[petsc-users] finite difference jacobian errors when given non-constant initial condition

[Mark Lohry]

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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20240420/8ef3fbd4/attachment.html>