NewmarkBeta.h

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//* This file is part of the MOOSE framework
//* https://www.mooseframework.org
//*
//* All rights reserved, see COPYRIGHT for full restrictions
//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
//*
//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "TimeIntegrator.h"
#include "MathUtils.h"

class NewmarkBeta;

template <>
InputParameters validParams<NewmarkBeta>();

class NewmarkBeta : public TimeIntegrator
{
public:
  NewmarkBeta(const InputParameters & parameters);
  virtual ~NewmarkBeta();

  virtual int order() override { return 1; }
  virtual void computeTimeDerivatives() override;
  virtual void computeADTimeDerivatives(DualReal & ad_u_dot,
                                        const dof_id_type & dof) const override;
  virtual void postResidual(NumericVector<Number> & residual) override;

protected:
  template <typename T, typename T2, typename T3, typename T4, typename T5>
  void computeTimeDerivativeHelper(T & u_dot,
                                   const T2 & u_old,
                                   const T3 & u_dot_old,
                                   T4 & u_dotdot,
                                   const T5 & u_dotdot_old) const;

  Real _beta;

  Real _gamma;

  Real & _du_dotdot_du;
};

template <typename T, typename T2, typename T3, typename T4, typename T5>
void
NewmarkBeta::computeTimeDerivativeHelper(
    T & u_dot, const T2 & u_old, const T3 & u_dot_old, T4 & u_dotdot, const T5 & u_dotdot_old) const
{
  u_dotdot -= u_old;
  u_dotdot *= 1.0 / _beta / _dt / _dt;
  MathUtils::addScaled(-1.0 / _beta / _dt, u_dot_old, u_dotdot);
  MathUtils::addScaled(-0.5 / _beta + 1.0, u_dotdot_old, u_dotdot);

  // compute first derivative
  // according to Newmark-Beta method
  // u_dot = first_term + second_term + third_term
  //       first_term = u_dot_old
  //      second_term = u_dotdot_old * (1 - gamma) * dt
  //       third_term = u_dotdot * gamma * dt
  u_dot = u_dot_old;
  MathUtils::addScaled((1.0 - _gamma) * _dt, u_dotdot_old, u_dot);
  MathUtils::addScaled(_gamma * _dt, u_dotdot, u_dot);
}