mfem::NewtonSolver applying a constant damping factor to the Newton update, optionally shortening it further with a backtracking line search on the residual norm. More...

#include <MFEMNewtonNonlinearSolver.h>

Inheritance diagram for Moose::MFEM::DampedNewtonSolver:

[legend]

Public Member Functions
	DampedNewtonSolver (MPI_Comm comm)

void	SetOperator (const mfem::Operator &op) override

void	SetDampingFactor (mfem::real_t damping_factor)
	Set the fraction of the full Newton update applied.

void	SetBacktracking (unsigned int max_its, mfem::real_t contraction_factor, mfem::real_t sufficient_decrease)
	Enable a backtracking line search taking at most max_its trial steps, each a factor contraction_factor shorter than the last, accepting the first whose residual norm satisfies the sufficient decrease condition with coefficient sufficient_decrease.

mfem::real_t	ComputeScalingFactor (const mfem::Vector &x, const mfem::Vector &b) const override
	Return the fraction of the Newton update to apply at the iterate x.

Protected Attributes
mfem::real_t	_damping_factor = 1.0
	Fraction of the full Newton update applied, and the line search's initial trial step.

unsigned int	_ls_max_its = 0
	Maximum number of trial steps taken by the line search; 0 disables backtracking.

mfem::real_t	_ls_contraction_factor = 0.5
	Factor a rejected trial step is multiplied by to obtain the next one.

mfem::real_t	_ls_sufficient_decrease = 1.0e-4
	Coefficient of the sufficient decrease (Armijo) condition on the residual norm.

mfem::Vector	_ls_x_trial
	Trial iterate x - t c evaluated by the line search.

mfem::Vector	_ls_r_trial
	Residual at the trial iterate.

Detailed Description

mfem::NewtonSolver applying a constant damping factor to the Newton update, optionally shortening it further with a backtracking line search on the residual norm.

Definition at line 22 of file MFEMNewtonNonlinearSolver.h.

Constructor & Destructor Documentation

◆ DampedNewtonSolver()

Moose::MFEM::DampedNewtonSolver::DampedNewtonSolver ( MPI_Comm comm )

inline

Definition at line 25 of file MFEMNewtonNonlinearSolver.h.

25: mfem::NewtonSolver(comm) {}

Member Function Documentation

◆ ComputeScalingFactor()

mfem::real_t Moose::MFEM::DampedNewtonSolver::ComputeScalingFactor	(	const mfem::Vector &	x,
		const mfem::Vector &	b
	)		const

override

Return the fraction of the Newton update to apply at the iterate x.

Without backtracking this is the constant damping factor. With backtracking it is the first trial step t, starting from the damping factor, satisfying ||F(x - t c) - b|| <= (1 - sufficient_decrease * t) * ||F(x) - b||, or 0 if no trial step satisfies it, which interrupts the Newton iteration.

Definition at line 42 of file MFEMNewtonNonlinearSolver.C.

{
  if (_ls_max_its == 0)
    return _damping_factor;
 
  // NewtonSolver::Mult leaves the residual F(x) - b in r and the Newton update in c.
  const auto have_b = (b.Size() == Height());
  const auto norm = Norm(r);
 
  auto scale = _damping_factor;
  for (const auto it : make_range(_ls_max_its))
  {
    add(x, -scale, c, _ls_x_trial);
    oper->Mult(_ls_x_trial, _ls_r_trial);
    if (have_b)
      _ls_r_trial -= b;
    const auto trial_norm = Norm(_ls_r_trial);
 
    if (print_options.iterations)
      mfem::out << "Newton line search iteration " << it << " : damping factor = " << scale
                << ", ||r|| = " << trial_norm << '\n';
 
    // Sufficient decrease (Armijo) condition on the residual norm, as used by the PETSc
    // backtracking line search SNESLINESEARCHBT.
    if (trial_norm <= (1.0 - _ls_sufficient_decrease * scale) * norm)
      return scale;
 
    scale *= _ls_contraction_factor;
  }
 
  if (print_options.warnings)
    mfem::out << "Newton line search: no trial step satisfied the sufficient decrease "
                 "condition!\n";
 
  // Interrupts the Newton iteration, which then reports no convergence.
  return 0.0;
}

◆ SetBacktracking()

void Moose::MFEM::DampedNewtonSolver::SetBacktracking	(	unsigned int	max_its,
		mfem::real_t	contraction_factor,
		mfem::real_t	sufficient_decrease
	)

Enable a backtracking line search taking at most max_its trial steps, each a factor contraction_factor shorter than the last, accepting the first whose residual norm satisfies the sufficient decrease condition with coefficient sufficient_decrease.

Definition at line 32 of file MFEMNewtonNonlinearSolver.C.

{
  _ls_max_its = max_its;
  _ls_contraction_factor = contraction_factor;
  _ls_sufficient_decrease = sufficient_decrease;
}

◆ SetDampingFactor()

void Moose::MFEM::DampedNewtonSolver::SetDampingFactor ( mfem::real_t damping_factor )

inline

Set the fraction of the full Newton update applied.

The backtracking line search, when enabled, starts from this trial step.

Definition at line 31 of file MFEMNewtonNonlinearSolver.h.

31{ _damping_factor = damping_factor; }

◆ SetOperator()

void Moose::MFEM::DampedNewtonSolver::SetOperator ( const mfem::Operator & op )

override

Definition at line 20 of file MFEMNewtonNonlinearSolver.C.

{
  mfem::NewtonSolver::SetOperator(op);
 
  _ls_x_trial.SetSize(width);
  _ls_x_trial.UseDevice(true);
 
  _ls_r_trial.SetSize(height);
  _ls_r_trial.UseDevice(true);
}