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Tempus_DIRK_FSA.hpp
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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_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
29namespace Tempus_Test {
30
31using Teuchos::RCP;
32using Teuchos::ParameterList;
33using Teuchos::sublist;
34using Teuchos::getParametersFromXmlFile;
35
39
40
41// ************************************************************
42// ************************************************************
43void test_sincos_fsa(const std::string& method_name,
44 const bool use_combined_method,
45 const bool use_dfdp_as_tangent,
46 Teuchos::FancyOStream &out, bool &success)
47{
48 std::vector<std::string> RKMethods;
49 RKMethods.push_back("General DIRK");
50 RKMethods.push_back("RK Backward Euler");
51 RKMethods.push_back("DIRK 1 Stage Theta Method");
52 RKMethods.push_back("RK Implicit 1 Stage 1st order Radau IA");
53 RKMethods.push_back("RK Implicit Midpoint");
54 RKMethods.push_back("SDIRK 2 Stage 2nd order");
55 RKMethods.push_back("RK Implicit 2 Stage 2nd order Lobatto IIIB");
56 RKMethods.push_back("SDIRK 2 Stage 3rd order");
57 RKMethods.push_back("EDIRK 2 Stage 3rd order");
58 RKMethods.push_back("EDIRK 2 Stage Theta Method");
59 RKMethods.push_back("SDIRK 3 Stage 4th order");
60 RKMethods.push_back("SDIRK 5 Stage 4th order");
61 RKMethods.push_back("SDIRK 5 Stage 5th order");
62 RKMethods.push_back("SDIRK 2(1) Pair");
63 RKMethods.push_back("RK Trapezoidal Rule");
64 RKMethods.push_back("RK Crank-Nicolson");
65
66 // Check that method_name is valid
67 if (method_name != "") {
68 auto it = std::find(RKMethods.begin(), RKMethods.end(), method_name);
69 TEUCHOS_TEST_FOR_EXCEPTION(it == RKMethods.end(), std::logic_error,
70 "Invalid RK method name '" << method_name << "'");
71 }
72
73 std::vector<double> RKMethodErrors;
74 if (use_combined_method) {
75 RKMethodErrors.push_back(0.000144507);
76 RKMethodErrors.push_back(0.0428449);
77 RKMethodErrors.push_back(0.000297933);
78 RKMethodErrors.push_back(0.0428449);
79 RKMethodErrors.push_back(0.000297933);
80 RKMethodErrors.push_back(0.000144507);
81 RKMethodErrors.push_back(0.000297933);
82 RKMethodErrors.push_back(8.65434e-06);
83 RKMethodErrors.push_back(1.3468e-06);
84 RKMethodErrors.push_back(0.000297933);
85 RKMethodErrors.push_back(5.44037e-07);
86 RKMethodErrors.push_back(2.77342e-09);
87 RKMethodErrors.push_back(1.21689e-10);
88 RKMethodErrors.push_back(0.000603848);
89 RKMethodErrors.push_back(0.000297933);
90 RKMethodErrors.push_back(0.000297933);
91 }
92 else {
93 RKMethodErrors.push_back(0.000125232);
94 RKMethodErrors.push_back(0.0428449);
95 RKMethodErrors.push_back(0.000221049);
96 RKMethodErrors.push_back(0.0383339);
97 RKMethodErrors.push_back(0.000221049);
98 RKMethodErrors.push_back(0.000125232);
99 RKMethodErrors.push_back(0.000272997);
100 RKMethodErrors.push_back(4.79475e-06);
101 RKMethodErrors.push_back(9.63899e-07);
102 RKMethodErrors.push_back(0.000297933);
103 RKMethodErrors.push_back(2.9362e-07);
104 RKMethodErrors.push_back(9.20081e-08);
105 RKMethodErrors.push_back(9.16252e-08);
106 RKMethodErrors.push_back(0.00043969);
107 RKMethodErrors.push_back(0.000297933);
108 RKMethodErrors.push_back(0.000297933);
109 }
110
111 Teuchos::RCP<const Teuchos::Comm<int> > comm =
112 Teuchos::DefaultComm<int>::getComm();
113 Teuchos::RCP<Teuchos::FancyOStream> my_out =
114 Teuchos::fancyOStream(Teuchos::rcpFromRef(std::cout));
115 my_out->setProcRankAndSize(comm->getRank(), comm->getSize());
116 my_out->setOutputToRootOnly(0);
117
118 for(std::vector<std::string>::size_type m = 0; m != RKMethods.size(); m++) {
119
120 // If we were given a method to run, skip this method if it doesn't match
121 if (method_name != "" && RKMethods[m] != method_name)
122 continue;
123
124 std::string RKMethod_ = RKMethods[m];
125 std::replace(RKMethod_.begin(), RKMethod_.end(), ' ', '_');
126 std::replace(RKMethod_.begin(), RKMethod_.end(), '/', '.');
127 std::vector<double> StepSize;
