NewtonSolver

class dolfin.cpp.la.NewtonSolver(*args)

Bases: dolfin.cpp.common.Variable

This class defines a Newton solver for nonlinear systems of equations of the form \(F(x) = 0\).

Overloaded versions

• NewtonSolver()

  Create nonlinear solver

• NewtonSolver(solver, factory)

  Create nonlinear solver using provided linear solver

  Arguments

  solver (GenericLinearSolver)

  The linear solver.

  factory (GenericLinearAlgebraFactory)

  The factory.

converged()

Convergence test. It may be overloaded using virtual inheritance and this base criterion may be called from derived, both in C++ and Python.

Arguments

r (GenericVector)

Residual for criterion evaluation.

nonlinear_problem (NonlinearProblem)

The nonlinear problem.

iteration (int)

Newton iteration number.

Returns

bool

Whether convergence occured.

static default_parameters()

Default parameter values

Returns

Parameters

Parameter values.

iteration()

Return Newton iteration number

Returns

int

The iteration number.

linear_solver()

Return the linear solver

Returns

GenericLinearSolver

The linear solver.

relative_residual()

Return current relative residual

Returns

float

Current relative residual.

residual()

Return current residual

Returns

float

Current residual.

solve()

Solve abstract nonlinear problem \(F(x) = 0\) for given \(F\) and Jacobian \(\dfrac{\partial F}{\partial x}\).

Arguments

nonlinear_function (NonlinearProblem)

The nonlinear problem.

x (GenericVector)

The vector.

Returns

(int, bool)

Pair of number of Newton iterations, and whether iteration converged)

thisown None

The membership flag