dmd/euler example

[bumpwy]

Finished the examples/dg_euler.py example.

The example was run with default inputs: python dg_euler.py on 4 cores, corresponding to the following options:
<<<
Options used:
--mesh periodic-square.mesh
--problem 1
--refine_serial 0
--refine_parallel 1
--order 3
--ode_solver 4
--t_final 2.0
--time_step -0.01
--cfl_number 0.3
--visualization False
--visit_datafiles False
--visualization_steps 50
--energy_fraction 0.9999
--rdim -1
--crbf 0.9

Comparison with libROM example shows identical output error numbers. Although, pylibROM appears to be somewhat slower.

pylibROM output
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Relative error of DMD dens at t_final: 2.0 is 0.0003180880
Relative error of DMD x_mom at t_final: 2.0 is 0.0002069844
Relative error of DMD y_mom at t_final: 2.0 is 0.0012537761
Relative error of DMD e at t_final: 2.0 is 0.0001376798
Elapsed time for solving FOM: 4.072901e+01
Elapsed time for training DMD: 9.936306e-01
Elapsed time for predicting DMD: 1.587152e-03

libROM output
<<<
Relative error of DMD density (dens) at t_final: 2 is 0.000318088
Relative error of DMD x-momentum (x_mom) at t_final: 2 is 0.00020698435
Relative error of DMD y-momentum (y_mom) at t_final: 2 is 0.0012537761
Relative error of DMD energy (e) at t_final: 2 is 0.0001376798
Elapsed time for solving FOM: 2.597199e-01 second
Elapsed time for training DMD: 8.866020e-01 second
Elapsed time for predicting DMD: 8.613530e-04 second

[bumpwy]

Hi @dreamer2368 I've addressed your comments