Test runs for nonlin-evol paper

Nonlinear symmetry example

• Jobfile: nlsfile
• Skript: nonlin_symmetry

Porous medium equation

• Jobfile: pmefile
• Skript: newton

Plan

1. make both runs work with the old scheme, somehow, adapt mu_ranges, nt, T and nelements accordingly
2. try the same configuration with the combined basis generation approach using two sub-tests:
   1. with a factor of M=4*N,
   2. discarding the reduced basis vector if error grows. and without the combined basis generation approach

Testing

For better tests, I want to have a small sized problem for all the 6(4) problems, that run in a very short time.

Results

This is the results section.

Porous medium equation

• 's011n' : separate bases, normal size, adaptive basis generation, started with

  newton([0,5], false, 0, 1, 1, 'normal', false, 4) 

  • EI epsilon of '1e-9' is reached after '140' basis functions 'stop_Mmax = 200', Lebesgue constant of '41.586' (max. poss.: '1.38e42')
  • 3 parameter space adaptations after '20' basis extensions, '525' parameter samples at last refinement step.
  • RB extension explodes after 26 extension steps, error estimator for 'N=26': '6e-2'
  • minimum error estimator '9.28e-3' at step '14'.
  • offline time: 6.9 h, four parallel computations
• 'c021nr': combined basis generation, two ei basis per extension steps, normal size, random parameter sampling (no adaptive parameter sampling)

  newton([0,5], true, 0, 2, 1, 'normal', true, 4) 

  • EI basis of size '201', 'stop_Mmax = 200', last two skipped because of this, one skipped for too low residual.
  • random parameter sample with '800' basis vectors
  • RB extension stops with 'stop_Nmax = 50' at estimated error '8.329e-4'. (stop_epsilon = '1e-5')
  • offline time: 9.9 h, four parallel computations
• 'c411n': combined basis generation, normal size, fixed 'M_by_N_ratio = 4', uniform parameter sampling (adaptive basis generation)

  newton([0,5], true, 4, 1, 1, 'normal', false, 4) 

  • did not stop although 'stop_Nmax = 50' and 'stop_Mmax = 200' were reached. Re-run on pris with 'stop_Nmax = 120', 'stop_Mmax = 400'.
  • Final result: Interrupted at 'N=58', 'M=230', because of increasing (exploding) error after 'epsilon = 5.3534e-04' has been reached at extension step '265' ('N=52', 'M=200') and just before last (fifth) parameter space refinement.
  • Five parameter sample adaptations, finest level with '1968' elements.
  • offline time: ? h, four parallel computations
• 'c021s': combined basis generation, small size, new algorithm for 'M_by_N_ratio = 0', uniform parameter sampling (adaptive basis generation)

  newton([0,5], true, 0, 2, 1, 'small', false, 4) 

  • did not stop although 'stop_Nmax = 50' and 'stop_Mmax = 200' were reached. Re-run on lockheed with 'stop_Nmax = 120', 'stop_Mmax = 400'.
  • Final result: Reached stop_epsilon barrier of '1e-5' with 'N=89', 'M=187'.
  • Five parameter sample adaptations, finest level with '1905' elements.
  • offline time: 8.4 h, four parallel computations
• 'c021n': combined basis generation, normal size, new algorithm for 'M_by_N_ratio = 0', uniform parameter sampling (adaptive basis generation)

  newton([0,5], true, 0, 2, 1, 'normal', false, 4) 

  • did not stop although 'stop_Nmax = 50' and 'stop_Mmax = 200' were reached. Re-run on jax with 'stop_Nmax = 120', 'stop_Mmax = 400'. still running..., error explodes at 'N=73'?, okay the basis is discarded then, maybe it still works...
  • Idea: Re-run with 'stop_epsilon = 1e-4' and/or lower 'ei_minimum_residual'

Nonlin-symmetry equation

• 's01ui': separate bases, implicit (Newton) discretization, started with

  nonlin_symmetry([0,5], false, 0, 1, false, false, 4); 

  • stopped at 'stop_Nmax = 135'. Re-run on scorpion with 'stop_Nmax = 250'.
  • Final results: epsilon limit 1e-5 reached with 'N=167', 'M=262',
  • Lebesgue constant: '67.1493' of '7.4107e+78' maximum possible value.
  • offline time: 2 h, four parallel processes
  • No parameter adaptation!
• 'c02ui': combined basis generation, implicit (Newton) discretization, started with

  nonlin_symmetry([0,5], true, 0, 2, false, false, 4); 

  • stopped at 'stop_Nmax = 135', 'stop_Mmax = 300', Re-run with 'stop_Nmax = 250', 'stop_Mmax = 400' on bigdaddy. Looks good...
• 'c31ui': combined basis generation, implicit (Newton) discretization, fixed 'M_by_N_ratio = 3',
• 'c02ue': combined basis generation, explicit discretization,