Re: [Libmesh-users] 答复: Not decreasing error bound

[David K. <dav...@ak...>]

(Note: Please reply-all so that the answers are recorded on the
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On Sun, Jan 28, 2018 at 9:33 PM, <cau...@gm...> wrote:

> Hi David,
>
>
>
> I solve the system with the command below:
>
>
>
> -ksp_type preonly -pc_type lu -pc_factor_mat_solver_package mumps
>
>
>
> It means that the system is solved by KSP with LU as preconditioning.
>

OK, that's good. I guess before you were using an iterative solver which
just wasn't converging fully. Using LU is a good approach here. I would
recommend MUMPS with LU for the reduced basis training unless your problem
is too large, in which case you have to switch to an iterative solver.



> Should I precise the asymmetric solver in my command? How to write it
> correctly? Thanks for your help.
>

No, what you have done is fine, since you asked for LU which is appropriate
for non-symmetric matrices. (In other problems if your system is symmetric
you can use MUMPS's cholesky solver instead, via "-pc_type cholesky".)

David



*发件人**:* David Knezevic [mailto:dav...@ak...]
*发送时间:* 2018年1月29日 10:05
*收件人:* Gauvain Wu <cau...@gm...>
*抄送:* libmesh-users <lib...@li...>
*主题:* Re: [Libmesh-users] Not decreasing error bound



Hello,



The convergence behavior that you describe is typical of reduced basis
convergence: It will plateau after an error reduction of about six orders
of magnitude or so. So it sounds like the convergence is working fine in
the sense that you got a reduction from 1.3569e7 to 41. When you get the
message "Exiting greedy because the same parameters were selected twice"
that is another indication that the greedy algorithm has plateaued.



I do not know why the RB solution and FE solution did not match well at the
end, though --- that of course indicates that something is wrong. One
thought; Did you make sure to use an asymmetric solver, since
thermoelasticity is not symmetric?



David





On Sat, Jan 27, 2018 at 4:13 AM, <cau...@gm...> wrote:

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

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