[petsc-users] finite difference jacobian errors when given non-constant initial condition
Zou, Ling
lzou at anl.gov
Sun Apr 21 14:36:55 CDT 2024
The other symptom is the same:
* Using coloring, finite differencing respects the specified non-zero pattern, but gives wrong (very large) Jacobian entries (J_ij)
* Using dense matrix assumption, finite differencing does not respect the non-zero pattern determined by your numeric, which is a clear sign of residual function code bug (your residual function does not respect your numeric).
-Ling
From: petsc-users <petsc-users-bounces at mcs.anl.gov> on behalf of Zou, Ling via petsc-users <petsc-users at mcs.anl.gov>
Date: Sunday, April 21, 2024 at 2:28 PM
To: Mark Lohry <mlohry at gmail.com>
Cc: PETSc <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] finite difference jacobian errors when given non-constant initial condition
Very interesting.
I happened to encounter something very similar a couple of days ago, which, of course, was due to a code bug I introduced. The code bug was in the residual function. I used a local vector to track ‘heat flux’, which should be zero-ed out at the beginning of each residual function evaluation. I did not zero it, and I observed very similar results, the Jacobian is completely wrong, with large values (J_ij keeps increasing after each iteration), and non-zero values are observed in locations which should be perfect zero. The symptom is very much like what you are seeing here. I suspect a similar bug. (Maybe you forgot zero the coefficients of P1 re-construction? Using constant value 1, reconstructed dphi/dx = 0, so however many iterations, still zero).
-Ling
From: Mark Lohry <mlohry at gmail.com>
Date: Sunday, April 21, 2024 at 12:35 PM
To: Zou, Ling <lzou at anl.gov>
Cc: PETSc <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] finite difference jacobian errors when given non-constant initial condition
The coloring I'm fairly confident is correct -- I use the same process for 3D unstructured grids and everything seems to work. The residual function is also validated. As a test I did as you suggested -- assume the matrix is dense -- and
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The coloring I'm fairly confident is correct -- I use the same process for 3D unstructured grids and everything seems to work. The residual function is also validated.
As a test I did as you suggested -- assume the matrix is dense -- and I get the same bad results, just now the zero blocks are filled.
Assuming dense, giving it a constant vector, all is good:
4.23516e-16 -1.10266 0.31831 -0.0852909 0 0 -0.31831 1.18795
1.10266 -4.23516e-16 -1.18795 0.31831 0 0 0.0852909 -0.31831
-0.31831 1.18795 2.11758e-16 -1.10266 0.31831 -0.0852909 0 0
0.0852909 -0.31831 1.10266 -4.23516e-16 -1.18795 0.31831 0 0
0 0 -0.31831 1.18795 2.11758e-16 -1.10266 0.31831 -0.0852909
0 0 0.0852909 -0.31831 1.10266 -4.23516e-16 -1.18795 0.31831
0.31831 -0.0852909 0 0 -0.31831 1.18795 4.23516e-16 -1.10266
Assuming dense, giving it sin(x), all is bad:
-1.76177e+08 -6.07287e+07 -6.07287e+07 -1.76177e+08 1.76177e+08 6.07287e+07 6.07287e+07 1.76177e+08
-1.31161e+08 -4.52116e+07 -4.52116e+07 -1.31161e+08 1.31161e+08 4.52116e+07 4.52116e+07 1.31161e+08
1.31161e+08 4.52116e+07 4.52116e+07 1.31161e+08 -1.31161e+08 -4.52116e+07 -4.52116e+07 -1.31161e+08
1.76177e+08 6.07287e+07 6.07287e+07 1.76177e+08 -1.76177e+08 -6.07287e+07 -6.07287e+07 -1.76177e+08
1.76177e+08 6.07287e+07 6.07287e+07 1.76177e+08 -1.76177e+08 -6.07287e+07 -6.07287e+07 -1.76177e+08
1.31161e+08 4.52116e+07 4.52116e+07 1.31161e+08 -1.31161e+08 -4.52116e+07 -4.52116e+07 -1.31161e+08
-1.31161e+08 -4.52116e+07 -4.52116e+07 -1.31161e+08 1.31161e+08 4.52116e+07 4.52116e+07 1.31161e+08
-1.76177e+08 -6.07287e+07 -6.07287e+07 -1.76177e+08 1.76177e+08 6.07287e+07 6.07287e+07 1.76177e+08
Scratching my head over here... I've been using these routines successfully for years in much more complex code.
On Sun, Apr 21, 2024 at 12:36 PM Zou, Ling <lzou at anl.gov<mailto:lzou at anl.gov>> wrote:
Edit:
* how do you do the coloring when using PETSc finite differencing? An incorrect coloring may give you wrong Jacobian. For debugging purpose, the simplest way to avoid an incorrect coloring is to assume the matrix is dense (slow but error proofing). If the numeric converges as expected, then fine tune your coloring to make it right and fast.
