sfepy.solvers.semismooth_newton module

class sfepy.solvers.semismooth_newton.SemismoothNewton(conf, **kwargs)[source]

The semi-smooth Newton method.

This method is suitable for solving problems of the following structure:

\begin{split}
  & F(y) = 0 \\
  & A(y) \ge 0 \;,\ B(y) \ge 0 \;,\ \langle A(y), B(y) \rangle = 0
\end{split}

The function F(y) represents the smooth part of the problem.

Regular step: y \leftarrow y - J(y)^{-1} \Phi(y)

Steepest descent step: y \leftarrow y - \beta J(y) \Phi(y)

Although fun_smooth_grad() computes the gradient of the smooth part only, it should return the global matrix, where the non-smooth part is uninitialized, but pre-allocated.

Kind: ‘nls.semismooth_newton’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:
semismooth : bool (default: True)

If True, use the semi-smooth algorithm. Otherwise a non-smooth equation is assumed (use a brute force).

i_max : int (default: 1)

The maximum number of iterations.

eps_a : float (default: 1e-10)

The absolute tolerance for the residual, i.e. ||f(x^i)||.

eps_r : float (default: 1.0)

The relative tolerance for the residual, i.e. ||f(x^i)|| /
||f(x^0)||.

macheps : float (default: 2.2204460492503131e-16)

The float considered to be machine “zero”.

lin_red : float (default: 1.0)

The linear system solution error should be smaller than (eps_a * lin_red), otherwise a warning is printed.

ls_on : float (default: 0.99999)

Start the backtracking line-search by reducing the step, if ||f(x^i)|| / ||f(x^{i-1})|| is larger than ls_on.

ls_red : 0.0 < float < 1.0 (default: 0.1)

The step reduction factor in case of correct residual assembling.

ls_red_warp : 0.0 < float < 1.0 (default: 0.001)

The step reduction factor in case of failed residual assembling (e.g. the “warp violation” error caused by a negative volume element resulting from too large deformations).

ls_min : 0.0 < float < 1.0 (default: 1e-05)

The minimum step reduction factor.

compute_jacobian(vec_x, fun_smooth_grad, fun_a_grad, fun_b_grad, vec_smooth_r, vec_a_r, vec_b_r)[source]
name = ‘nls.semismooth_newton’