-snes_test_jacobian - compare the user provided Jacobian with one computed via finite differences to check for errors. If a threshold is given, display only those entries whose difference is greater than the threshold.
-snes_test_jacobian_view - display the user provided Jacobian, the finite difference Jacobian and the difference between them to help users detect the location of errors in the user provided Jacobian.

There are many, many reasons Newton can fail, usually they are due to bugs in the function evaluation or Jacobian evaluation. Occasionly they are due to it being a very difficult non-linear problem. You first need to use the tools above to verify there are no bugs anywhere.

Barry

On Nov 21, 2024, at 7:11 AM, David Jiawei LUO LIANG <12431140@mail.sustech.edu.cn> wrote:

I am using the Newton iteration to solve a nonlinear 1D heat equation problem by using FEM.

I attached my source code named "SNES_heat.cpp"

when I run the code
0 SNES Function norm 1.206289245288e+01
1 SNES Function norm 7.128802192789e+00
2 SNES Function norm 6.608812909525e+00

you can find that it only iterate 3 steps, and then do all the function evaluation and finally just stop the program.

I think it is not reasonble. I check my code, it is correct if I set it as a linear problem. it means my Jacobian and Residual function is correct.

But when I set it as a nonlinear, the residual seems reduces as not expected.

I doubt that whether my understanding of the newton iteration is different from SNES's newton iteration process.

David Jiawei LUO LIANG
南方科技大学/学生/研究生/2024
广东省深圳市南山区学苑大道1088号

<SNES_heat.cpp>