Adds `gradient_squared` method to `FiniteVolume`

[medha-14]

Description

Fixes #2979

Type of change

Please add a line in the relevant section of CHANGELOG.md to document the change (include PR #) - note reverse order of PR #s. If necessary, also add to the list of breaking changes.

• [ ] New feature (non-breaking change which adds functionality)
• [ ] Optimization (back-end change that speeds up the code)
• [ ] Bug fix (non-breaking change which fixes an issue)

Key checklist:

• [x] No style issues: $ pre-commit run (or $ nox -s pre-commit) (see CONTRIBUTING.md for how to set this up to run automatically when committing locally, in just two lines of code)
• [ ] All tests pass: $ python run-tests.py --all (or $ nox -s tests)
• [ ] The documentation builds: $ python run-tests.py --doctest (or $ nox -s doctests)

You can run integration tests, unit tests, and doctests together at once, using $ python run-tests.py --quick (or $ nox -s quick).

Further checks:

• [ ] Code is commented, particularly in hard-to-understand areas
• [ ] Tests added that prove fix is effective or that feature works

[codecov[bot]]

Codecov Report

:x: Patch coverage is 7.14286% with 13 lines in your changes missing coverage. Please review. :white_check_mark: Project coverage is 98.72%. Comparing base (df2dbbd) to head (48cfa9a). :warning: Report is 1 commits behind head on develop.

Files with missing lines	Patch %	Lines
src/pybamm/spatial_methods/finite_volume.py	7.14%	13 Missing :warning:

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #4540      +/-   ##
===========================================
- Coverage    98.77%   98.72%   -0.05%     
===========================================
  Files          321      321              
  Lines        27717    27741      +24     
===========================================
+ Hits         27377    27388      +11     
- Misses         340      353      +13     

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[kratman]

@medha-14 This PR should also add tests and use the gradient squared function where appropriate

[medha-14]

I have written a test for the gradient_squared method . Could you please advise on where I should incorporate the use of the gradient_squared method ?

[agriyakhetarpal]

I noticed that in the gradient_matrix method above the lines you touched, we could try building the gradient matrix directly in sparse format instead of converting to it later as a potential further improvement – by just pre-allocating all indices at once, and passing them to scipy.sparse.block_diag in favour of the current Kronecker product. Some part of the time there is spent in the array creation alongside the matrix construction, so maybe we can get a 2-4x improvement for larger matrices. Would you like to try that (not in this PR but in a separate one)? I'll be able to help, shall you need it.

[medha-14]

I noticed that in the gradient_matrix method above the lines you touched, we could try building the gradient matrix directly in sparse format instead of converting to it later as a potential further improvement – by just pre-allocating all indices at once, and passing them to scipy.sparse.block_diag in favour of the current Kronecker product. Some part of the time there is spent in the array creation alongside the matrix construction, so maybe we can get a 2-4x improvement for larger matrices. Would you like to try that (not in this PR but in a separate one)? I'll be able to help, shall you need it.

@agriyakhetarpal, I would like to give this a go and explore the implementation further. I’d be grateful for any additional insights or recommendations you might have as I move forward.

[medha-14]

Any recommendations on how to improve the tests I have written for this one? or any other things I can change?

[medha-14]

Thanks, @medha-14! The code looks fine to me as long as coverage passes – I'm happy to approve it after that. I just have one additional comment.

I will prioritize fixing the coverage as soon as possible.

[kratman]

@medha-14 Is this still being worked on?

[medha-14]

Yes, I’m still on it . I’ve had a bit of a gap but will be picking it up again.