[petsc-users] fieldsplit-preconditioner for block-system of linear equations

[Matthew Knepley]

On Thu, Oct 1, 2015 at 3:32 AM, Eike Mueller <E.Mueller at bath.ac.uk> wrote:

> Hi Matt,
>
>
> thanks a lot for your answer. Assembling the matrices into one large
> matrix should be ok, since I have control over that.
>
>
> But am I right in assuming that the vectors have to be stored as one large
> PETSc vector? So when X = (x^(1),x^(2),...,x^(k)), where x^(i) are the
> individual vectors of length n_i, then I have to store X as one PETSc
> vector of length n_1+n_2+...+n_k? In the data structure I use, storage for
> the vectors is already allocated, so currently I use
>
> VecCreateSeqWithArray() to construct k separate PETSc vectors. Sounds like
> I can't do that, but have to create one big PETSc vector, and copy the data
> into that? That's ok, if it's the only option, since the overhead should
> not be too large, but I wanted to check before doing something unnecessary.
>
 You should be able to use
http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecGetSubVector.html

  Thanks,

     Matt

> Thanks,
>
>
> Eike
>
>
> ------------------------------
> *From:* Matthew Knepley <knepley at gmail.com>
> *Sent:* 30 September 2015 15:27
> *To:* Eike Mueller
> *Cc:* petsc-users at mcs.anl.gov
> *Subject:* Re: [petsc-users] fieldsplit-preconditioner for block-system
> of linear equations
>
> On Wed, Sep 30, 2015 at 3:00 AM, Eike Mueller <E.Mueller at bath.ac.uk>
> wrote:
>
>> Dear PETSc,
>>
>> I am solving a linear system of equations
>>
>> (1) A.X = B
>>
>> where the vector X is divided into chunks, such that X= (x_1,x_2,…,x_k)
>> and each of the vectors x_i has length n_i (same for the vector
>> B=(b_1,b_2,…,b_k)). k=5 in my case, and n_i >> 1. This partitioning implies
>> that the matrix has a block-structure, where the submatrices A_{ij} are of
>> size n_i x n_j. So explicitly for k=3:
>>
>>         A_{1,1}.x_1 + A_{1,2}.x_2 + A_{1,3}.x_3 = b_1
>> (2)    A_{2,1}.x_1 + A_{2,2}.x_2 + A_{2,3}.x_3 = b_2
>>         A_{3,1}.x_1 + A_{3,2}.x_2 + A_{3,3}.x_3 = b_3
>>
>> I now want to solve this system with a Krylov-method (say, GMRES) and
>> precondition it with a field-split preconditioner, such that the
>> Schur-complement is formed in the 1-block. I know how to do this if I have
>> assembled the big matrix A, and I store all x_i in one big vector X (I
>> construct the index-sets corresponding to the vectors x_1 and (x_2,x_3),
>> and then call PCFieldSplitSetIS()). This all works without any problems.
>>
>> However, I now want to do this for an existing code which
>>
>> 1. Assembles the matrices A_{ij} separately (i.e. they are not stored as
>> part of a big matrix A, but are stored in independent memory locations)
>> 2. Stores the vectors x_i separately, i.e. they are not stored as parts
>> of one big chunk of memory of size n_1+…+n_k
>>
>> I can of course implement the matrix application via a matrix shell, but
>> is there still an easy way of using the fieldsplit preconditioner?
>>
>
> From your description, it sounds like you could use
>
>
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatGetLocalSubMatrix.html
>
> to assemble your separate matrices directly into a large matrix.
> Furthermore, if it really benefits you
> to have separate memory, you can change the matrix type from MATIJ to
> MATNEST dynamically,
> but none of your code would change. This would let you check things with
> LU, but still optimize when
> necessary.
>
>   Thanks,
>
>       Matt
>
>
>> The naive way I can think of is to allocate a new big matrix A, and copy
>> the A_{ij} into the corresponding blocks. Then allocate big vectors x and
>> b, and also copy in/out the data before and after the solve. This, however,
>> seems to be wasteful, so before I go down this route I wanted to double
>> check if there is a way around it, since this seems to be a very common
>> problem?
>>
>> Thanks a lot,
>>
>> Eike
>>
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>



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