# [petsc-dev] About the problem of Lagrange multiplier

Matthew Knepley knepley at gmail.com
Fri Apr 8 08:01:27 CDT 2022

On Fri, Apr 8, 2022 at 1:34 AM 高亚贺 <gaoyahe at buaa.edu.cn> wrote:

> Dear Mr./Ms.，
>
>
> In fact, I want to solve a discretized equation like this
>
> where *K, U=*[*u*1 *u*2 *…**un*]T and *F *are fields sit on the vertices,
> and can easily be created by ‘DMCreateMatrix’ or ‘DMCreateGlobalVector’.
> *λ* is the Lagrange multiplier vector.
>

How is lambda discretized?

Thanks,

Matt

> The augmented *Q *(non-square) is the constraint coefficient matrix and
> has the form as
>
>
> The *Q* is employed here to satisfy the following constraints
>
>
> So how to build the entire system in-place in one big matrix* (K*λ)?
> Could you give me more specific suggestions on this problem?
>
>
> Thank you very much!
>
>
> Best regards,
>
> Yahe
>
>
>
> -----原始邮件-----
> *发件人:*"Barry Smith" <bsmith at petsc.dev>
> *发送时间:*2022-04-07 23:10:20 (星期四)
> *收件人:* "Matthew Knepley" <knepley at gmail.com>
> *抄送:* "高亚贺" <gaoyahe at buaa.edu.cn>, PETSc <petsc-users at mcs.anl.gov>
> *主题:* Re: [petsc-users] question
>
>
>   DMStag may also be useful for your needs (and far simpler to use than
> DMPLEX) depending on where your Lagrange multipliers live. Note that
> regardless you should not need to be copying entire large submatrices
> around into bigger matrices; you can build the entire system in-place in
> one big matrix. MatNest is also a possibility depending on exactly what you
> are doing.
>
>   If you explain what your Lagrange multipliers are (the constraints) we
> may be able to make more specific suggestions.
>
> Barry
>
>
>
>
> On Apr 7, 2022, at 8:26 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Thu, Apr 7, 2022 at 8:16 AM 高亚贺 via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>>
>> Dear Mr./Ms.，
>>
>>
>> I have used ‘DMCreateMatrix’ to create a matrix *K*, and also the
>> ‘DMCreateGlobalVector’ to create two vectors *U* (to be solved) and *F *(right-hand
>> side), i.e. *KU*=*F*. Now, I want to add some complex constraints to
>> this system through lagrangian multiplier method, and the constraint matrix
>> is *Q*. The *KU*=*F *transforms to
>>
>> <1649328463919.png>
>>
>>    How to create *K**λ*, and how to effectively copy values* K* and *Q*
>> to *K**λ*? Does the newly created *K**λ* and *F**λ *still have an
>> advantage of DMDA? Or do you have any other good suggestions for this kind
>> of problem?
>>
>
> DMDA can only really handle collocated discretizations, meaning all fields
> sit on the vertices. If you can discretize your problem this way, then just
> give it two fields and assemble K_\lambda as normal. If not, then you might
> look at DMPlex which supports a wider range of discretizations.
>
>   Thanks,
>
>      Matt
>
>
>> Thank you very much!
>>
>>
>> Best regards,
>>
>> A PETSc user
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
>
>

--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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