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:

• 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]

Codecov Report

Attention: Patch coverage is 7.14286% with 13 lines in your changes missing coverage. Please review.

Project coverage is 99.21%. Comparing base (9ac0b5b) to head (91aeea5).

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

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #4540      +/-   ##
===========================================
- Coverage    99.27%   99.21%   -0.06%     
===========================================
  Files          300      300              
  Lines        22795    22809      +14     
===========================================
+ Hits         22630    22631       +1     
- Misses         165      178      +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 ?

[brosaplanella]

Just some changes, mostly to improve coverages, but getting there!

[agriyakhetarpal]

Here, boundary_conditions is mentioned in the function's signature, but it doesn't look like it's used in the logic of the function anywhere?

[medha-14]

Thank you for the feedback. I've updated the gradient_squared function to correctly handle boundary conditions, and I've adjusted the tests accordingly to verify these changes.

[agriyakhetarpal]

Thanks, @medha-14!

[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.