[petsc-users] DMDA with dof=4, multigrid solver

Barry Smith bsmith at mcs.anl.gov
Sat Mar 7 14:17:00 CST 2015 

> On Mar 7, 2015, at 1:17 PM, Sun, Hui <hus003 at ucsd.edu> wrote:
> 
> Here is one more problem along this line. The matrix A created in this way may not have a natural global numbering. Let's say, if we are on grid point (i,j,k), the element in A with row (i,j,k) and column 1 is not necessarily at row position (i+(j+k*my)*mx globally. I mean, how do I set the correspondence between the MatStencils and int for the index? Should I use something like ISLocalToGlobalMapping? 

  You can.

   Look at the routines in PETSc that form the matrices like DMCreateMatrix_DA_3d_MPIAIJ() and modify it for the matrix you need.

   BTW: what is the matrix you a creating for. PETSc also creates matrices that interpolate between levels of DMDA like DMCreateInterpolation_DA_3D_Q1() it's structure might be useful for you.

  Barry


> 
> Best,
> Hui
> 
> 
> ________________________________________
> From: Barry Smith [bsmith at mcs.anl.gov]
> Sent: Wednesday, March 04, 2015 10:53 AM
> To: Sun, Hui
> Cc: petsc-users at mcs.anl.gov
> Subject: Re: [petsc-users] DMDA with dof=4, multigrid solver
> 
>> On Mar 4, 2015, at 8:53 AM, Sun, Hui <hus003 at ucsd.edu> wrote:
>> 
>> I thought DMDAcreateMatrix would already specify the size of the matrix to be N by N, where N is the number of unknowns in the grid. And each processor takes care of a submatrix of size N_i by N_i.
> 
>  Not really. Each process "owns" certain entire rows of the matrix. Different processors cannot contain parts of the same rows.
>> 
>> However, I wish to form a matrix of size M by N, where N is the number of unknowns in the grid, and  1<<M<<N. Furthermore, I wish to divide the M by N matrix A into the processors, in such a way, that each processor has a submatrix of size M by N_i.
> 
>   PETSc doesn't provide a matrix format where sets of columns are on different processes. It only provides formats where certain rows are on each process. Depending on what you want to do with your matrix; for example if you only need to do Matrix-Vector products with your matrix, you could store by row the transpose of the matrix you want and use MatMultTranspose() to do the multiply.
> 
>   To create such a "transposed matrix" you can call DMGetGlobalVector(), VecGetOwnershipRange(v,&start,&end); then call MatCreateMPIAIJ(comm, end-start,PETSC_DECIDE,PETSC_DETERMINE,M,0,NULL,0,NULL,&A);  With this matrix you can then call MatMultTranspose(A,v,w);
> 
>   Barry
> 
> 
>>> DMDAGetLocalInfo
> 
> 
> 
>> 
>> Hui
>> 
>> 
>> ________________________________________
>> From: Barry Smith [bsmith at mcs.anl.gov]
>> Sent: Wednesday, March 04, 2015 5:27 AM
>> To: Sun, Hui
>> Cc: petsc-users at mcs.anl.gov
>> Subject: Re: [petsc-users] DMDA with dof=4, multigrid solver
>> 
>> If at all possible you should use DMCreateMatrix() it manages everything for you. Why can't you use it?
>> 
>> Barry
>> 
>> 
>> 
>>> On Mar 4, 2015, at 1:20 AM, Sun, Hui <hus003 at ucsd.edu> wrote:
>>> 
>>> Thank you Barry for giving me some hint of using DMDAGetLocalInfo() to determine the local size. However, I'm still confused about the process of creating such a matrix, which is composed of serial rows of DMDA parallel vectors.
>>> 
>>> Should I somehow use the following functions?
>>> MatCreate
>>> DMDAGetLocalInfo
>>> ISLocalToGlobalMappingCreate
>>> MatSetLocalToGlobalMapping
>>> MatGetLocalSubMatrix
>>> 
>>> However, I still need some more help on putting everything together to create such a matrix. I'd really appreciate your time.
>>> 
>>> Best,
>>> Hui
>>> 
>>> ________________________________________
>>> From: Barry Smith [bsmith at mcs.anl.gov]
>>> Sent: Sunday, March 01, 2015 9:24 AM
>>> To: Sun, Hui
>>> Cc: petsc-users at mcs.anl.gov
>>> Subject: Re: [petsc-users] DMDA with dof=4, multigrid solver
>>> 
>>>> On Mar 1, 2015, at 12:30 AM, Sun, Hui <hus003 at ucsd.edu> wrote:
>>>> 
>>>> Thank you Barry. I have yet two more questions:
>>>> 
>>>> 1) If I have a DMDA and I use KSPSetComputeOperators and KSPSetComputeRHS to set up matrices and rhs, and I use geometric mg, what if I want to change my rhs many times? Should I write many KSPSetComputeRHS, and register them with ksp? Or is there a simple way to just register the rhs with ksp as a vector?
>>>> 
>>>> 2) How do I create a Mat, whose cols follow the DMDA parallelization, and whose rows are serial?
>>> 
>>> Normally one uses DMCreateMatrix() to get the matrices; it has the correct parallel layout and the correct nonzero pattern.   If you create the matrices yourself you need to first call DMDAGetLocalInfo() and from that information determine how many local rows you have.
>>> 
>>>> 
