Consolidate in-place implementations for ConservativePDSProblems and PDSProblems

[SKopecz]

Problem: Currently, every algorithm requires two separate in-place implementations: one for ConservativePDSProblem and one for PDSProblem. Because the latter requires additional destruction vectors, they use different cache structures, leading to significant code duplication.

Solution: This PR consolidates these implementations by adopting the strategy used in the out-of-place version. By using Nothing for destruction vectors in ConservativePDSProblems and leveraging multiple dispatch, we can now use a single unified code path.

Impact:

• Reduces code duplication significantly.

• Simplifies maintenance and the implementation of future algorithms.

• Consistent behavior between in-place and out-of-place APIs.

[SKopecz]

The PR currently contains the consolidation for MPRK22.

prob = prob_pds_linmod_inplace
alg = MPRK22(1.0)

Before:

julia> @benchmark solve($prob, $alg; save_everystep = false)
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
 Range (min … max):  76.319 μs …  26.239 ms  ┊ GC (min … max): 0.00% … 99.53%
 Time  (median):     81.111 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   91.810 μs ± 325.420 μs  ┊ GC (mean ± σ):  5.61% ±  1.71%

  █▆▄▃▄▆▆▅▃▂▂▁▁▁▁                                              ▁
  ██████████████████▇▇█▇▇▇▆▆▇▆▆▆▅▆▆▆▆▆▆▆▇▆▆▆▆▆▅▆▆▆▅▅▅▄▄▆▅▅▆▅▅▅ █
  76.3 μs       Histogram: log(frequency) by time       173 μs <

 Memory estimate: 45.47 KiB, allocs estimate: 955.

After:

julia> @benchmark solve($prob, $alg; save_everystep = false)
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
 Range (min … max):  77.018 μs …  33.066 ms  ┊ GC (min … max): 0.00% … 99.57%
 Time  (median):     87.283 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   93.850 μs ± 373.274 μs  ┊ GC (mean ± σ):  5.36% ±  1.41%

  ▅▃▂▄█▅▄▃▂▆▇▆▅▄▂▂▁▁▁ ▁                                        ▂
  █████████████████████▇▇█▇▇▇▅▆▆▆▇▅▄▆▆▅▅▅▆▄▅▄▅▄▄▂▅▅▄▄▂▄▅▅▄▂▄▃▅ █
  77 μs         Histogram: log(frequency) by time       151 μs <

 Memory estimate: 45.47 KiB, allocs estimate: 955.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

📢 Thoughts on this report? Let us know!

[coveralls]

Pull Request Test Coverage Report for Build 23067024649

Details

• 34 of 34 (100.0%) changed or added relevant lines in 2 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-0.2%) to 97.305%

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Totals
Change from base Build 22594658557:	-0.2%
Covered Lines:	1661
Relevant Lines:	1707

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💛 - Coveralls

[SKopecz]

The in-place implementations of all MPRK and SSPMPRK algorithms have been consolidated. The implementation of MPDeC schemes is different, therefore I wouldn't change it.

[ranocha]

Thanks! This looks reasonable to me. I just have some minor suggestions.

[ranocha]

Thanks!