[petsc-users] Euclid or Boomeramg vs ILU: questions.

[Sanjay Govindjee]

Mark's suggestion will definitely help a lot.  Remove the displacement 
bc equations or include them in the matrix by zeroing out the row and 
putting a 1 on the diagonal.  The Lagrange multiplier will cause grief.

On 8/20/21 11:21 AM, Mark Adams wrote:
> Constraints are a pain with scalable/iterative solvers. If you order 
> the constraints last then ILU should work as well as it can work, but 
> AMG gets confused by the constraint equations.
> You could look at PETSc's Stokes solvers, but it would be best if you 
> could remove the constrained equations from your system if they are 
> just simple point wise BC's.
> Mark
>
> On Fri, Aug 20, 2021 at 8:53 AM Наздрачёв Виктор 
> <numbersixvs at gmail.com <mailto:numbersixvs at gmail.com>> wrote:
>
>     *Hello, dear PETSc team!*
>
>     I have a 3D elasticity with heterogeneous properties problem.
>     There is unstructured grid with aspect ratio varied from 4 to 25.
>     Dirichlet BCs (bottom zero displacements) are imposed via linear
>     constraint equations using Lagrange multipliers. Also, Neumann
>     (traction) BCs are imposed on side edges of mesh. Gravity load is
>     also accounted for.
>
>     I can solve this problem with *dgmres solver* and *ILU* as a
>     *preconditioner*. But ILU doesn`t support parallel computing, so I
>     decided to use Euclid or Boomeramg as a preconditioner. The issue
>     is in slow convergence and high memory consumption, much higher,
>     than for ILU.
>
>     E.g., for source matrix size 2.14 GB with *ILU-0
>     preconditioning* memory consumption is about 5.9 GB, and the
>     process converges due to 767 iterations, and with *Euclid-0
>     preconditioning* memory consumption is about 8.7 GB, and the
>     process converges due to 1732 iterations.
>
>     One of the following preconditioners is currently in use: *ILU-0,
>     ILU-1, Hypre (Euclid), Hypre (boomeramg)*.
>
>     As a result of computations */(logs and memory logs are
>     attached)/*, the following is established for preconditioners:
>
>     1. *ILU-0*: does not always provide convergence (or provides, but
>     slow); uses an acceptable amount of RAM; does not support parallel
>     computing.
>
>     2. *ILU-1*: stable; memory consumption is much higher than that of
>     ILU-0; does not support parallel computing.
>
>     3. *Euclid*: provides very slow convergence, calculations are
>     performed several times slower than for ILU-0; memory consumption
>     greatly exceeds both ILU-0 and ILU-1; supports parallel computing.
>     Also “drop tolerance” doesn’t provide enough accuracy in some
>     cells, so I don’t use it.
>
>     4. *Boomeramg*: provides very slow convergence, calculations are
>     performed several times slower than for ILU-0; memory consumption
>     greatly exceeds both ILU-0 and ILU-1; supports parallel computing.
>
>     In this regard, the following questions arose:
>
>     1. Is this behavior expected for HYPRE in computations with 1 MPI
>     process? If not, is that problem can be related to *PETSc* or *HYPRE*?
>
>     2. Hypre (Euclid) has much fewer parameters than ILU. Among them
>     is the factorization level *"-pc_hypre_euclid_level <now -2:
>     formerly -2>: Factorization levels (None)"* and its default value
>     looks very strange, moreover, it doesn’t matter what factor is
>     chosen -2, -1 or 0. Could it be that the parameter is confused
>     with Column pivot tolerance in ILU - *"-pc_factor_column_pivot
>     <-2.: -2.>: Column pivot tolerance (used only for some
>     factorization) (PCFactorSetColumnPivot)"*?
>
>     3. What preconditioner would you recommend to: optimize
>     *convergence*, *memory* consumption, add *parallel computing*?
>
>     4. How can we theoretically estimate memory costs with *ILU,
>     Euclid, Boomeramg*?
>
>     5. At what stage are memory leaks most likely?
>
>     In any case, thank you so much for your attention! Will be
>     grateful for any response.
>
>     Kind regards,
>     Viktor Nazdrachev
>     R&D senior researcher
>     Geosteering Technologies LLC
>

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