Prom linear elasticity

[bumpwy]

Running the example

1. first two offline phases for nu=0.2 & 0.4

python linear_elasticity_global_rom.py -offline -id 0 -nu 0.2
python linear_elasticity_global_rom.py -offline -id 1 -nu 0.4

2. the merge phase:

python linear_elasticity_global_rom.py -merge -ns 2

3. final offline phase FOM for nu=0.3

python linear_elasticity_global_rom.py -offline -id 2 -nu 0.3
results:

PCG Iterations = 17
Final PCG Relative Residual Norm = 4.35538e-09
Creating file: basis2_snapshot.000000
Elapsed time for assembling FOM: 0.002839803695678711 second
Elapsed time for solving FOM: 0.005137205123901367 second

4. online phase ROM for nu=0.3

python linear_elasticity_global_rom.py -online -id 3 -nu 0.3
results:

Size of linear system: 1170
Opening file: basis.000000
On rank 0, spatial basis dimension is 1170 x 2
Relative error of ROM for E=2.5 and nu=0.3 is 0.0005710430923335614
Elapsed time for assembling ROM: 0.02164936065673828 second
Elapsed time for solving ROM: 1.1920928955078125e-05 second

[dreamer2368]

Running on quartz on my end showed the consistent result as shown in PR.

[siuwuncheung]

Thanks @bumpwy! Look good to me overall.

[bumpwy]

Hi @siuwuncheung thanks for the review I have edited the code accordingly.