Where can I find the linear solver documentation?

Open discussion for MAGMA library (Matrix Algebra on GPU and Multicore Architectures)
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Klausb
Posts: 21
Joined: Thu Oct 05, 2017 3:04 pm

Where can I find the linear solver documentation?

Post by Klausb » Sun Oct 08, 2017 4:12 pm

Hello,

I am looking for a documentation describes the setup of the MAGMA linear solvers BiCG, BiCGSTAB, CG, IDR ... and the parameters for their configuration in my application code. I assume I am overlooking something but I couldn't find it.

Klaus

hartwig anzt
Posts: 90
Joined: Tue Sep 02, 2014 5:44 pm

Re: Where can I find the linear solver documentation?

Post by hartwig anzt » Tue Oct 10, 2017 5:25 am

Dear Klaus,
I do admit that this is currently not very well documented. What we have is:
http://icl.cs.utk.edu/projectsfiles/mag ... dgesv.html
and then click on the specific solvers. For the description of the solver_par object, please look into sparse/include/magmasparse_types.h
If you have specific questions to a solver, I am happy to help. And I will try to improve the documentation in future.
Thanks, Hartwig

Klausb
Posts: 21
Joined: Thu Oct 05, 2017 3:04 pm

Next steps

Post by Klausb » Tue Oct 10, 2017 12:12 pm

Dear Hartwig,

originally I worked with the following solvers which, in combination, were really fast to solve my physics problem but only 2D on the CPU, now I have to move to 3D with GPU support I think because the 3D case will have about 30.000.000 cells:

For symmetric matrices:

PCG + IC preconditioner
Start-up:
1 matrix-vector multiply
1 parallel reduction
Per iteration
1 matrix-vector multiply
3 parallel reductions
+ preconditioner - applied 1x

All other CG solvers I tried (from other libraries) crashed at an early stage of the simulation!

I tried GMRES + AMG preconditioner too but it's about 6x slower and some GMRES implementations are "rough" so the end results (of the physics problem simulation) are not as good.


For asymmetric matrices BiCG (because it's faster) and BiCGStab (when BiCG was not stable and crashed):

PBiCG + Simplified Diagonal-based Incomplete LU preconditioner
Start-up
2 matrix-vector multiplies
1 parallel reduction
Per iteration
2 matrix-vector multiplies
3 parallel reductions
+ preconditioner - applied 2x


PbiCGStab + Simplified Diagonal-based Incomplete LU preconditioner
Start-up
1 matrix-vector multiply
1 parallel reduction
Per iteration
2 matrix-vector multiplies
6 parallel reductions
+ preconditioner - applied 2x


Three questions:

1: Which magma solvers would you see as replacements for the ones described above? (just as a starting point for tests)

2: What could be the benefit from iterative refinement?

3: How could I estimate the hardware power needed (CPUs + GPUs) to solve my 3D problem (assume double precision)?

Thank you for your help!

Klaus

JacksonZWimpub
Posts: 1
Joined: Sat Nov 04, 2017 4:41 am
Location: Russia
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Where can I find the linear solver documentation

Post by JacksonZWimpub » Sat Nov 25, 2017 4:11 am

Dear All,

What are the subroutines that Im supposed to call to solve the linear ODEs in that form MXCXKX = F where none of the variables denoted as M, C, K and F are function of the time?

Does anybody can enlighten me on that?

Regards,

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mgates3
Posts: 842
Joined: Fri Jan 06, 2012 2:13 pm

Re: Where can I find the linear solver documentation?

Post by mgates3 » Tue Nov 28, 2017 11:24 am

Are you using the MAGMA computational algebra system, http://magma.maths.usyd.edu.au/magma/ ?
If so, you're at the wrong site.

This forum is for the MAGMA linear algebra for GPUs library, http://icl.utk.edu/magma/

-mark

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