[petsc-users] multiply a mpibaij matrix by its block diagonal inverse

[Matthew Knepley]

On Wed, Feb 14, 2018 at 9:29 AM, Xiangdong <epscodes at gmail.com> wrote:

> The reason for the operation invdiag(A)*A is to have a decoupled
> matrix/physics for preconditioning. For example, after the transformation,
> the diagonal block is identity matrix ( e.g. [1,0,0;0,1,0;0,0,1]  for
> bs=3). One can extract a submatrix (e.g. corresponding to only first
> unknown) and apply special preconditioners for the extracted/decoupled
> matrix. The motivation is that after the transformation, one can get a
> better decoupled matrix to preserve the properties of the unknowns.
>

Barry's point is that this operation is usually rolled into the
preconditioner itself, as in his example of PBJACOBI. Are you building this
preconditioner yourself?

   Matt


> Thanks.
>
> Xiangdong
>
> On Tue, Feb 13, 2018 at 6:27 PM, Smith, Barry F. <bsmith at mcs.anl.gov>
> wrote:
>
>>
>>  In general you probably don't want to do this. Most good preconditioners
>> (like AMG) rely on the matrix having the "natural" scaling that arises from
>> the discretization and doing a scaling like you describe destroys that
>> natural scaling. You can use PCPBJACOBI to use point block Jacobi
>> preconditioner on the matrix without needing to do the scaling up front.
>> The ILU preconditioners for BAIJ matrices work directly with the block
>> structure so again pre-scaling the matrix buys you nothing. PETSc doesn't
>> have any particularly efficient routines for computing what you desire, the
>> only way to get something truly efficient is to write the code directly
>> using the BAIJ data structure, doable but probably not worth it.
>>
>>   Barry
>>
>>
>> > On Feb 13, 2018, at 5:21 PM, Xiangdong <epscodes at gmail.com> wrote:
>> >
>> > Hello everyone,
>> >
>> > I have a block sparse matrices A created from the DMDA3d. Before
>> passing the matrix to ksp solver, I want to apply a transformation to this
>> matrix: namely A:= invdiag(A)*A. Here invdiag(A) is the inverse of the
>> block diagonal of A. What is the best way to get the transformed matrix?
>> >
>> > At this moment, I created a new mat IDA=inv(diag(A)) by looping through
>> each row and call MatMatMult to get B=invdiag(A)*A, then destroy the
>> temporary matrix B. However, I prefer the in-place transformation if
>> possible, namely, without the additional matrix B for memory saving purpose.
>> >
>> > Do you have any suggestion on compute invdiag(A)*A for mpibaij matrix?
>> >
>> > Thanks for your help.
>> >
>> > Best,
>> > Xiangdong
>> >
>> >
>> >
>> >
>>
>>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
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https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
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