Tempus_StepperNewmarkImplicitAForm_decl.hpp

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//                Tempus: Copyright (2017) Sandia Corporation
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#ifndef Tempus_StepperNewmarkImplicitAForm_decl_hpp
#define Tempus_StepperNewmarkImplicitAForm_decl_hpp

#include "Tempus_StepperImplicit.hpp"
#include "Tempus_WrapperModelEvaluatorSecondOrder.hpp"

namespace Tempus {


/** \brief Newmark time stepper in acceleration form (a-form).
 *
 *  Here, we implement the Newmark scheme in predictor/corrector form;
 *  see equations (34)-(35) in: A. Mota, W. Klug, M. Ortiz,  "Finite element
 *  simulation of firearm injury to the human cranium",  Computational
 *  Mechanics 31(1) 115-121 (2003).
 *
 *  Newmark has two parameters: \f$\beta\f$
 *  and \f$\gamma\f$, both of which need to be in the range \f$[0,1]\f$.
 *  Newmark can be an explicit or implicit method, depending on
 *  the value of the \f$\beta\f$ parameter. If \f$\beta = 0\f$, the method
 *  is explicit.  Regardless of whether the method is implicit
 *  or explicit, a linear solve is required.  This linear solve can be
 *  optimized, however, for the explicit case by lumping the mass matrix.
 *  This optimization can be invoked by running "Newmark Explicit d-Form"
 *  Stepper through the Piro::TempusSolver class.
 *
 *  Newmark is second order accurate if \f$\gamma =  0.5\f$; otherwise it
 *  is first order accurate.  Some additional properties about the Newmark
 *  scheme can be found
 *<a href="http://opensees.berkeley.edu/wiki/index.php/Newmark_Method">here</a>.
 *
 *  The governing equation solved by this stepper is
 *  \f[
 *    \mathbf{M}\, \ddot{\mathbf{x}} + \mathbf{C}\, \dot{\mathbf{x}}
 *    + \mathbf{K}\, \mathbf{x} + \mathbf{F}(t) = 0
 *  \f]
 *  For the A-form (i.e., solving for the acceleration,
 *  \f$\mathbf{a} = \ddot{\mathbf{x}}\f$), we have the following implicit ODE
 *  \f[
 *       \mathbf{M}\, \mathbf{a} + \mathbf{C}\, \mathbf{v}
 *     + \mathbf{K}\, \mathbf{d} + \mathbf{F}(t) =
 *       \mathbf{f}(\mathbf{d}, \mathbf{v}, \mathbf{a}, t) = 0
 *  \f]
 *  where \f$\mathbf{v} = \dot{\mathbf{x}}\f$ and \f$\mathbf{d} = \mathbf{x}\f$.
 *
 *  <b> Algorithm </b>
 *  The algorithm for the Newmark implicit A-form with predictors and
 *  correctors is
 *   - \f$\mathbf{d}^{\ast} = \mathbf{d}^{n-1} + \Delta t \mathbf{v}^{n-1}
 *                            + \Delta t^2 (1-2 \beta) \mathbf{a}^{n-1} / 2\f$
 *   - \f$\mathbf{v}^{\ast} =
 *        \mathbf{v}^{n-1} + \Delta t (1-\gamma) \mathbf{a}^{n-1}\f$
 *   - Solve
 *        \f$\mathbf{f}(\mathbf{d}^n, \mathbf{v}^n, \mathbf{a}^n, t^n) = 0\f$
 *     for \f$\mathbf{a}^n\f$ where
 *     - \f$\mathbf{d}^n = \mathbf{d}^{\ast} + \beta \Delta t^2 \mathbf{a}^n\f$
 *     - \f$\mathbf{v}^n = \mathbf{v}^{\ast} + \gamma \Delta t \mathbf{a}^n\f$
 *
 *  The First-Step-As-Last (FSAL) principle is part of the Newmark
 *  implicit A-Form as the acceleration from the previous time step is
 *  used for the predictors.  The default is to set useFSAL=true,
 *  and useFSAL=false will be ignored.
 */
template<class Scalar>
class StepperNewmarkImplicitAForm
 : virtual public Tempus::StepperImplicit<Scalar>
{
public:

  /** \brief Default constructor.
   *
   *  - Constructs with a default ParameterList.
   *  - Can reset ParameterList with setParameterList().
   *  - Requires subsequent setModel() and initialize() calls before calling
   *    takeStep().
  */
  StepperNewmarkImplicitAForm();

