[Libmesh-users] Not decreasing error bound

[<cau...@gm...>]

Hi all,

 

I made a thermoelasticity model based on the cantilever example,
reduced_basis_ex5, by adding a new temperature variable. At the beginning of
the basis training procedure, the maximum error bound drops sharply from
1.35694e+07 to 41 as the dimension of the basis increases from 0 to 5. After
that, although the basis dimension keeps growing, the error bound stops
decreasing and stays at a certain number. The relative training tolerance is
set at 1.e-7 and the mesh is a T-shaped pipe. 

 

---- Basis dimension: 5 ----

Performing RB solves on training set

Maximum error bound is 2.42578

 

Performing truth solve at parameter:

h: 1.055972e+01

h_Tinf: 2.472563e+02

heat_flux: 4.261782e+01

 

---- Basis dimension: 6 ----

Performing RB solves on training set

Maximum error bound is 2.43818

 

Performing truth solve at parameter:

h: 1.151397e+01

h_Tinf: 2.473108e+02

heat_flux: 4.481571e+01

 

---- Basis dimension: 7 ----

Performing RB solves on training set

Maximum error bound is 2.44673

 

Exiting greedy because the same parameters were selected twice

 

The RB result obtained from this basis differs a lot from the FEM result. I
searched archives of the mailing list and found that this phenomenon might
result from an overly low training tolerance. However, the initial error
bound being nearly e+07, if I select a less strict tolerance, I will end up
having an unsatisfying error and probably a worse result. Could you please
suggest me some advice? I would be grateful for your response. 

 

Best regards,

Gauvain