Fix type instability in MeshArray constructor (Issue #78)

[hsugawa8651]

Summary

This PR fixes the type instability issue reported in #78, which causes excessive memory allocations when creating
MeshArray objects.

Problem

The mesh field in MeshArray struct was not type-stable, leading to:

• Excessive allocations (>800MB for simple operations)
• Poor performance in broadcast operations
• Type inference failures

Solution

Implemented type stabilization through:

1. Function barriers to isolate type-unstable code
2. Type stabilization helpers (_stabilize_mesh_type, _create_mesharray_typed)
3. Performance optimizations with @inline, @inbounds, @simd
4. Improved broadcast implementation with type-stable copyto!

Changes

• Modified src/mesharrays/dense.jl to add type stability improvements
  - Preserved original code as dense_original.jl for reference

Testing

Comprehensive testing shows:

• ✅ All mesh types are now concrete
• ✅ Memory allocations reduced dramatically
• ✅ Function type stability verified with @code_warntype
• ✅ All 1590 tests pass

Performance Verification

Here's a simple benchmark demonstrating the improvement:

using GreenFunc, GreenFunc.MeshArrays, CompositeGrids

# Create grids
k1 = CompositeGrids.SimpleG.Uniform([0.0, 1.0], 100)
k2 = CompositeGrids.SimpleG.Uniform([0.0, 1.0], 100)

# Create MeshArrays
ma1 = MeshArray(k1, k2; dtype=Float64)
ma2 = MeshArray(k1, k2; dtype=Float64)

# Fill with data
ma1.data .= rand(size(ma1.data)...)
ma2.data .= rand(size(ma2.data)...)

# Warmup
ma1 .+= ma2

# Measure allocations
@allocated ma1 .+= ma2  # Returns: 224 bytes
@allocated ma1 .*= 2.0  # Returns: 128 bytes

Results:

• Broadcast .+= operation: 224 bytes (down from >800MB reported in Type-instability problem #78)
• Broadcast .*= operation: 128 bytes
• Consistent low allocations for both small and large arrays

Fixes #78

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 78.58%. Comparing base (8e08d6a) to head (db75c05).
⚠️ Report is 31 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #116      +/-   ##
==========================================
+ Coverage   75.81%   78.58%   +2.77%     
==========================================
  Files          12       11       -1     
  Lines         430      439       +9     
==========================================
+ Hits          326      345      +19     
+ Misses        104       94      -10     

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[hsugawa8651]

Closing to incorporate CompatHelper dependency updates. Will resubmit with updated branch shortly.

[hsugawa8651]

Reopening after incorporating CompatHelper dependency updates:

• Added Statistics = "1" compat entry
• Added DelimitedFiles = "1" compat entry
• Maintains Julia 1.10 and 1.11 compatibility

[hsugawa8651]

Note: This PR includes the CompatHelper updates from PR #111 (DelimitedFiles) and PR #112 (Statistics), so those PRs can be closed upon merging this one.

[kunyuan]

Thank you very much for the updates!