# NewtonSolver residuals go to zero, meaningless solution

**URL:** <https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925>\
**Category:** dolfinx\
**Created:** [August 8, 2023, 6:00pm UTC](https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925 "2023-08-08T18:00:38Z")\
**Posts on this page:** 7\
**Page:** 1

<div class="post-metadata">

**Author:** ![Mark](https://avatars.discourse-cdn.com/v4/letter/m/e9c0ed/32.png) [@Mark](https://fenicsproject.discourse.group/u/Mark)\
**Post date:** [August 8, 2023, 6:00pm UTC](https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925/1 "2023-08-08T18:00:38Z")

</div>

I am trying to solve a nonlinear Poisson equation. I hit some unexpected behaviour for a certain set of inputs, and I am unable to make sense of it. The `NewtonSolver` behaviour is puzzling to me, this is the solver output. Residuals are huge and then collapse to zero. Needless to say the solution is not ok.

```auto
2023-08-08 19:39:59.834 ( 238.182s) [main] petsc.cpp:675 INFO| PETSc Krylov solver starting to solve system.
2023-08-08 19:39:59.841 ( 238.189s) [main] NewtonSolver.cpp:36 INFO| Newton iteration 3: r (abs) = 2.87352e+115 (tol = 1e-10) r (rel) = 1.63805e+114(tol = 1e-06)
2023-08-08 19:39:59.843 ( 238.191s) [main] petsc.cpp:675 INFO| PETSc Krylov solver starting to solve system.
2023-08-08 19:39:59.851 ( 238.199s) [main] NewtonSolver.cpp:36 INFO| Newton iteration 4: r (abs) = 0 (tol = 1e-10) r (rel) = 0(tol = 1e-06)
2023-08-08 19:39:59.851 ( 238.199s) [main] NewtonSolver.cpp:255 INFO| Newton solver finished in 4 iterations and 10008 linear solver iterations.

```

This is a MWE

```auto
import ufl
import numpy as np

from mpi4py import MPI
from petsc4py import PETSc

from dolfinx import mesh, fem, io, nls, log
from dolfinx.plot import create_vtk_mesh
def q(u):
    return ufl.exp(u)
L, W, S = [1.66666667, 1.66666667, 1.]
domain = mesh.create_rectangle(MPI.COMM_WORLD, np.array([[0,0],[L, W]]), [20,20], cell_type=mesh.CellType.quadrilateral)
x = ufl.SpatialCoordinate(domain)
u_ufl = x[1]*ufl.sin(2*3.14*x[0])*ufl.cos(S*3.14*x[1])
u_ufl_np = f"x[1]*np.sin(2*np.pi*x[0])*np.cos({S}*np.pi*x[1])"
f = - ufl.div(q(u_ufl)*ufl.grad(u_ufl))
V = fem.FunctionSpace(domain, ("CG", 2))
u_exact = lambda x: eval(u_ufl_np)
u_D = fem.Function(V)
u_D.interpolate(u_exact)
fdim = domain.topology.dim - 1
boundary_facets = mesh.locate_entities_boundary(domain, fdim, lambda x: np.full(x.shape[1], True, dtype=bool))
bc = fem.dirichletbc(u_D, fem.locate_dofs_topological(V, fdim, boundary_facets))
uh = fem.Function(V)
v = ufl.TestFunction(V)
F = q(uh)*ufl.dot(ufl.grad(uh), ufl.grad(v))*ufl.dx - f*v*ufl.dx
problem = fem.petsc.NonlinearProblem(F, uh, bcs=[bc])
solver = nls.petsc.NewtonSolver(MPI.COMM_WORLD, problem)
solver.convergence_criterion = "incremental"
solver.rtol = 1e-6
#solver.rtol = 1e-1
solver.report = True
##########
ksp = solver.krylov_solver
opts = PETSc.Options()
option_prefix = ksp.getOptionsPrefix()
opts[f"{option_prefix}ksp_type"] = "cg"
opts[f"{option_prefix}pc_type"] = "gamg"
opts[f"{option_prefix}pc_factor_mat_solver_type"] = "mumps"
ksp.setFromOptions()
##########
log.set_log_level(log.LogLevel.INFO)
n, converged = solver.solve(uh)
assert(converged)
print(f"Number of interations: {n:d}")

            

```

For inputs as `L, W, S = [1.66666667, 1.1, 1.]` works fine, for example.  
Any hints please?

