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

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

On Sun, Jan 28, 2018 at 11:24 PM, <cau...@gm...> wrote:

> OK, now that the choice of solver does not pose a problem, I consider
> using SCM to calculate the lower bound of the coercivity constant (αLB)
> instead of setting it 1 since αLB may vary a lot with the parameters and
> the selection of basis will be affected if we simply set αLB equal to 1.
>
>
>
> Hence, I refer to reduced_basis_ex2 where the SCM is implemented.
> However, I meet the error below when running the example.
>
>
>
> “Assembling affine operator 1 of 3
> Assembling affine operator 2 of 3
> Assembling affine operator 3 of 3
> Assembling affine vector 1 of 1
> Assembling output vector, (1,1) of (4,1)
> Assembling output vector, (2,1) of (4,1)
> Assembling output vector, (3,1) of (4,1)
> Assembling output vector, (4,1) of (4,1)
>
> B_min(0) = 1.20285e-33
> Eigen solver for computing B_max did not converge”
>
>
>
> Where does the problem come from and how to address it? I would appreciate
> your suggestion.
>


Are you using "-eps_type lapack"? If not, I would try that.

David








*发件人**:* David Knezevic [mailto:dav...@ak...]
*发送时间:* 2018年1月29日 10:45
*收件人:* Gauvain Wu <cau...@gm...>; libmesh-users <
lib...@li...>
*主题:* Re: 答复: [Libmesh-users] Not decreasing error bound



(Note: Please reply-all so that the answers are recorded on the
libMesh-users list for future reference.)





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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