[petsc-users] Implementation of Power Iteration method in PETSc

[Yingjie Wu]

Thank you, Fande.

I've seen you in moose usergroup before.


I've just learned about SLEPC, and I wonder if I want to do neutron
eigenvalue calculations and use finite difference to discrete grids, would
it be difficult to implement it in SLEPC? Is there such an example(finite
difference + linear eigenvalue)?Because I don't know much about finite
element.Or am I still using a loop of KSP in PETSc?I'm a newcomer to petsc,
please give me some advice


Thanks,

Yingjie


Fande Kong <fdkong.jd at gmail.com> 于2018年9月27日周四 上午12:25写道：

> I have implemented this algorithm in SLEPC. Take a look at this example
> http://slepc.upv.es/documentation/current/src/eps/examples/tutorials/ex34.c.html
>
> The motivation of the algorithm is also for neutron calculations (a
> moose-based application).
>
> Fande,
>
> On Wed, Sep 26, 2018 at 10:02 AM Yingjie Wu <yjwu16 at gmail.com> wrote:
>
>> Dear Petsc developer:
>> Hi,
>>
>> Thank you very much for your previous reply,  they really helped me a
>> lot.
>>
>> I've been doing neutron calculations recently, and I want to use the
>> power Iteration method to calculate the neutron flux, essentially to solve
>> linear equations, but after each solution is done, a scalar *K* is
>> updated to form a new right end term *b*, and the next linear equation
>> system is solved until the convergence criterion is satisfied. The flow of
>> the source iteration algorithm is as follows:
>>
>>
>> 1: *Φ*(0) = arbitrary nonzero vector 2: K(0) = arbitrary nonzero
>> constant 3: *for* n = 1; 2; 3; ::: do 4: *b *= 1 / K(n-1) *F * Φ(n-1)
>> 5: *Φ*(n) * M   = *b* 6: K(n) = k(n-1)* (F * *Φ*(n)  ,F *Φ*(n)  ) / (F
>> *Φ*(n-1)  ,F  *Φ*(n-1)  )
>>
>> 7: check convergence of eigenvalue and eigenvector 8: *end for*
>>
>>
>> (F , M are the coefficient matrix.)
>>
>>
>> The difficulty is that I need to set up an extra loop to regulate KSP.
>> Does PETSc have such an example? How do I implement this algorithm in
>> PETsc? Please tell me the key functions if possible.
>>
>>
>> Thanks,
>>
>> Yingjie
>>
>>
>>
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