Substitute BatchedTridiagonalSolver in SmootherTake

[julianlitz]

Summary

This PR refactors SmootherTake to use the new BatchedTridiagonalSolver class, replacing the previous vector-based approach with individual SymmetricTridiagonalSolver instances.
Beyond this core substitution, the PR includes significant improvements to code organization, documentation, and structure.

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Key Changes

1. Batched Solver Integration

2. Code Reorganization

• applyAscOrtho.cpp: Contains orthogonal stencil application
• solveAscSystem.cpp: Contains line-wise linear system solvers

3. Enhanced Documentation

Added comprehensive header documentation explaining:

• The coupled circle-radial smoothing algorithm

• Mathematical formulation:
  A_sc * u_sc = f_sc − A_sc^ortho * u_sc^ortho

• Update sequence: Black-Circle → White-Circle → Black-Radial → White-Radial

• Matrix structure and sparsity patterns

• Boundary condition handling

4. Stencil and Indexing Cleanup

• Eliminate unused code sections

5. Solver Workflow Improvements

• Reverted to GMGPolar v1 coloring scheme where even-indexed lines are black and odd-indexed lines are white
• Removed dynamic coloring logic that defined the outermost circle as black. The simpler, fixed coloring scheme improves code clarity while maintaining equivalent convergence properties.

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Benefits

• Performance: Batched solver enables better vectorization and cache locality
• Maintainability: Clear separation of concerns, reduced code duplication, simpler coloring logic
• Readability: Extensive documentation makes the algorithm transparent; fixed coloring scheme is easier to follow
• Extensibility: Batched approach scales more naturally to multiple systems
• Correctness: Simplified control flow reduces risk of indexing errors

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Testing Notes

Performance validation required before merge

I have not been able to verify whether the new BatchedTridiagonalSolver yields satisfactory performance compared to the previous vector-based approach.
Before merging this PR, I highly recommend that @EmilyBourne (or another team member) benchmarks the solver (Take + No extrapolation)
After adding export OMP_NUM_THREADS=$maxOpenMPThreads to run.sh, the new BatchedTridiagonalSolver does yield satisfactory performance. Using omp_set_num_threads(maxOpenMPThreads()) is not sufficient to set the correct thread count for Kokkos.

All functional tests should pass without modification.
The coloring scheme change alters the iteration order but should not impact convergence or solution quality.

Merge Request - GuideLine Checklist

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• There is at least one issue associated with the pull request.
• New code adheres with the coding guidelines
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If functions were changed or functionality was added:

• Tests for new functionality has been added
• A local test was succesful

If new functionality was added:

• There is appropriate documentation of your work. (use doxygen style comments)

If new third party software is used:

• Did you pay attention to its license? Please remember to add it to the wiki after successful merging.

If new mathematical methods or epidemiological terms are used:

• Are new methods referenced? Did you provide further documentation?

Checks by code reviewer(s):

• Is the code clean of development artifacts e.g., unnecessary comments, prints, ...
• The ticket goals for each associated issue are reached or problems are clearly addressed (i.e., a new issue was introduced).
• There are appropriate unit tests and they pass.
• The git history is clean and linearized for the merge request. All reviewers should squash commits and write a simple and meaningful commit message.
• Coverage report for new code is acceptable.
• No large data files have been added to the repository. Maximum size for files should be of the order of KB not MB. In particular avoid adding of pdf, word, or other files that cannot be change-tracked correctly by git.

[codecov]

Codecov Report

❌ Patch coverage is 97.91667% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 91.64%. Comparing base (57159b7) to head (5ef0b11).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/Smoother/SmootherTake/matrixStencil.cpp	75.00%	3 Missing ⚠️
src/Smoother/SmootherTake/solveAscSystem.cpp	97.77%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #171      +/-   ##
==========================================
+ Coverage   90.27%   91.64%   +1.36%     
==========================================
  Files          92       93       +1     
  Lines        5730     6317     +587     
==========================================
+ Hits         5173     5789     +616     
+ Misses        557      528      -29     

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