---

<div class="post-metadata">

**Author:** ![nate](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/nate/32/17_2.png) [@nate](https://fenicsproject.discourse.group/u/nate)\
**Post date:** [August 8, 2023, 6:21pm UTC](https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925/2 "2023-08-08T18:21:34Z")

</div>

I cannot reproduce your issue. Which version of petsc/dolfinx are you using?

 ![image](https://global.discourse-cdn.com/free1/uploads/fenicsproject1/original/2X/3/318e2eb1d75d26f7cd3cc9c5efc5e40b5e9b98de.jpeg)

```bash
2023-08-08 14:20:53.636 ( 0.155s) [main] petsc.cpp:698 INFO| PETSc Krylov solver starting to solve system.
2023-08-08 14:20:53.652 ( 0.170s) [main] petsc.cpp:698 INFO| PETSc Krylov solver starting to solve system.
2023-08-08 14:20:53.675 ( 0.194s) [main] NewtonSolver.cpp:36 INFO| Newton iteration 2: r (abs) = 5.00946 (tol = 1e-10) r (rel) = 0.285564(tol = 1e-06)
2023-08-08 14:20:53.678 ( 0.197s) [main] petsc.cpp:698 INFO| PETSc Krylov solver starting to solve system.
2023-08-08 14:20:53.693 ( 0.212s) [main] NewtonSolver.cpp:36 INFO| Newton iteration 3: r (abs) = 0.81439 (tol = 1e-10) r (rel) = 0.0464242(tol = 1e-06)
2023-08-08 14:20:53.696 ( 0.215s) [main] petsc.cpp:698 INFO| PETSc Krylov solver starting to solve system.
2023-08-08 14:20:53.712 ( 0.230s) [main] NewtonSolver.cpp:36 INFO| Newton iteration 4: r (abs) = 0.0488795 (tol = 1e-10) r (rel) = 0.00278637(tol = 1e-06)
2023-08-08 14:20:53.714 ( 0.233s) [main] petsc.cpp:698 INFO| PETSc Krylov solver starting to solve system.
2023-08-08 14:20:53.730 ( 0.249s) [main] NewtonSolver.cpp:36 INFO| Newton iteration 5: r (abs) = 0.000293275 (tol = 1e-10) r (rel) = 1.67181e-05(tol = 1e-06)
2023-08-08 14:20:53.733 ( 0.251s) [main] petsc.cpp:698 INFO| PETSc Krylov solver starting to solve system.
2023-08-08 14:20:53.747 ( 0.266s) [main] NewtonSolver.cpp:36 INFO| Newton iteration 6: r (abs) = 1.60868e-08 (tol = 1e-10) r (rel) = 9.17024e-10(tol = 1e-06)
2023-08-08 14:20:53.747 ( 0.266s) [main] NewtonSolver.cpp:255 INFO| Newton solver finished in 6 iterations and 237 linear solver iterations.

```

---

<div class="post-metadata">

**Author:** ![Mark](https://avatars.discourse-cdn.com/v4/letter/m/e9c0ed/32.png) [@Mark](https://fenicsproject.discourse.group/u/Mark)\
**Post date:** [August 8, 2023, 6:26pm UTC](https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925/3 "2023-08-08T18:26:10Z")

</div>

Oh my.  
I have Dolfinx 0.6.0, installed via conda on Mac OS, two days ago actually. Trying to find out the PETSc version. Thanks a lot

---

<div class="post-metadata">

**Author:** ![Mark](https://avatars.discourse-cdn.com/v4/letter/m/e9c0ed/32.png) [@Mark](https://fenicsproject.discourse.group/u/Mark)\
**Post date:** [August 8, 2023, 7:24pm UTC](https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925/4 "2023-08-08T19:24:21Z")

</div>

I have tried to see if I can compute your right solution using the Jupyter Lab environment from the docker image `docker run --init -ti -p 8888:8888 dolfinx/lab:stable # Access at http://localhost:8888`, as found in [installation docs](https://github.com/FEniCS/dolfinx/blob/main/README.md#installation).

Using the same MWE I get the error

```auto
ArityMismatch: Failure to conjugate test function in complex Form

```

As suggsted in other posts on this discourse site, I changed the line with the form definition from , as in the MWE

```auto
F = q(uh)*ufl.dot(ufl.grad(uh), ufl.grad(v))*ufl.dx - f*v*ufl.dx

```

to

```auto
type or paste code here

```

just to get another error

```auto
ArityMismatch: Adding expressions with non-matching form arguments ('conj(v_0)',) vs ('v_0',).

