[petsc-users] Different precision from MatAssembly/MatView

[Noam T.]

A bit more information:

Looking at the solution of the system of equations, knowing the exact RHS vector:
---
[-0.00197, 0.00203, -0.00197]
---

SNES gives the solution:
---
3.316262462871E-03, -4.189244774965E-03, 2.468317119413E-03
---

which is indeed (closer to) the solution for the jacobian shown in MatView (the "lower precision" one). The "exact" solution would be:
---

3.282607248309093b-3, -4.241572005990172b-3,, 2.425030835360701b-3
---

which is already different form the second decimal digit.

***
Requesting a low precision to have SNES do a few iterations, shows that the built jacobian seems to deviate more and more form the computed one after some iterations, e.g.:

Computed (printed from in-code):
---
0.536488494840 0.066474939660 0.198813816284
0.066474939660 0.529482312614 -0.002835445071
0.198813816284 -0.002835445071 0.530589055263
---

MatView:
---
row 0: (0, 0.538491) (1, 0.0662019) (2, 0.198808)
row 1: (0, 0.0662019) (1, 0.526981) (2, -0.00257554)
row 2: (0, 0.198808) (1, -0.00257554) (2, 0.529883) ---

Only one digit is correct/the same in entries [1,2], [2,1] and [2,2].

Thank you.
Noam

On Sunday, March 15th, 2026 at 3:29 PM, Noam T. <dontbugthedevs at proton.me> wrote:

> Hello,
>
> Looking at the assembly of the Jacobian using MatView, I noticed values were somewhat different from the computed ones in the jacobian function (DMSNESSetJacobian). For the test, I used a single Q1 element, with 4 quadrature points, so the exact Jacobian matrix can be computed analytically.
>
> In the jacobian function, after looping through all quadrature points, printing the matrix to stdout shows:
>
> ----
> 0.531360000000 0.066670000000 0.197333333327
> 0.066670000000 0.535360000000 -0.003333333327
> 0.197333333327 -0.003333333327 0.527413333333
> ----
>
> (showing only the 3 free DoFs). The 2x2 submatrix in [0:1] has exactly four/five nonzero digits, as shown above. The rest of the elements have a periodic 3 ending (a couple of digits at the end are off, but that's fine).
>
> This same matrix is the one added to the global jacobian during the quadrature loop, with "DMPlexMatSetClosure". After looping, calling "MatAssemblyBegin/End", then MatView:
>
> ----
>
> Mat Object: 1 MPI process
> type: seqaij
> row 0: (0, 0.531387) (1, 0.0666733) (2, 0.197338)
> row 1: (0, 0.0666733) (1, 0.535387) (2, -0.0033385)
> row 2: (0, 0.197338) (1, -0.0033385) (2, 0.52744) ----
>
> Values are close, but definitely not the same as computed. Are these values from "MatView" the ones actually stored in the matrix? It seems there is some precision loss in the process.
>
> Interestingly, computing the jacobian through finite differences, shows the same result for the "hand-coded" jacobian, whereas the finite differences ones is the "exact" one (same as first one above):
>
> ----
> ||J - Jfd||_F/||J||_F = 4.90736e-05, ||J - Jfd||_F = 4.74265e-05
> Hand-coded Jacobian ----------
> Mat Object: 1 MPI process
> type: seqaij
> row 0: (0, 0.531387) (1, 0.0666733) (2, 0.197338)
> row 1: (0, 0.0666733) (1, 0.535387) (2, -0.0033385)
> row 2: (0, 0.197338) (1, -0.0033385) (2, 0.52744)
> Finite difference Jacobian ----------
> Mat Object: 1 MPI process
> type: seqaij
> row 0: (0, 0.53136) (1, 0.06667) (2, 0.197333)
> row 1: (0, 0.06667) (1, 0.53536) (2, -0.00333333)
> row 2: (0, 0.197333) (1, -0.00333333) (2, 0.527413)
> Hand-coded minus finite-difference Jacobian with tolerance 1e-05 ----------
> Mat Object: 1 MPI process
> type: seqaij
> row 0: (0, 2.66554e-05)
> row 1: (1, 2.66554e-05)
> row 2: (2, 2.6558e-05)  ----
>
> The main code is in Fortran, using double precision variables, in case it is relevant.
>
> Thank you.
>
> Noam
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