Re: [Libmesh-users] Unusual results of transient RB with 7 parameters

[吴家桦Gauvain <cau...@gm...>]

Thanks for replying.

I did omit the inertia terms in my PDE. Regarding the greedy convergence of
7 parameter transient case, the maximum error bound decreases as usual,
from about 40000 to 0.00197 but the result is abnormal like what is
described in my first mail. In fact, 3 parameter (thermal conditions)
transient case works well and so does 7 parameter steady case. The problem
arises when I attempt to combine them together by replacing the assembly
function of the stiffness matrix in 3 parameter transient case with that of
7 parameter steady case.

Regards,
Gauvain

2018-02-27 21:21 GMT+08:00 David Knezevic <dav...@ak...>:

> On Tue, Feb 27, 2018 at 4:03 AM, 吴家桦Gauvain <cau...@gm...>
> wrote:
>
>> Hi all,
>>
>> I am trying to make a transient thermoelastic RB model. Both Internal heat
>> flux and external heat exchange described by Newton's law of cooling(Robin
>> boundary condition) are considered. It works well when the three thermal
>> conditions (heat flux, heat transfer coefficient and ambient temperature)
>> are chosen as parameters. However, abnormal results are observed when the
>> material properties (Young's modulus, Poisson's ratio, thermal expansion
>> coefficient and heat conductivity) are added as parameters: Three
>> displacement components remain 0 and the temperature increases drastically
>> as the time goes by. What's more, I notice that the difference between the
>> first and the second POD eigenvalues is extremely large:
>>
>> POD Eigenvalues:
>> eigenvalue 0 = 4.4536e+08
>> eigenvalue 1 = 2.45303e-07
>> ...
>> last eigenvalue = -1.90536e-07
>>
>> The matrix assembly should not pose problem because it runs well in steady
>> case and I simply copy the assembly functions without any modification.
>> Thus I am really confused and I cannot figure out where the problem is.
>> Could you give me some suggestions? Thanks a lot.
>>
>
> Good to hear that it works well in the steady case.
>
> Regarding the transient case, I have a few comments:
>
> - The default implementation for transient RB that is used in the examples
> is intended for parabolic PDEs, like the heat equation. I guess your PDE is
> parabolic since you omit the hyperbolic parts (i.e. the inertia terms) from
> the elasticity part of the system?
>
> - 7 parameters is quite a lot of parameters, so you may just be having
> trouble with greedy convergence?
>
> My main suggestion would be to try to get a simple transient problem
> working first, then add more complexity to it until you reach the problem
> that you're interested in, e.g. you could start with the heat equation and
> then add elasticity terms.
>
> Regards,
> David
>
>
>


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