<double> dxdp_view(*DxDp);
166 const int num_g = DgDp->domain()->dim();
167 for (int i=0; i<num_g; ++i)
168 for (int j=0; j<num_param; ++j)
169 dxdp_view(i,j) = dgdp_view(j,i);
170 }
171 RCP<const Thyra::VectorBase<double> > x_exact =
172 model->getExactSolution(time).get_x();
173 RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
174 Thyra::createMembers(model->get_x_space(), num_param);
175 for (int i=0; i<num_param; ++i)
176 Thyra::assign(DxDp_exact->col(i).ptr(),
177 *(model->getExactSensSolution(i, time).get_x()));
178
179 // Plot sample solution and exact solution
180 if (comm->getRank() == 0 && n == nTimeStepSizes-1) {
181 typedef Thyra::DefaultProductVector<double> DPV;
182 typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
183
184 std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_AdjSens.dat");
185 RCP<const SolutionHistory<double> > solutionHistory =
186 integrator->getSolutionHistory();
187 for (int i=0; i<solutionHistory->getNumStates(); i++) {
188 RCP<const SolutionState<double> > solutionState =
189 (*solutionHistory)[i];
190 const double time_i = solutionState->getTime();
191 RCP<const DPV> x_prod_plot =
192 Teuchos::rcp_dynamic_cast<const DPV>(solutionState->getX());
193 RCP<const Thyra::VectorBase<double> > x_plot =
194 x_prod_plot->getVectorBlock(0);
195 RCP<const DMVPV > adjoint_prod_plot =
196 Teuchos::rcp_dynamic_cast<const DMVPV>(x_prod_plot->getVectorBlock(1));
197 RCP<const Thyra::MultiVectorBase<double> > adjoint_plot =
198 adjoint_prod_plot->getMultiVector();
199 RCP<const Thyra::VectorBase<double> > x_exact_plot =
200 model->getExactSolution(time_i).get_x();
201 ftmp << std::fixed << std::setprecision(7)
202 << time_i
203 << std::setw(11) << get_ele(*(x_plot), 0)
204 << std::setw(11) << get_ele(*(x_plot), 1)
205 << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 0)
206 << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 1)
207 << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 0)
208 << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 1)
209 << std::setw(11) << get_ele(*(x_exact_plot), 0)
210 << std::setw(11) << get_ele(*(x_exact_plot), 1)
211 << std::endl;
212 }
213 ftmp.close();
214 }
215
216 // Calculate the error
217 RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
218 RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
219 Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
220 Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
221 StepSize.push_back(dt);
222 double L2norm = Thyra::norm_2(*xdiff);
223 L2norm *= L2norm;
224 Teuchos::Array<double> L2norm_DxDp(num_param);
225 Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
226 for (int i=0; i<num_param; ++i)
227 L2norm += L2norm_DxDp[i]*L2norm_DxDp[i];
228 L2norm = std::sqrt(L2norm);
229 ErrorNorm.push_back(L2norm);
230
231 //*my_out << " n = " << n << " dt = " << dt << " error = " << L2norm
232 // << std::endl;
233 }
234
235 if (comm->getRank() == 0) {
236 std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_AdjSens-Error.dat");
237 double error0 = 0.8*ErrorNorm[0];
238 for (int n=0; n<(int)StepSize.size(); n++) {
239 ftmp << StepSize[n] << " " << ErrorNorm[n] << " "
240 << error0*(pow(StepSize[n]/StepSize[0],order)) << std::endl;
241 }
242 ftmp.close();
243 }
244
245 //if (RKMethods[m] == "SDIRK 5 Stage 4th order") {
246 // StepSize.pop_back(); StepSize.pop_back();
247 // ErrorNorm.pop_back(); ErrorNorm.pop_back();
248 //} else if (RKMethods[m] == "SDIRK 5 Stage 5th order") {
249 // StepSize.pop_back(); StepSize.pop_back(); StepSize.pop_back();
250 // ErrorNorm.pop_back(); ErrorNorm.pop_back(); ErrorNorm.pop_back();
251 //}
252
253 // Check the order and intercept
254 double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
255 *my_out << " Stepper = " << RKMethods[m] << std::endl;
256 *my_out << " =========================" << std::endl;
257 *my_out << " Expected order: " << order << std::endl;
258 *my_out << " Observed order: " << slope << std::endl;
259 *my_out << " =========================" << std::endl;
260 TEST_FLOATING_EQUALITY( slope, order, 0.03 );
261 TEST_FLOATING_EQUALITY( ErrorNorm[0], RKMethodErrors[m], 5.0e-4 );
262
263 }
264 Teuchos::TimeMonitor::summarize();
265}
266
267} // namespace Tempus_Test
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