  /// Constructor
  StepperNewmarkImplicitAForm(
    const Teuchos::RCP<const Thyra::ModelEvaluator<Scalar> >& appModel,
    Teuchos::RCP<Teuchos::ParameterList> pList = Teuchos::null);

  /// \name Basic stepper methods
  //@{
    virtual void setModel(
      const Teuchos::RCP<const Thyra::ModelEvaluator<Scalar> >& appModel);

    virtual void setObserver(
      Teuchos::RCP<StepperObserver<Scalar> > /* obs */ = Teuchos::null){}

    /// Initialize during construction and after changing input parameters.
    virtual void initialize();

    /// Set the initial conditions and make them consistent.
    virtual void setInitialConditions (
      const Teuchos::RCP<SolutionHistory<Scalar> >& solutionHistory);

    /// Take the specified timestep, dt, and return true if successful.
    virtual void takeStep(
      const Teuchos::RCP<SolutionHistory<Scalar> >& solutionHistory);

    /// Get a default (initial) StepperState
    virtual Teuchos::RCP<Tempus::StepperState<Scalar> >
      getDefaultStepperState();
    virtual Scalar getOrder() const {
      if (gamma_ == 0.5) return 2.0;
      else return 1.0;
    }
    virtual Scalar getOrderMin() const {return 1.0;}
    virtual Scalar getOrderMax() const {return 2.0;}

    virtual bool isExplicit()         const {return false;}
    virtual bool isImplicit()         const {return true;}
    virtual bool isExplicitImplicit() const
      {return isExplicit() and isImplicit();}
    virtual bool isOneStepMethod()   const {return true;}
    virtual bool isMultiStepMethod() const {return !isOneStepMethod();}

    virtual OrderODE getOrderODE()   const {return SECOND_ORDER_ODE;}
  //@}

  /// Return W_xDotxDot_coeff = d(xDotDot)/d(xDotDot).
  virtual Scalar getW_xDotDot_coeff (const Scalar) const {return Scalar(1.0);}
  /// Return alpha = d(xDot)/d(xDotDot).
  virtual Scalar getAlpha(const Scalar dt) const { return gamma_*dt; }
  /// Return beta  = d(x)/d(xDotDot).
  virtual Scalar getBeta (const Scalar dt) const { return beta_*dt*dt; }

  /// \name ParameterList methods
  //@{
    void setParameterList(const Teuchos::RCP<Teuchos::ParameterList> & pl);
    Teuchos::RCP<Teuchos::ParameterList> getNonconstParameterList();
    Teuchos::RCP<Teuchos::ParameterList> unsetParameterList();
    Teuchos::RCP<const Teuchos::ParameterList> getValidParameters() const;
    Teuchos::RCP<Teuchos::ParameterList> getDefaultParameters() const;
  //@}

  /// \name Overridden from Teuchos::Describable
  //@{
    virtual std::string description() const;
    virtual void describe(Teuchos::FancyOStream        & out,
                          const Teuchos::EVerbosityLevel verbLevel) const;
  //@}

    void predictVelocity(Thyra::VectorBase<Scalar>& vPred,
                             const Thyra::VectorBase<Scalar>& v,
                             const Thyra::VectorBase<Scalar>& a,
                             const Scalar dt) const;

    void predictDisplacement(Thyra::VectorBase<Scalar>& dPred,
                               const Thyra::VectorBase<Scalar>& d,
                               const Thyra::VectorBase<Scalar>& v,
                               const Thyra::VectorBase<Scalar>& a,
                               const Scalar dt) const;

    void correctVelocity(Thyra::VectorBase<Scalar>& v,
                             const Thyra::VectorBase<Scalar>& vPred,
                             const Thyra::VectorBase<Scalar>& a,
                             const Scalar dt) const;

    void correctDisplacement(Thyra::VectorBase<Scalar>& d,
                               const Thyra::VectorBase<Scalar>& dPred,
                               const Thyra::VectorBase<Scalar>& a,
                               const Scalar dt) const;
private:

  Scalar beta_;
  Scalar gamma_;

  Teuchos::RCP<Teuchos::FancyOStream> out_;

};
} // namespace Tempus

#endif // Tempus_StepperNewmarkImplicitAForm_decl_hpp