Add normal NCP options for mortar contact

[Andreas-Lepak]

closes #33322

Reason

LM mortar normal contact currently exposes only the min-function NCP residual for the normal weighted-gap constraint. That preserves exact complementarity, but it gives users no input-level way to try smooth-min or Fischer-Burmeister forms when active-set transitions make nonlinear solves difficult.

Design

• Add normal_ncp_function = MIN | SMOOTH_MIN | FISCHER_BURMEISTER | SMOOTH_FISCHER_BURMEISTER.
• Add normal_ncp_smoothing_width for the smooth normal NCP functions.
• Apply the selected residual in the static and dynamic LM mortar weighted-gap constraints, including the frictional subclasses that inherit the normal constraint.
• Thread the parameters through ContactAction for formulation = mortar and reject them for non-mortar contact formulations.
• Use a finite generalized derivative for exact Fischer-Burmeister at the origin so exact-touch states do not produce invalid AD derivatives.
• Document the smoothing-width scale and add focused regression coverage for direct constraint use and action-based contact use.

Impact

Existing inputs and results are unchanged because MIN remains the default. Users gain optional smooth-min and Fischer-Burmeister normal NCP residuals for LM mortar contact. Penalty mortar and node-face contact are unchanged.

[moosebuild]

Job Documentation, step Docs: sync website on d89a464 wanted to post the following:

View the site here

This comment will be updated on new commits.

[lindsayad]

Can you rebase to remove all the recipe failures? It would be great to see some results (perhaps tabular) that shows some solver characteristics with the different NCP choices

[Andreas-Lepak]

Can you rebase to remove all the recipe failures? It would be great to see some results (perhaps tabular) that shows some solver characteristics with the different NCP choices

I used the mortar LM 3D ironing problem also used in: #33358

The three new options all let the simulation run a littlle bit further before failure for the frictional case. For the frictionless case the SMOOTH_MIN performs a bit better than the other option, but it is not a big difference.

Scenario	NCP function	Smoothing width	Final time	Accepted steps	Failed steps	Total nonlinear iterations	Completed
friction	MIN	0	0.278314	17	5	90	no
friction	SMOOTH_MIN	1e-4	0.294246	54	10	282	no
friction	FISCHER_BURMEISTER	0	0.294169	28	7	152	no
friction	SMOOTH_FISCHER_BURMEISTER	1e-5	0.294418	80	11	420	no
frictionless	MIN	0	1.000000	21	0	70	yes
frictionless	SMOOTH_MIN	1e-4	1.000000	20	0	56	yes
frictionless	FISCHER_BURMEISTER	0	1.000000	24	0	99	yes
frictionless	SMOOTH_FISCHER_BURMEISTER	1e-5	1.000000	24	0	101	yes

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[moosebuild]

Job Test, step Results summary on d89a464 wanted to post the following:

Framework test summary

Compared against a3c1a50 in job civet.inl.gov/job/3983715.

No change

Modules test summary

Compared against a3c1a50 in job civet.inl.gov/job/3983715.

Added tests

Test	Time (s)	Memory (MB)
contact/test:mortar_dynamics.block-dynamics-action-smooth-min-normal-ncp	1.20	119.87
contact/test:bouncing-block-contact.weighted_vel_pdass/action_smooth_fischer_burmeister_normal_ncp	0.64	176.79
contact/test:bouncing-block-contact.weighted_gap/fischer_burmeister_exact_touch_normal_ncp	0.60	77.49
contact/test:bouncing-block-contact.weighted_gap/smooth_normal_ncp_requires_width	0.58	66.13

[lindsayad]

I used the mortar LM 3D ironing problem also used in: #33358

I can't tell exactly what input this is. You're putting up a lot of PRs; it would help me if you can be as explicit as possible.

So it seems like the min function is superior to FB for frictionless contact. Frictional is a little harder for me to parse. Could you maybe post another table with the number of accepted and failed timestep counts and the number of nonlinear iterations removed and instead have two columns, one with average dt per (accepted) time step and another with average number of nonlinear iterations per (accepted) time step?