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

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

On Sun, Jan 28, 2018 at 9:57 PM, <cau...@gm...> wrote:

> Sorry for habitually clicking “reply” instead of “reply all” and I resend
> it now.
>
>
>
> 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.
> Should I precise the asymmetric solver in my command? How to write it
> correctly? Thanks for your help.
>

No, what you did is fine since LU is appropriate for non-symmetric
problems. (See my previous email for a bit more detail.)

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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