>>>> By the way, I've figured out and fixed the bugs in my code concerning using mg with DMDA having 4 dof. It has to do with the interpolations. Now I can see mg works well with 4 dof DMDA.
>>>> 
>>>> Best,
>>>> Hui
>>>> 
>>>> ________________________________________
>>>> From: Barry Smith [bsmith at mcs.anl.gov]
>>>> Sent: Saturday, February 28, 2015 9:35 AM
>>>> To: Sun, Hui
>>>> Cc: petsc-users at mcs.anl.gov
>>>> Subject: Re: [petsc-users] DMDA with dof=4, multigrid solver
>>>> 
>>>>> On Feb 27, 2015, at 7:25 PM, Sun, Hui <hus003 at ucsd.edu> wrote:
>>>>> 
>>>>> Thank you Barry. Another question: I observe that in those ksp examples, whenever multigrid is used, DMDA is also used, besides, KSPSetComputeOperators and KSPSetComputeRHS are also used.
>>>>> 
>>>>> Is it true that
>>>>> 1) Only DMDA can use mg?
>>>> 
>>>> No this is not true
>>>> 
>>>>> 2) We have to set up matrices and rhs using KSPSetComputeOperators  and KSPSetComputeRHS?
>>>> 
>>>> No you do not have to
>>>> 
>>>>> We cannot create a matrix and add it to KSP if we want to use mg?
>>>> 
>>>> Yes you can.
>>>> 
>>>> There are many many variants of multigrid one can do with PETSc; we don't have the time to have examples of all the possibilities.
>>>> 
>>>> More details
>>>> 
>>>>> 1) Only DMDA can use mg?
>>>> 
>>>> Because DMDA provides structured grids with easy interpolation between levels and it is easy for users to write Jacobians we have many examples that use the DMDA. However, so long as YOU (or something) can provide interpolation between the multigrid levels you can use multigrid. For example PCGAMG uses algebraic multigrid to generate the interpolations. If you have your own interpolations you can provide them with PCMGSetInterpolation() (when you use PCMG with DMDA PETSc essentially handles those details automatically for you).
>>>> 
>>>>> 2) We have to set up matrices and rhs using KSPSetComputeOperators  and KSPSetComputeRHS?
>>>> 
>>>> Normally with geometric multigrid one discretizes the operator on each level of the grid. Thus the user has to provide several matrices (one for each level). KSPSetComputeOperators() is ONE way that the user can provide them. You can also provide them by call PCMGetSmoother(pc,level,&ksp) and then call KSPSetOperators(ksp,...) for each of the levels (KSPSetComputeOperators() essentially does the book keeping for you).
>>>> 
>>>>> We cannot create a matrix and add it to KSP if we want to use mg?
>>>> 
>>>> As I said in 2 normally multigrid requires you to provide a discretized operator at each level. But with Galerkin coarse grids (which is what algebraic multigrid users and can also be used by geometric multigrid) the user does not provide coarser grid operators instead the code computes them automatically from the formula R*A*P where R is the restriction operator used in multigrid and P is the interpolation operator (usually the transpose of P).
>>>> 
>>>> If you are looking for a simple automatic multigrid then you want to use PCGAMG in PETSc, it does algebraic multigrid and doesn't require you provide interpolations or coarser operators. However algebraic multigrid doesn't work for all problems; though it does work for many. Try it with -pc_type gamg
>>>> 
>>>> Barry
>>>> 
>>>>> 
>>>>> Best,
>>>>> Hui
>>>>> 
>>>>> ________________________________________
>>>>> From: Barry Smith [bsmith at mcs.anl.gov]
>>>>> Sent: Friday, February 27, 2015 5:11 PM
>>>>> To: Sun, Hui
>>>>> Cc: petsc-users at mcs.anl.gov
>>>>> Subject: Re: [petsc-users] DMDA with dof=4, multigrid solver
>>>>> 
>>>>>> On Feb 27, 2015, at 6:36 PM, Sun, Hui <hus003 at ucsd.edu> wrote:
>>>>>> 
>>>>>> I'm trying to work on 4 Poisson's equations defined on a DMDA grid, Hence the parameter dof in DMDACreate3d should be 4, and I've set stencil width to be 4, and stencil type to be star.
>>>>> 
>>>>> Use a stencil width of 1, not 4. The stencil width is defined in terms of dof.
>>>>>> 
>>>>>> If I run the code with -pc_type ilu and -ksp_type gmres, it works alright.
>>>>>> 
>>>>>> However, if I run with pc_type mg, it gives me an error saying that when it is doing MatSetValues, the argument is out of range, and there is a new nonzero at (60,64) in the matrix. However, that new nonzero is expected to be there, the row number 60 corresponds to i=15 and c=0 in x direction, and the column number 64 corresponds to i=16 and c=0 in x direction. So they are next to each other, and the star stencil with width 1 should include that. I have also checked with the memory allocations, and I'm found no problem.
>>>>>> 
>>>>>> So I'm wondering if there is any problem of using multigrid on a DMDA with dof greater than 1?
>>>>> 
>>>>> No it handles dof > 1 fine.
>>>>> 
>>>>> Send your code.
>>>>> 
>>>>> Barry
>>>>> 
>>>>>> 
>>>>>> Thank you!

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