Hi Hong,
That sounds like a more reasonable approach, I had no idea the
PETSc/MUMPS interface could provide such a level of control on the solve
process. Therefore, after assembling the matrix A_0, I should do
something along the lines of:
MatGetFactor(A_0, MATSOLVERMUMPS, MAT_FACTOR_LU, F)
MatLUFactorSymbolic(F, A_0, NULL, NULL, info)
MatLUFactorNumeric(F, A_0, info)
and then call MatSolve? However I don't understand, I thought F would
remain the same during the whole process but it's an input parameter of
MatSolve so I'd need one F_m for each A_m? Which is not what you
mentioned (do one symbolic factorization only)
On a side note, after preallocating and assembling the first matrix,
should I create/assemble all the others with
MatDuplicate(A_0, MAT_DO_NOT_COPY_VALUES, A_m)
Calls to MatSetValues( ... )
MatAssemblyBegin(A_m, MAT_FINAL_ASSEMBLY)
MatAssemblyEnd(A_m, MAT_FINAL_ASSEMBLY)
Is that the recommended/most scalable way of duplicating a matrix + its
non-zero structure?
Thank you for your support and suggestions,
Thibaut
On 23/07/2019 18:38, Zhang, Hong wrote:
Thibaut:
Thanks for taking the time. I would typically run that on a small
cluster node of 16 or 32 physical cores with 2 or 4 sockets. I use
16 or
32 MPI ranks and bind them to cores.
The matrices would ALL have the same size and the same nonzero
structure
- it's just a few numerical values that would differ.
You may do one symbolic factorization of A_m, use it in the m-i loop:
- numeric factorization of A_m
- solve A_m x_m,i = b_m,i
in mumps, numeric factorization and solve are scalable. Repeated
numeric factorization of A_m are likely faster than reading data files
from the disc.
Hong
This is a good point you've raised as I don't think MUMPS is able to
exploit that - I asked the question in their users list just to be
sure.
There are some options in SuperLU dist to reuse permutation
arrays, but
there's no I/O for that solver. And the native PETSc LU solver is not
parallel?
I'm using high-order finite differences so I'm suffering from a
lot of
fill-in, one of the reasons why storing factorizations in RAM is not
viable. In comparison, I have almost unlimited disk space.
I'm aware my need might seem counter-intuitive, but I'm really
willing
to sacrifice performance in the I/O part. My code is already heavily
based on PETSc (preallocation, assembly for matrices/vectors) coupled
with MUMPS I'm minimizing the loss of efficiency.
Thibaut
On 23/07/2019 17:13, Smith, Barry F. wrote:
> What types of computing systems will you be doing the
computations? Roughly how many MPI_ranks?
>
> Are the matrices all the same size? Do they have the same or
different nonzero structures? Would it be possible to use the same
symbolic representation for all of them and just have different
numerical values?
>
> Clusters and large scale computing centers are notoriously
terrible at IO; often IO is orders of magnitude slower than
compute/memory making this type of workflow unrealistically slow.
From a cost analysis point of view often just buying lots of
memory might be the most efficacious approach.
>
> That said, what you suggest might require only a few lines of
code (though determining where to put them is the tricky part)
depending on the MUMPS interface for saving a filer to disk. What
we would do is keep the PETSc wrapper that lives around the MUMPS
matrix Mat_MUMPS but using the MUMPS API save the information in
the DMUMPS_STRUC_C id; and then reload it when needed.
>
> The user level API could be something like
>
> MatMumpsSaveToDisk(Mat) and MatMumpsLoadFromDisk(Mat) they
would just money with DMUMPS_STRUC_C id; item.
>
>
> Barry
>
>
>> On Jul 23, 2019, at 9:24 AM, Thibaut Appel via petsc-users
<petsc-users@mcs.anl.gov <mailto:petsc-users@mcs.anl.gov>> wrote:
>>
>> Dear PETSc users,
>>
>> I need to solve several linear systems successively, with LU
factorization, as part of an iterative process in my Fortran
application code.
>>
>> The process would solve M systems (A_m)(x_m,i) = (b_m,i) for
m=1,M at each iteration i, but computing the LU factorization of
A_m only once.
>> The RHSs (b_m,i+1) are computed from all the different (x_m,i)
and all depend upon each other.
>>
>> The way I envisage to perform that is to use MUMPS to compute,
successively, each of the LU factorizations (m) in parallel and
store the factors on disk, creating/assembling/destroying the
matrices A_m on the go.
>> Then whenever needed, read the factors in parallel to solve the
systems. Since version 5.2, MUMPS has a save/restore feature that
allows that, see http://mumps.enseeiht.fr/doc/userguide_5.2.1.pdf
<http://mumps.enseeiht.fr/doc/userguide_5.2.1.pdf> p.20, 24 and 58.
>>
>> In its current state, the PETSc/MUMPS interface does not
incorporate that feature. I'm an advanced Fortran programmer but
not in C so I don't think I would do an amazing job having a go
inside src/mat/impls/aij/mpi/mumps/mumps.c.
>>
>> I was picturing something like creating as many KSP objects as
linear systems to be solved, with some sort of flag to force the
storage of LU factors on disk after the first call to KSPSolve.
Then keep calling KSPSolve as many times as needed.
>>
>> Would you support such a feature?
>>
>> Thanks for your support,
>>
>> Thibaut
