Convergence troubles about shenfun HOT 16 CLOSED

Hi Thilo,
Thanks for reporting this bug. I did some checking and found a rather deep error that had to do with the inhomogeneous boundary conditions and the non-standard domain sizes you are using. I will push a fix as soon as possible. If you're using the shenfun source code, then you can fix it by replacing this line with scb=sc.

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I just realised that fixing the bug did not actually fix your code. It just fixed all other problems that used inhomogeneous boundary conditions and non-standard domain. Which may have been a recently introduced bug if you did managed to solve your problem for one of the cases above. I guess I will have to look some more.

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I don't think your variational forms are identical, so I don't understand how you can expect both methods to work?

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For the pure Dirichlet problem both variational forms should be valid because in both cases the boundary integral vanishes as the test function vanishes on the entire boundary.

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But I should be able to derive one from the other, and I can't.

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By use of the divergence theorem I was able to derive one form from the other.

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Hi Mikael,
in the following image I derived the equivalence of the two weak forms. Maybe you could take a look at it. The notation is a little different, I hope that is not a problem.

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Hi Mikael,
do you think that the two forms are equivalent? If you find some time to look into it, please let me know.

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Hi Thilo,
Sorry, forgot about it. There are some issues with your note that I don't believe are correct and I don't really have time to look closely into it. Do you by any chance have a supervisor or someone to discuss these derivations with? For one, $\boldsymbol{u} \cdot \nabla$ is not the same as $\nabla \cdot \boldsymbol{u}$.

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Hi Mikael,
I discussed the equivalence of the two variational forms with my supervisor and we both agreed that the two forms seem to be equivalent. I have changed the derivation in my comment above to index notation so it is now a bit more readable. If you find some time, I would be grateful if you could take a look at it.

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Hi Thilo,
I'm sorry for having been reluctant to look into this. It's very difficult and timeconsuming to find bugs when the reproducing code is 200 lines, and when it's not even obvious that it is a shenfun issue. However, I did have a look and quickly isolated the problem to the div div terms like inner(lambd*div(u), div(v)). There was an error in the precomputed matrices, and if you comment out line 1336

#((SD, 1), (SD, 0)): functools.partial(CSDSDmat, scale=-1.),

then it should work for the latest version of shenfun.
Actually, I realised this has deeper roots and will have to be fixed in inner. So great that you found and reported the error:-)

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Hi Mikael,

first of all thanks for taking the time to review this.

I tried commenting out the line

 File "/home/student01/Dokumente/Projects/convergence_problem.py", line 61, in <module>
    vector_tensor_spaces.append(TensorProductSpace(comm, tuple(tensor_spaces)))

  File "/home/student01/Dokumente/Projects/shenfun/shenfun/tensorproductspace.py", line 322, in __init__
    base.bc.set_tensor_bcs(base, self)

  File "/home/student01/Dokumente/Projects/shenfun/shenfun/tensorproductspace.py", line 1602, in set_tensor_bcs
    b_hat = T.forward(b).copy()

  File "/home/student01/anaconda3/lib/python3.7/site-packages/mpi4py_fft/mpifft.py", line 73, in __call__
    self._xfftn[-1](**kw)

  File "/home/student01/Dokumente/Projects/shenfun/shenfun/spectralbase.py", line 1389, in __call__
    return self.func(input_array, output_array, **kw)

  File "/home/student01/Dokumente/Projects/shenfun/shenfun/spectralbase.py", line 1389, in __call__
    return self.func(input_array, output_array, **kw)

  File "/home/student01/Dokumente/Projects/shenfun/shenfun/spectralbase.py", line 262, in forward
    self.bc.add_mass_rhs(self.forward.output_array)

  File "/home/student01/Dokumente/Projects/shenfun/shenfun/tensorproductspace.py", line 1678, in add_mass_rhs
    self.set_boundary_dofs(u)

  File "/home/student01/Dokumente/Projects/shenfun/shenfun/tensorproductspace.py", line 1718, in set_boundary_dofs
    u[self.base.si[-(M)+i]] = self.bcs[i]

  File "/home/student01/anaconda3/lib/python3.7/site-packages/sympy/core/expr.py", line 358, in __float__
    raise TypeError("can't convert expression to float")

TypeError: can't convert expression to float

If you find some time, please let me know if you can successfully run the script with the latest version of shenfun.

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Well, this looks more like a regular bug:-) I'll check it out.

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With my version of shenfun it runs with:

error (analytical solution): 2.5716607593388476e-16

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Are you using the latest version of shenfun from github? I may have fixed the problem you see quite recently.

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I just cloned the latest version and now it works :) Thanks again!

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