Nonlinear elasticity projection rom example

[dreamer2368]

Example commands with 3d mesh (as in librom.net)

python3 nonlinear_elasticity_global_rom.py --mesh ../data/beam-hex-nurbs.mesh -offline -dt 0.01 -tf 5.0 -s 14 -vs 10 -sc 3.90 -id 0
python3 nonlinear_elasticity_global_rom.py --mesh ../data/beam-hex-nurbs.mesh -offline -dt 0.01 -tf 5.0 -s 14 -vs 10 -sc 4.10 -id 1
python3 nonlinear_elasticity_global_rom.py --mesh ../data/beam-hex-nurbs.mesh -merge -ns 2 -dt 0.01 -tf 5.0
python3 nonlinear_elasticity_global_rom.py --mesh ../data/beam-hex-nurbs.mesh -offline -dt 0.01 -tf 5.0 -s 14 -vs 5 -sc 3.92 -id 2
python3 nonlinear_elasticity_global_rom.py --mesh ../data/beam-hex-nurbs.mesh -online -dt 0.01 -tf 5.0 -s 14 -vs 5 -hyp -rvdim 40 -rxdim 10 -hdim 71 -nsr 200 -sc 3.92

FOM result

tep 500, t = 5.000000, EE = 1.41649e-03, KE = 4.71724e-04, ΔTE = -2.91350e-03
Elapsed time for time integration loop 1.86668e+02
Elapsed time for entire simulation 2.10924e+02

ROM result

Elapsed time for time integration loop 3.47888e+01
Relative error of ROM position (x) at t_final: 5.000000 is 5.08981700e-03
Relative error of ROM velocity (v) at t_final: 5.000000 is 9.11743695e+00
Elapsed time for entire simulation 6.63521e+01

[dreamer2368]

@chldkdtn @siuwuncheung @bumpwy @pravija12345 , this PR is now ready for review.

[bumpwy]

everything runs fine now with the docker (albeit slow). Although, the relative error for the ROM predicted velocity seems a bit high. Is that of concern?

[dreamer2368]

everything runs fine now with the docker (albeit slow). Although, the relative error for the ROM predicted velocity seems a bit high. Is that of concern?

I also noticed that. Although, this is consistent with the c++ libROM result, so it should be rather considered as the performance of the method itself.

[siuwuncheung]

I think this is general enough to be used in other examples, so it may be a good idea to move it to the library.