Speed up idp correction function

[bennibolm]

This PR speeds up the implementation of perform_idp_correction! by

• looping over subcell interfaces for i in 2:nnodes(dg) instead of nodes for i in eachnode(dg) since no ifs are needed anymore.
• using multiply_add_to_node_vars!

Performance difference for polynomial degree of 3 (I'm using 1024 elements):

julia> @btime Trixi.perform_idp_correction!($u, $dt, $mesh, $equations, $solver, $cache)
  173.679 μs (0 allocations: 0 bytes)

julia> @btime Trixi.perform_idp_correction_new!($u, $dt, $mesh, $equations, $solver, $cache)
  137.115 μs (0 allocations: 0 bytes)

Polynomial degree of 5:

julia> @btime Trixi.perform_idp_correction!($u, $dt, $mesh, $equations, $solver, $cache)
  466.543 μs (0 allocations: 0 bytes)

julia> @btime Trixi.perform_idp_correction_new!($u, $dt, $mesh, $equations, $solver, $cache)
  308.394 μs (0 allocations: 0 bytes)

This was with Julia 1.12 on 1 thread.

[github-actions]

Review checklist

This checklist is meant to assist creators of PRs (to let them know what reviewers will typically look for) and reviewers (to guide them in a structured review process). Items do not need to be checked explicitly for a PR to be eligible for merging.

Purpose and scope

• The PR has a single goal that is clear from the PR title and/or description.
• All code changes represent a single set of modifications that logically belong together.
• No more than 500 lines of code are changed or there is no obvious way to split the PR into multiple PRs.

Code quality

• The code can be understood easily.
• Newly introduced names for variables etc. are self-descriptive and consistent with existing naming conventions.
• There are no redundancies that can be removed by simple modularization/refactoring.
• There are no leftover debug statements or commented code sections.
• The code adheres to our conventions and style guide, and to the Julia guidelines.

Documentation

• New functions and types are documented with a docstring or top-level comment.
• Relevant publications are referenced in docstrings (see example for formatting).
• Inline comments are used to document longer or unusual code sections.
• Comments describe intent ("why?") and not just functionality ("what?").
• If the PR introduces a significant change or new feature, it is documented in NEWS.md with its PR number.

Testing

• The PR passes all tests.
• New or modified lines of code are covered by tests.
• New or modified tests run in less then 10 seconds.

Performance

• There are no type instabilities or memory allocations in performance-critical parts.
• If the PR intent is to improve performance, before/after time measurements are posted in the PR.

Verification

• The correctness of the code was verified using appropriate tests.
• If new equations/methods are added, a convergence test has been run and the results
  are posted in the PR.

Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.85%. Comparing base (acc3215) to head (e1d0170).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2644   +/-   ##
=======================================
  Coverage   96.85%   96.85%           
=======================================
  Files         546      546           
  Lines       43208    43211    +3     
=======================================
+ Hits        41849    41852    +3     
  Misses       1359     1359           

Flag	Coverage Δ
unittests	96.85% <100.00%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[DanielDoehring]

Cool!

Some minor comments regarding code explanatory

[bennibolm]

The failing downstream test is expected since the test results from the sedov blast example slightly changed. I will adapt the file in Trixi2Vtk.jl when this one here is merged.

[bennibolm]

Since the first 3d PR is merged, I will also add the updated version of the 3d correction stage in this PR.

[bennibolm]

I added the new (updated) version of the 3d correction stage in e407366.
We get a similar speed up:
Polynomial degree of 3 (512 elements):

julia> @btime Trixi.perform_idp_correction!($u, $dt, $mesh, $equations, $solver, $cache)
  824.662 μs (0 allocations: 0 bytes)
julia> @btime Trixi.perform_idp_correction_new!($u, $dt, $mesh, $equations, $solver, $cache)
  740.468 μs (0 allocations: 0 bytes)

and with polynomial degree of 5:

julia> @btime Trixi.perform_idp_correction!($u, $dt, $mesh, $equations, $solver, $cache)
  3.046 ms (0 allocations: 0 bytes)
julia> @btime Trixi.perform_idp_correction_new!($u, $dt, $mesh, $equations, $solver, $cache)
  2.499 ms (0 allocations: 0 bytes)