From: petsc-users <petsc-users-bounces at mcs.anl.gov<mailto:petsc-users-bounces at mcs.anl.gov>> on behalf of Zou, Ling via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>
Date: Sunday, April 21, 2024 at 11:29 AM
To: Mark Lohry <mlohry at gmail.com<mailto:mlohry at gmail.com>>, PETSc <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>
Subject: Re: [petsc-users] finite difference jacobian errors when given non-constant initial condition
Hi Mark, I am working on a project having similar numeric you have, one-dimensional finite volume method with second-order slope limiter TVD, and PETSc finite differencing gives perfect Jacobian even for complex problems.
So, I tend to believe that your implementation may have some problem. Some lessons I learned during my code development:
* how do you do the coloring when using PETSc finite differencing? An incorrect coloring may give you wrong Jacobian. The simplest way to avoid an incorrect coloring is to assume the matrix is dense (slow but error proofing).
* Residual function evaluation not correctly implemented can also lead to incorrect Jacobian. In your case, you may want to take a careful look at the order of execution, when to update your unknown vector, when to perform P1 reconstruction, and when to evaluate the residual.
-Ling
From: petsc-users <petsc-users-bounces at mcs.anl.gov<mailto:petsc-users-bounces at mcs.anl.gov>> on behalf of Mark Lohry <mlohry at gmail.com<mailto:mlohry at gmail.com>>
Date: Saturday, April 20, 2024 at 1:35 PM
To: PETSc <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>
Subject: [petsc-users] finite difference jacobian errors when given non-constant initial condition
I have a 1-dimensional P1 discontinuous Galerkin discretization of the linear advection equation with 4 cells and periodic boundaries on [-pi,+pi]. I'm comparing the results from SNESComputeJacobian with a hand-written Jacobian. Being linear,
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I have a 1-dimensional P1 discontinuous Galerkin discretization of the linear advection equation with 4 cells and periodic boundaries on [-pi,+pi]. I'm comparing the results from SNESComputeJacobian with a hand-written Jacobian. Being linear, the Jacobian should be constant/independent of the solution.
When I set the initial condition passed to SNESComputeJacobian as some constant, say f(x)=1 or 0, the petsc finite difference jacobian agrees with my hand coded-version. But when I pass it some non-constant value, e.g. f(x)=sin(x), something goes horribly wrong in the petsc jacobian. Implementing my own rudimentary finite difference approximation (similar to how I thought petsc computes it) it returns the correct jacobian to expected error. Any idea what could be going on?
Analytically computed Jacobian:
4.44089e-16 -1.10266 0.31831 -0.0852909 0 0 -0.31831 1.18795
1.10266 -4.44089e-16 -1.18795 0.31831 0 0 0.0852909 -0.31831
-0.31831 1.18795 4.44089e-16 -1.10266 0.31831 -0.0852909 0 0
0.0852909 -0.31831 1.10266 -4.44089e-16 -1.18795 0.31831 0 0
0 0 -0.31831 1.18795 4.44089e-16 -1.10266 0.31831 -0.0852909
0 0 0.0852909 -0.31831 1.10266 -4.44089e-16 -1.18795 0.31831
0.31831 -0.0852909 0 0 -0.31831 1.18795 4.44089e-16 -1.10266
-1.18795 0.31831 0 0 0.0852909 -0.31831 1.10266 -4.44089e-16
petsc finite difference jacobian when given f(x)=1:
4.44089e-16 -1.10266 0.31831 -0.0852909 0 0 -0.31831 1.18795
1.10266 -4.44089e-16 -1.18795 0.31831 0 0 0.0852909 -0.31831
-0.31831 1.18795 4.44089e-16 -1.10266 0.31831 -0.0852909 0 0
0.0852909 -0.31831 1.10266 -4.44089e-16 -1.18795 0.31831 0 0
0 0 -0.31831 1.18795 4.44089e-16 -1.10266 0.31831 -0.0852909
0 0 0.0852909 -0.31831 1.10266 -4.44089e-16 -1.18795 0.31831
0.31831 -0.0852909 0 0 -0.31831 1.18795 4.44089e-16 -1.10266
-1.18795 0.31831 0 0 0.0852909 -0.31831 1.10266 -4.44089e-16
petsc finite difference jacobian when given f(x) = sin(x):
-1.65547e+08 -3.31856e+08 -1.25427e+09 4.4844e+08 0 0 1.03206e+08 7.86375e+07
9.13788e+07 1.83178e+08 6.92336e+08 -2.4753e+08 0 0 -5.69678e+07 -4.34064e+07
3.7084e+07 7.43387e+07 2.80969e+08 -1.00455e+08 -5.0384e+07 -2.99747e+07 0 0
3.7084e+07 7.43387e+07 2.80969e+08 -1.00455e+08 -5.0384e+07 -2.99747e+07 0 0
0 0 2.80969e+08 -1.00455e+08 -5.0384e+07 -2.99747e+07 -2.31191e+07 -1.76155e+07
0 0 2.80969e+08 -1.00455e+08 -5.0384e+07 -2.99747e+07 -2.31191e+07 -1.76155e+07
9.13788e+07 1.83178e+08 0 0 -1.24151e+08 -7.38608e+07 -5.69678e+07 -4.34064e+07
-1.65547e+08 -3.31856e+08 0 0 2.24919e+08 1.3381e+08 1.03206e+08 7.86375e+07
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