[petsc-users] Eliminating rows and columns which are zeros

Fri Feb 3 10:41:05 CST 2023

Hello Barry,

I would like to better understand pc_type redistribute usage.

I am plan to use pc_type redistribute in the context of adaptive mesh refinement on a structured grid in 2D. My base mesh (level 0) is indexed from 0 to N-1 elements and refined mesh (level 1) is indexed from 0 to 4(N-1) elements. When I construct system matrix A on (level 1); I probably only use 20% of 4(N-1)  elements, however the indexes are scattered in the range of 0 to 4(N-1). That leaves 80% of the rows and columns of the system matrix A on (level 1) to be zero. From your earlier response, I believe this would be a use case for petsc_type redistribute.

Question (1)

If N is really large, I would have to allocate memory of size 4(N-1) for the system matrix A on (level 1). How does pc_type redistribute help? Because, I did end up allocating memory for a large system, where most of the rows and columns are zeros. Is most of the allotted memory not wasted? Is this the correct usage?

Question (2)

I tried using pc_type redistribute for a two level system.
I have attached the output only for  (level 1)
The solution converges to right solution but still petsc outputs some error messages.

[0]PETSC ERROR: WARNING! There are option(s) set that were not used! Could be the program crashed before they were used or a spelling mistake, etc!
[0]PETSC ERROR: Option left: name:-options_left (no value)

But the there were no unused options

#PETSc Option Table entries:
-ksp_type preonly
-options_left
-pc_type redistribute
-redistribute_ksp_converged_reason
-redistribute_ksp_monitor_true_residual
-redistribute_ksp_type cg
-redistribute_ksp_view
-redistribute_pc_type jacobi
#End of PETSc Option Table entries
There are no unused options.
Program ended with exit code: 0

Question (2)

[0;39m[0;49m[0]PETSC ERROR: Object is in wrong state

[0]PETSC ERROR: Matrix is missing diagonal entry in row 0 (65792)

What does this error message imply? Given I only use 20% of 4(N-1) indexes, I can imagine most of the diagonal entrees are zero. Is my understanding correct?

Question (3)

[0]PETSC ERROR: #5 MatZeroRowsColumnsIS() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6124

I am using MatZeroRowsColumnsIS to set the homogenous Dirichelet boundary. I don’t follow why I get this error message as the linear system converges to the right solution.

Thank you for your help.

Kind regards,
Karthik.

From: Barry Smith <bsmith at petsc.dev>
Date: Tuesday, 10 January 2023 at 18:50
To: Chockalingam, Karthikeyan (STFC,DL,HC) <karthikeyan.chockalingam at stfc.ac.uk>
Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Eliminating rows and columns which are zeros

  Yes, after the solve the x will contain correct values for ALL the locations including the (zeroed out rows). You use case is exactly what redistribute it for.

  Barry

On Jan 10, 2023, at 11:25 AM, Karthikeyan Chockalingam - STFC UKRI <karthikeyan.chockalingam at stfc.ac.uk> wrote:

Thank you Barry. This is great!

I plan to solve using ‘-pc_type redistribute’ after applying the Dirichlet bc using
MatZeroRowsColumnsIS(A, isout, 1, x, b);

While I retrieve the solution data from x (after the solve) – can I index them using the original ordering (if I may say that)?

Kind regards,
Karthik.

From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Date: Tuesday, 10 January 2023 at 16:04
To: Chockalingam, Karthikeyan (STFC,DL,HC) <karthikeyan.chockalingam at stfc.ac.uk<mailto:karthikeyan.chockalingam at stfc.ac.uk>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>
Subject: Re: [petsc-users] Eliminating rows and columns which are zeros

https://petsc.org/release/docs/manualpages/PC/PCREDISTRIBUTE/#pcredistribute   -pc_type redistribute

It does everything for you. Note that if the right hand side for any of the "zero" rows is nonzero then the system is inconsistent and the system does not have a solution.

Barry

On Jan 10, 2023, at 10:30 AM, Karthikeyan Chockalingam - STFC UKRI via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:

Hello,

I am assembling a MATIJ of size N, where a very large number of rows (and corresponding columns), are zeros. I would like to potentially eliminate them before the solve.

For instance say N=7

0 0  0  0 0 0 0
0 1 -1  0 0 0 0
0 -1 2  0 0 0 -1
0 0  0  0 0 0 0
0 0  0  0 0 0 0
0 0  0  0 0 0 0
0 0  -1 0 0 0 1

I would like to reduce it to a 3x3

1 -1 0
-1 2 -1
0 -1 1

I do know the size N.

Q1) How do I do it?
Q2) Is it better to eliminate them as it would save a lot of memory?
Q3) At the moment, I don’t know which rows (and columns) have the zero entries but with some effort I probably can find them. Should I know which rows (and columns) I am eliminating?

Thank you.

Karthik.

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