NOX::Direction::Newton Class Reference

Newton direction computation More...

#include <NOX_Direction_Newton.H>

Inheritance diagram for NOX::Direction::Newton:

Collaboration diagram for NOX::Direction::Newton:
List of all members.

Public Member Functions

 Newton (const NOX::Utils &u, NOX::Parameter::List &params)
virtual ~Newton ()
virtual bool reset (NOX::Parameter::List &params)
 Reset direction based on possibly new parameters.
virtual bool compute (NOX::Abstract::Vector &dir, NOX::Abstract::Group &grp, const NOX::Solver::Generic &solver)
 Compute the direction vector, dir, for a specific method given the current group, grp.

Protected Member Functions

virtual bool resetForcingTerm (const NOX::Abstract::Group &soln, const NOX::Abstract::Group &oldSoln, int niter, const NOX::Solver::Generic &solver)

Detailed Description

Newton direction computation

Computes the Newton direction by solving the Newton system.

\[ Jd = -F \]

Here $J$ is the n x n Jacobian matrix at the current iterate, $F$ is the n-vector representing the nonlinear function at the current iterate, and $d$ is the n-vector that we are solving for.

If we use an iterative linear solver for the Newton system, then this is called an inexact Newton method. The tolerance used to terminate the linear solve is called the forcing term. The forcing term may be constant, or it may be adjustable. In either case, at iteration $k$ we require,

\[ \frac{\|J_k d_k - (-F_k)\|}{\|F_k\|} \leq \eta_k. \]

Here $\eta_k$ is the forcing term for iteration $k$.

This solution tolerance is to be enforced by the user's implementation of NOX::Abstract::Group::computeNewton; it is passed in as the "Tolerance" in the parameter list for that function.
Adjustable forcing terms were introduced by Eisenstat and Walker (1982); here they are implemented as described in Pernice and Walker (1998). We have two choices for adjustable forcing terms:




"Direction"/"Newton"/"Linear Solver":

When using a forcing term, it's critically important the the residual of the original system is used in the comparison. This can be an issue if scaling or left preconditioning is applied to the linear system.

Member Function Documentation

bool NOX::Direction::Newton::compute NOX::Abstract::Vector dir,
NOX::Abstract::Group grp,
const NOX::Solver::Generic solver

Compute the direction vector, dir, for a specific method given the current group, grp.

The grp is not const so that we can compute the F vector, the Jacobian matrix, the Newton vector, and so on.

Const access to the solver is used for getting additional information such as the past solution, the iteration number, and so on.

Implements NOX::Direction::Generic.

bool NOX::Direction::Newton::resetForcingTerm const NOX::Abstract::Group soln,
const NOX::Abstract::Group oldSoln,
int  niter,
const NOX::Solver::Generic solver
[protected, virtual]

Called each iteration to reset the forcing term (ie, the convergence tolerance for the linear solver).

The documentation for this class was generated from the following files:
Generated on Thu Sep 18 12:42:27 2008 for NOX by doxygen