Goal

The primary goal of Example 1: Utilize Thyra is to replace the raw arrays used in Example 0: Basic Problem with Thyra vectors, while preserving the same van der Pol problem, the same hand-written Forward Euler stepping logic, the same simple tabular solution output, and the same regression-testing workflow.

New concepts introduced from Teuchos and Thyra are:

Teuchos::RCP
- Teuchos::RCP is Trilinos' reference-counted smart pointer and plays a role similar to std::shared_ptr
Thyra::VectorBase
- replaces raw C++ arrays as the abstract vector representation
Thyra::VectorSpaceBase
- defines the vector space for the state
Thyra::DetachedVectorView and Thyra::ConstDetachedVectorView
- provide direct element access to Thyra vectors
Thyra::V_VpStV, Thyra::V_V, Thyra::norm, and Thyra::norm_2
- provide abstract vector algebra operations

This transition is the first step toward expressing the application in terms of abstract numerical interfaces rather than concrete array storage. That abstraction is what later allows Tempus steppers, model evaluators, and solver infrastructure to work with the application state.

What stays the same

The van der Pol equations are unchanged.
The timestepper is still Forward Euler.
The application still controls the time loop directly.
The output table still reports the step index, time, , and .
The regression check follows the same role and uses the same gold values.

Selected code excerpts

The code excerpts below highlight the main changes needed to move from raw arrays to Thyra vectors.

Memory allocation

Setup Thyra vectors. The raw double arrays are replaced by Thyra vectors, which are created from a Thyra::VectorSpaceBase. This step also introduces Teuchos::RCP for memory management.

Before

double x_n[2];

double xDot_n[2];

After

int vectorLength = 2;
RCP<const Thyra::VectorSpaceBase<double> > xSpace =
  Thyra::defaultSpmdVectorSpace<double>(vectorLength);
 
RCP<Thyra::VectorBase<double> > x_n    = Thyra::createMember(xSpace);
RCP<Thyra::VectorBase<double> > xDot_n = Thyra::createMember(xSpace);

The state is now represented through abstract vector interfaces rather than fixed-size arrays.

Assign initial conditions

Initialize Thyra vectors. Initial values are assigned through Thyra::DetachedVectorView. The local scope ensures the detached views are destroyed immediately after use.

Before

x_n   [0] = 2.0;
x_n   [1] = 0.0;
xDot_n[0] = 0.0;
xDot_n[1] = -2.0/epsilon;

After

{ // Scope to delete DetachedVectorViews
  Thyra::DetachedVectorView<double> x_n_view(*x_n);
  x_n_view[0] = 2.0;
  x_n_view[1] = 0.0;
  Thyra::DetachedVectorView<double> xDot_n_view(*xDot_n);
  xDot_n_view[0] = 0.0;
  xDot_n_view[1] = -2.0/epsilon;
}

Evaluate the right-hand side

Evaluate the right-hand side. The van der Pol right-hand side is still evaluated directly in the application code, but element access now goes through detached vector views.

Before

xDot_n[0] = x_n[1];

xDot_n[1] = ((1.0 - x_n[0]*x_n[0])*x_n[1] - x_n[0])/epsilon;

After

{
  Thyra::ConstDetachedVectorView<double> x_n_view(*x_n);
  Thyra::DetachedVectorView<double> xDot_n_view(*xDot_n);
  xDot_n_view[0] = x_n_view[1];
  xDot_n_view[1] =
    ((1.0-x_n_view[0]*x_n_view[0])*x_n_view[1]-x_n_view[0])/epsilon;
}

Element-wise access is still possible, but it now uses Thyra utilities.

Perform Forward Euler

Use Thyra vector algebra. The Forward Euler update is expressed with Thyra::V_VpStV, which performs the vector operation $x^{n+1} = x^n + dt\,\dot{x}^n$ .

Before

x_np1[0] = x_n[0] + dt*xDot_n[0];

x_np1[1] = x_n[1] + dt*xDot_n[1];

After

Thyra::V_VpStV(x_np1.ptr(), *x_n, dt, *xDot_n);

Promote to the next time step

Use Thyra vector assignment. The accepted solution is copied into the current state using Thyra::V_V.

Before

x_n[0] = x_np1[0];
x_n[1] = x_np1[1];
n++;

After

Thyra::V_V(x_n.ptr(), *x_np1);

n++;

How to compare the examples

A more detailed comparison can be viewed by diffing:

From the packages/tempus directory, a focused comparison of the main time-integration logic between these two examples can be generated locally in bash or zsh with:

git diff --no-index \
  <(sed -n '87,172p' examples/00_Basic_Problem/00_Basic_Problem.cpp) \
  <(sed -n '70,164p' examples/01_Utilize_Thyra/01_Utilize_Thyra.cpp)

This ignores leading header lines (e.g., #include statements and Doxygen comments) and trailing regression-testing lines.

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