128 std::vector<double> ErrorNorm;
129 const int nTimeStepSizes = 3; // 7 for error plots
130 double dt = 0.05;
131 double order = 0.0;
132 for (int n=0; n<nTimeStepSizes; n++) {
133
134 // Read params from .xml file
135 RCP<ParameterList> pList =
136 getParametersFromXmlFile("Tempus_DIRK_SinCos.xml");
137
138 // Setup the SinCosModel
139 RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
140 scm_pl->set("Use DfDp as Tangent", use_dfdp_as_tangent);
141 RCP<SinCosModel<double> > model =
142 Teuchos::rcp(new SinCosModel<double>(scm_pl));
143
144 // Set the Stepper
145 RCP<ParameterList> pl = sublist(pList, "Tempus", true);
146 pl->sublist("Default Stepper").set("Stepper Type", RKMethods[m]);
147 if (RKMethods[m] == "SDIRK 2 Stage 2nd order") {
148 pl->sublist("Default Stepper").set("gamma", 0.2928932188134524);
149 } else if (RKMethods[m] == "SDIRK 2 Stage 3rd order") {
150 pl->sublist("Default Stepper")
151 .set<std::string>("Gamma Type", "3rd Order A-stable");
152 }
153
154 dt /= 2;
155
156 // Setup sensitivities
157 ParameterList& sens_pl = pl->sublist("Sensitivities");
158 if (use_combined_method)
159 sens_pl.set("Sensitivity Method", "Combined");
160 else
161 sens_pl.set("Sensitivity Method", "Staggered");
162 sens_pl.set("Use DfDp as Tangent", use_dfdp_as_tangent);
163 ParameterList& interp_pl =
164 pl->sublist("Default Integrator").sublist("Solution History").sublist("Interpolator");
165 interp_pl.set("Interpolator Type", "Lagrange");
166 interp_pl.set("Order", 4); // All RK methods here are at most 5th order
167
168 // Setup the Integrator and reset initial time step
169 pl->sublist("Default Integrator")
170 .sublist("Time Step Control").set("Initial Time Step", dt);
171 RCP<Tempus::IntegratorForwardSensitivity<double> > integrator =
172 Tempus::createIntegratorForwardSensitivity<double>(pl, model);
173 order = integrator->getStepper()->getOrder();
174
175 // Initial Conditions
176 // During the Integrator construction, the initial SolutionState
177 // is set by default to model->getNominalVales().get_x(). However,
178 // the application can set it also by integrator->initializeSolutionHistory.
179 RCP<Thyra::VectorBase<double> > x0 =
180 model->getNominalValues().get_x()->clone_v();
181 const int num_param = model->get_p_space(0)->dim();
182 RCP<Thyra::MultiVectorBase<double> > DxDp0 =
183 Thyra::createMembers(model->get_x_space(), num_param);
184 for (int i=0; i<num_param; ++i)
185 Thyra::assign(DxDp0->col(i).ptr(),
186 *(model->getExactSensSolution(i, 0.0).get_x()));
187 integrator->initializeSolutionHistory(0.0, x0, Teuchos::null, Teuchos::null,
188 DxDp0, Teuchos::null, Teuchos::null);
189
190 // Integrate to timeMax
191 bool integratorStatus = integrator->advanceTime();
192 TEST_ASSERT(integratorStatus)
193
194 // Test if at 'Final Time'
195 double time = integrator->getTime();
196 double timeFinal = pl->sublist("Default Integrator")
197 .sublist("Time Step Control").get<double>("Final Time");
198 double tol = 100.0 * std::numeric_limits<double>::epsilon();
199 TEST_FLOATING_EQUALITY(time, timeFinal, tol);
200
201 // Time-integrated solution and the exact solution
202 RCP<const Thyra::VectorBase<double> > x = integrator->getX();
203 RCP<const Thyra::MultiVectorBase<double> > DxDp = integrator->getDxDp();
204 RCP<const Thyra::VectorBase<double> > x_exact =
205 model->getExactSolution(time).get_x();
206 RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
207 Thyra::createMembers(model->get_x_space(), num_param);
208 for (int i=0; i<num_param; ++i)
209 Thyra::assign(DxDp_exact->col(i).ptr(),
210 *(model->getExactSensSolution(i, time).get_x()));
211
212 // Plot sample solution and exact solution
213 if (comm->getRank() == 0 && n == nTimeStepSizes-1) {
214 typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;
215
216 std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_Sens.dat");
217 RCP<const SolutionHistory<double> > solutionHistory =
218 integrator->getSolutionHistory();
219 RCP< Thyra::MultiVectorBase<double> > DxDp_exact_plot =
