OOF2: The Manual
Name
Newton (Newton) — Solve nonlinear equations with Newton's method.
Synopsis
Newton
(relative_tolerance
,absolute_tolerance
,maximum_iterations
)
Details

Base class:
NonlinearSolverBase

Parameters:
relative_tolerance
 Relative tolerance for convergence to a nonlinear solution. Type: A real number.
absolute_tolerance
 Absolute tolerance for convergence to a nonlinear solution. Type: A real number.
maximum_iterations
 Maximum number of iterations for convergence to a nonlinear solution. Type: Integer.
Description
Newton
is a nonlinear
solver used in AdvancedSolverMode for solving nonlinear
equations of the form
It implements Newton's method, which uses the derivative
of the nonlinear term with respect to the vector
of unknowns,
(i.e, Field
values), to compute
successive approximations to the solution. The iteration stops when
the norm of the residual after the
n^{th} step,
A_{n}, satisfies
where =relative_tolerance
and =absolute_tolerance
,
or when the maximum_iterations
limit is exceeded.
Newton's method generally converges in fewer iterations than Picard, but may require more work per iteration.
Newton's method relies upon knowing the derivatives of the nonlinear
function with respect to the unknowns, . This information comes from the
Material
Properties
, which determine the exact form of the
equations being solved. Nonlinear Properties
that are built into
OOF2 provide routines to compute the derivatives, but Properties
defined in OOF2 extensions might not. In this
case, Newton
will compute the derivatives
numerically. This will make Newton
perform
more computations on each iteration and quite possibly also require
more iterations. The parameters used for the numerical
differentiation may be set by the OOF.Settings.Mesh_Defaults.Numerical_Differentiation
command.