Teuchos::RCP<Rythmos::VanderPolModel>
Rythmos::vanderPolModel(const RCP<ParameterList> &pl)
{
RCP<VanderPolModel> model = vanderPolModel();
model->setParameterList(pl);
return(model);
}
Teuchos::RCP<Rythmos::VanderPolModel>
Rythmos::vanderPolModel(bool implicit)
{
RCP<VanderPolModel> model = vanderPolModel();
model->setImplicitFlag(implicit);
return(model);
}
TEUCHOS_UNIT_TEST( Rythmos_ImplicitBDFStepper, exactNumericalAnswer_BE_nonlinear ) {
double epsilon = 0.5;
RCP<ParameterList> modelPL = Teuchos::parameterList();
{
modelPL->set("Implicit model formulation",true);
modelPL->set("Coeff epsilon",epsilon);
}
RCP<VanderPolModel> model = vanderPolModel();
model->setParameterList(modelPL);
Thyra::ModelEvaluatorBase::InArgs<double> model_ic = model->getNominalValues();
RCP<TimeStepNonlinearSolver<double> > nlSolver = timeStepNonlinearSolver<double>();
{
RCP<ParameterList> nlPL = Teuchos::parameterList();
nlPL->set("Default Tol",1.0e-10);
nlPL->set("Default Max Iters",20);
nlSolver->setParameterList(nlPL);
}
RCP<ParameterList> stepperPL = Teuchos::parameterList();
{
ParameterList& pl = stepperPL->sublist("Step Control Settings");
pl.set("minOrder",1);
pl.set("maxOrder",1);
ParameterList& vopl = pl.sublist("VerboseObject");
vopl.set("Verbosity Level","none");
}
RCP<ImplicitBDFStepper<double> > stepper = implicitBDFStepper<double>(model,nlSolver,stepperPL);
stepper->setInitialCondition(model_ic);
double h = 0.1;
std::vector<double> x_0_exact;
std::vector<double> x_1_exact;
std::vector<double> x_0_dot_exact;
std::vector<double> x_1_dot_exact;
{
x_0_exact.push_back(2.0); // IC
x_1_exact.push_back(0.0);
x_0_exact.push_back(1.982896621392518e+00); // matlab
x_1_exact.push_back(-1.710337860748234e-01);
x_0_exact.push_back(1.951487185706842e+00); // matlab
x_1_exact.push_back(-3.140943568567556e-01);
x_0_exact.push_back(1.908249109758246e+00); // matlab
x_1_exact.push_back(-4.323807594859574e-01);
x_0_dot_exact.push_back(0.0);
x_1_dot_exact.push_back(0.0);
for ( int i=1 ; i< Teuchos::as<int>(x_0_exact.size()) ; ++i ) {
x_0_dot_exact.push_back( (x_0_exact[i]-x_0_exact[i-1])/h );
x_1_dot_exact.push_back( (x_1_exact[i]-x_1_exact[i-1])/h );
//std::cout << "x_0_dot_exact["<<i<<"] = "<<x_0_dot_exact[i] << std::endl;
//std::cout << "x_1_dot_exact["<<i<<"] = "<<x_1_dot_exact[i] << std::endl;
}
}
double tol_discrete = 1.0e-12;
double tol_continuous = 1.0e-2;
{
// Get IC out
double t = 0.0;
RCP<const VectorBase<double> > x;
RCP<const VectorBase<double> > xdot;
{
// Get x out of stepper.
Array<double> t_vec;
Array<RCP<const VectorBase<double> > > x_vec;
Array<RCP<const VectorBase<double> > > xdot_vec;
t_vec.resize(1); t_vec[0] = t;
stepper->getPoints(t_vec,&x_vec,&xdot_vec,NULL);
x = x_vec[0];
xdot = xdot_vec[0];
}
{
Thyra::ConstDetachedVectorView<double> x_view( *x );
TEST_FLOATING_EQUALITY( x_view[0], x_0_exact[0], tol_discrete );
TEST_FLOATING_EQUALITY( x_view[1], x_1_exact[0], tol_discrete );
Thyra::ConstDetachedVectorView<double> xdot_view( *xdot );
TEST_FLOATING_EQUALITY( xdot_view[0], x_0_dot_exact[0], tol_discrete );
TEST_FLOATING_EQUALITY( xdot_view[1], x_1_dot_exact[0], tol_discrete );
}
}
for (int i=1 ; i < Teuchos::as<int>(x_0_exact.size()); ++i) {
// Each time step
double t = 0.0+i*h;
double h_taken = stepper->takeStep(h,STEP_TYPE_FIXED);
TEST_ASSERT( h_taken == h );
RCP<const VectorBase<double> > x;
RCP<const VectorBase<double> > xdot;
{
// Get x out of stepper.
Array<double> t_vec;
Array<RCP<const VectorBase<double> > > x_vec;
Array<RCP<const VectorBase<double> > > xdot_vec;
t_vec.resize(1); t_vec[0] = t;
stepper->getPoints(t_vec,&x_vec,&xdot_vec,NULL);
x = x_vec[0];
xdot = xdot_vec[0];
}
{
Thyra::ConstDetachedVectorView<double> x_view( *x );
TEST_FLOATING_EQUALITY( x_view[0], x_0_exact[i], tol_discrete );
TEST_FLOATING_EQUALITY( x_view[1], x_1_exact[i], tol_discrete );
Thyra::ConstDetachedVectorView<double> xdot_view( *xdot );
TEST_FLOATING_EQUALITY( xdot_view[0], x_0_dot_exact[i], tol_discrete );
TEST_FLOATING_EQUALITY( xdot_view[1], x_1_dot_exact[i], tol_discrete );
}
// Now compare this to the continuous exact solution:
{
Thyra::ModelEvaluatorBase::InArgs<double> inArgs = model->getExactSolution(t);
RCP<const VectorBase<double> > x_continuous_exact = inArgs.get_x();
RCP<const VectorBase<double> > xdot_continuous_exact = inArgs.get_x_dot();
{
Thyra::ConstDetachedVectorView<double> x_view( *x );
Thyra::ConstDetachedVectorView<double> xce_view( *x_continuous_exact );
TEST_FLOATING_EQUALITY( x_view[0], xce_view[0], tol_continuous );
TEST_FLOATING_EQUALITY( x_view[1], xce_view[1], tol_continuous*10 );
Thyra::ConstDetachedVectorView<double> xdot_view( *xdot );
Thyra::ConstDetachedVectorView<double> xdotce_view( *xdot_continuous_exact );
TEST_FLOATING_EQUALITY( xdot_view[0], xdotce_view[0], tol_continuous*10 );
TEST_FLOATING_EQUALITY( xdot_view[1], xdotce_view[1], tol_continuous*10 );
}
}
}
}