220 Thyra::createMembers(model->get_x_space(), num_param);
221 for (int i=0; i<solutionHistory->getNumStates(); i++) {
222 RCP<const SolutionState<double> > solutionState =
223 (*solutionHistory)[i];
224 double time_i = solutionState->getTime();
225 RCP<const DMVPV> x_prod_plot =
226 Teuchos::rcp_dynamic_cast<const DMVPV>(solutionState->getX());
227 RCP<const Thyra::VectorBase<double> > x_plot =
228 x_prod_plot->getMultiVector()->col(0);
229 RCP<const Thyra::MultiVectorBase<double> > DxDp_plot =
230 x_prod_plot->getMultiVector()->subView(Teuchos::Range1D(1,num_param));
231 RCP<const Thyra::VectorBase<double> > x_exact_plot =
232 model->getExactSolution(time_i).get_x();
233 for (int j=0; j<num_param; ++j)
234 Thyra::assign(DxDp_exact_plot->col(j).ptr(),
235 *(model->getExactSensSolution(j, time_i).get_x()));
236 ftmp << std::fixed << std::setprecision(7)
237 << time_i
238 << std::setw(11) << get_ele(*(x_plot), 0)
239 << std::setw(11) << get_ele(*(x_plot), 1);
240 for (int j=0; j<num_param; ++j)
241 ftmp << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 0)
242 << std::setw(11) << get_ele(*(DxDp_plot->col(j)), 1);
243 ftmp << std::setw(11) << get_ele(*(x_exact_plot), 0)
244 << std::setw(11) << get_ele(*(x_exact_plot), 1);
245 for (int j=0; j<num_param; ++j)
246 ftmp << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 0)
247 << std::setw(11) << get_ele(*(DxDp_exact_plot->col(j)), 1);
248 ftmp << std::endl;
249 }
250 ftmp.close();
251 }
252
253 // Calculate the error
254 RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
255 RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
256 Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
257 Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
258 StepSize.push_back(dt);
259 double L2norm = Thyra::norm_2(*xdiff);
260 L2norm *= L2norm;
261 Teuchos::Array<double> L2norm_DxDp(num_param);
262 Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
263 for (int i=0; i<num_param; ++i)
264 L2norm += L2norm_DxDp[i]*L2norm_DxDp[i];
265 L2norm = std::sqrt(L2norm);
266 ErrorNorm.push_back(L2norm);
267
268 //*my_out << " n = " << n << " dt = " << dt << " error = " << L2norm
269 // << std::endl;
270 }
271
272 if (comm->getRank() == 0) {
273 std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_Sens-Error.dat");
274 double error0 = 0.8*ErrorNorm[0];
275 for (int n=0; n<(int)StepSize.size(); n++) {
276 ftmp << StepSize[n] << " " << ErrorNorm[n] << " "
277 << error0*(pow(StepSize[n]/StepSize[0],order)) << std::endl;
278 }
279 ftmp.close();
280 }
281
282 //if (RKMethods[m] == "SDIRK 5 Stage 4th order") {
283 // StepSize.pop_back(); StepSize.pop_back();
284 // ErrorNorm.pop_back(); ErrorNorm.pop_back();
285 //} else if (RKMethods[m] == "SDIRK 5 Stage 5th order") {
286 // StepSize.pop_back(); StepSize.pop_back(); StepSize.pop_back();
287 // ErrorNorm.pop_back(); ErrorNorm.pop_back(); ErrorNorm.pop_back();
288 //}
289
290 // Check the order and intercept
291 double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
292 *my_out << " Stepper = " << RKMethods[m] << std::endl;
293 *my_out << " =========================" << std::endl;
294 *my_out << " Expected order: " << order << std::endl;
295 *my_out << " Observed order: " << slope << std::endl;
296 *my_out << " =========================" << std::endl;
297
298 // Can only seem to get at most 4th order when using staggered method
299 double order_expected = use_combined_method ? order : std::min(order,4.0);
300 TEST_FLOATING_EQUALITY( slope, order_expected, 0.03 );
301 TEST_FLOATING_EQUALITY( ErrorNorm[0], RKMethodErrors[m], 5.0e-4 );
302
303 }
304 Teuchos::TimeMonitor::summarize();
305}
306
307} // namespace Tempus_Test
std::string method_name
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...
Sine-Cosine model problem from Rythmos. This is a canonical Sine-Cosine differential equation.
void test_sincos_fsa(const bool use_combined_method, const bool use_dfdp_as_tangent, Teuchos::FancyOStream &out, bool &success)