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Tempus: Add Stepper Initial Conditions

Created by: ccober6

Adding a Stepper initial conditions has several benefits:

  • Ensure that the initial SolutionState is consistent, i.e., x, xDot, and xDotDot satisfy the governing equation at the initial time.
  • Currently explicit Steppers are not consistent until the next time step fills in the currentState. This change will make the SolutionState consistent within the time step.
  • For explicit Steppers with a consistent SolutionState, the residual can be determined and compared to residuals from implicit Steppers. This is SPARC's main driver for this change.
  • For DAEs, making the initial condition consistent is critical to obtain the correct solution.

@trilinos/tempus

Expectations

  • Changes for this issue should not effect solutions.

Definition of Done

  • First convert Forward Euler.
  • Convert all other explicit Steppers, ERK, Leapfrog, ...
  • Convert all implicit Steppers
  • Passes all tests.