```

I am gobsmacked, is the Jupyter Lab environment the most up to date, how come you can run the same MWE with no problems?

Thank you so much for your invaluable support

---

<div class="post-metadata">

**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\
**Post date:** [August 8, 2023, 7:46pm UTC](https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925/5 "2023-08-08T19:46:58Z")

</div>

> [@Mark](#):
>
> Using the same MWE I get the error
> 
> ```auto
> ArityMismatch: Failure to conjugate test function in complex Form
> 
> ```
> 
> As suggsted in other posts on this discourse site, I changed the line with the form definition from , as in the MWE
> 
> ```auto
> F = q(uh)*ufl.dot(ufl.grad(uh), ufl.grad(v))*ufl.dx - f*v*ufl.dx
> 
> ```
> 
> to
> 
> ```auto
> type or paste code here
> 
> ```
> 
> just to get another error
> 
> ```auto
> ArityMismatch: Adding expressions with non-matching form arguments ('conj(v_0)',) vs ('v_0',).
> 
> ```
> 
> I am gobsmacked, is the Jupyter Lab environment the most up to date, how come you can run the same MWE with no problems?

Make sure that you are using the real mode kernel. If you are running it in jupyterlab, you can change the kernel to the one that does not have complex in the name.

If you are running a script on commandline, you should call `source dolfinx-real-mode` to set appropriate env variables

---

<div class="post-metadata">

**Author:** ![Mark](https://avatars.discourse-cdn.com/v4/letter/m/e9c0ed/32.png) [@Mark](https://fenicsproject.discourse.group/u/Mark)\
**Post date:** [August 8, 2023, 8:06pm UTC](https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925/6 "2023-08-08T20:06:40Z")

</div>

Got it, its called Python 3 kernel, fooled me as I was expecting “Dolfinx” somewhere in the name.  
And it reproduces Nate’s result. Need only to figure out what’s wring with my conda installation.  
Thank you so much

---

<div class="post-metadata">

**Author:** ![conpierce8](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/conpierce8/32/2464_2.png) [@conpierce8](https://fenicsproject.discourse.group/u/conpierce8)\
**Post date:** [August 8, 2023, 8:45pm UTC](https://fenicsproject.discourse.group/t/newtonsolver-residuals-go-to-zero-meaningless-solution/11925/7 "2023-08-08T20:45:46Z")

</div>

I get the correct solution using my conda installation and `docker.io/dolfinx/lab:stable`, but garbage when using `docker.io/dolfinx/lab:nightly`. Is it a PETSc issue? (3.19 vs 3.17?)

# Conda installation

```bash
python -c "import petsc4py, dolfinx; print(dolfinx. __version__ , dolfinx.git_commit_hash); print(petsc4py. __version__ )"

```

```x
0.6.0 7ac1d50b477b430858a9d3f53289bb950900528d
3.17.4

```

This installation uses the conda builds from around February or so:

```bash
conda list fenics

```

```x
# packages in environment at /home/conpi/miniconda3/envs/dolfinx-r:
#
# Name Version Build Channel
fenics-basix 0.6.0 py310hdf3cbec_0 conda-forge
fenics-dolfinx 0.6.0 py310hf97048e_101 conda-forge
fenics-ffcx 0.6.0 pyh56297ac_0 conda-forge
fenics-libbasix 0.6.0 h1284905_0 conda-forge
fenics-libdolfinx 0.6.0 h4cb9d57_101 conda-forge
fenics-ufcx 0.6.0 h56297ac_0 conda-forge
fenics-ufl 2023.1.1 pyhd8ed1ab_1 conda-forge

```

# Docker `dolfinx/lab:stable`

```python
print(dolfinx. __version__ , dolfinx.git_commit_hash)
print(petsc4py. __version__ )

```

```x
0.6.0 24f86a9ce57df6978070dbee22b3eae8bb77235f
3.17.5

```

# Docker `dolfinx/lab:nightly`

```python
print(dolfinx. __version__ , dolfinx.git_commit_hash)
print(petsc4py. __version__ )

```

```x
0.7.0.0 deac4f1cba124f09302f8bb501777f3e25a827c4
3.19.3

```

Solution:

 ![image](https://global.discourse-cdn.com/free1/uploads/fenicsproject1/original/2X/9/90f6470013c225b1c28d98c7020cf1c8ada99906.png)