Re: [eigen] Best Solver for Large but Sparse Linear System

Re: [eigen] Best Solver for Large but Sparse Linear System

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To: "eigen@xxxxxxxxxxxxxxxxxxx" <eigen@xxxxxxxxxxxxxxxxxxx>
Subject: Re: [eigen] Best Solver for Large but Sparse Linear System
From: "Pfannmoeller, Joerg Peter" <JPFANNMOELLER@xxxxxxxxxxxxxxx>
Date: Tue, 3 Sep 2019 18:15:18 +0000
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Thread-topic: [eigen] Best Solver for Large but Sparse Linear System

Hello all,

thank you Benoit but I was hoping to get an answer specific to the eigen library. In my project a end-user friendly solution is necessary. I can not program anything on my own that is much too time consuming. If there is a solver that can be applied to many different matrices with the sparsity that I described above and can be either parallelized, multithreaded, or GPU "accelerated" I would prefer to apply this solver. Is there anything in like this in the eigen library? Can your version of LSQR be used for this purpose?

Best Joerg

From: Benoit Bardet <benoit.bardet@xxxxxxxxx>
Sent: Tuesday, September 3, 2019 11:12 AM
To: eigen@xxxxxxxxxxxxxxxxxxx <eigen@xxxxxxxxxxxxxxxxxxx>
Subject: Re: [eigen] Best Solver for Large but Sparse Linear System

External Email - Use Caution

Hi Joerg,

It depends on your matrix condition factor (not sure of the name in english).

A way I like for bad condition number is IncompleteLUT preconditionner with GMRES. Try different fill factor for ILUT.

For better matrix, UMFPACK is very efficient. I'm not sure it is in eigen. Maybe with Diagonal preconditionner.

You can use CG as well with Diag precond.

This page gives example to make a first benchmarking (without precond).. https://eigen.tuxfamily.org/dox/group__MatrixfreeSolverExample.html

But do the benchmark on a real matrix, not a random one. And benchmark in time and not in iterations.

I used GMRES for 8e6 by 8e6 matrix with about 10 non Zero as well per line (Finite Element with bad meshes). Be careful with memory.

Regards.

Le mar. 3 sept. 2019 à 16:52, Pfannmoeller, Joerg Peter <JPFANNMOELLER@xxxxxxxxxxxxxxx> a écrit :

Hello Eigen-Experts,

I have a linear system with a matrix size of about 2E+06 x 2E+06. The maximum number of non-zero matrix elements in each row is 10. Which solver would you recommend for this system?

Best Joerg

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References:
- [eigen] Best Solver for Large but Sparse Linear System
  - From: Pfannmoeller, Joerg Peter
- Re: [eigen] Best Solver for Large but Sparse Linear System
  - From: Benoit Bardet

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