#include "Thyra_ModelEvaluator.hpp"
#include "Thyra_StateFuncModelEvaluatorBase.hpp"
#include "Teuchos_ParameterListAcceptorDefaultBase.hpp"
#include "Teuchos_ParameterList.hpp"

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Classes
class	Tempus_Test::HarmonicOscillatorModel< Scalar >
	Consider the ODE: $m\ddot{x} + c\dot{x} + kx=f$ where $k \geq 0$ is a constant, is a constant damping parameter, is a constant forcing parameter, and is a constant mass parameter, with initial conditions are: $\begin{eqnarray} x(0) & = & 0\\ \dot{x}(0) & = & 1 \end{eqnarray}$ It is straight-forward to show that the exact solution to this ODE is: $\begin{eqnarray} x(t) & = & t(1+0.5\tilde{f}t), \hspace{3.6cm} if \hspace{0.2cm} k = c = 0 \\ & = & \frac{(\tilde{c}-\tilde{f})}{\tilde{c}^2}(1-e^{-\tilde{c}t}) + \frac{f}{c}t, \hspace{1.9cm} if \hspace{0.2cm} k = 0, c\neq 0 \\ & = & \frac{1}{\sqrt{\tilde{k}}}\sin(\sqrt{\tilde{k}}t) + \frac{f}{k}\left(1-\cos(\sqrt{\tilde{k}}t) \right), \hspace{0.2cm} if \hspace{0.2cm} k > 0, c = 0 \end{eqnarray}$ where $\tilde{c}\equiv c/m$ , $\tilde{k}\equiv k/m$ and $\tilde{f}\equiv f/m$ . While it is possible to derive the solution to this ODE for the case when and $c \neq 0$ , we do not consider that case here. When , , and , our ODE simplies to a canonical differential equation model of a ball thrown up in the air, with a parabolic trajectory solution, namely $x(t) = t(1-0.5t)$ where $t\in [0,2]$ . An EpetraExt version of this simplified version of the test is implemented in Piro::MockModelEval_B (see Trilinos/packages/piro/test), where it is used to test the Piro (EpetraExt) Newmark-Beta scheme (see input_Solver_NB.xml input file). When and , this test is equivalent to the SinCos model.. More...

Namespaces
	Tempus_Test

Classes

Namespaces