Threaded Sparse Multiplication - Scaling

Test Configuration:
Matrix type: 2D Laplacian (5-point stencil)
Operation: A × A using ⊛ operator
Julia threads: 8
Benchmarking: BenchmarkTools.jl
Date: 2025-12-14 10:52:53

Speedup vs Single-Threaded Standard (*)

Matrix Size	1 thread	2 threads	4 threads	8 threads
1 × 1	0.90×	0.90×	0.89×	0.90×
9 × 9	0.97×	0.96×	0.97×	0.95×
100 × 100	1.01×	1.00×	1.00×	1.00×
1K × 1K	1.00×	1.07×	1.29×	1.05×
10K × 10K	1.01×	1.24×	2.12×	2.94×
100K × 100K	1.00×	1.46×	2.53×	3.87×
1M × 1M	1.00×	1.39×	2.34×	3.63×
10M × 10M	1.00×	1.38×	2.43×	3.45×

Notes:

Speedup = (single-threaded * time) / (threaded ⊛ time with N threads)
Green: ≥1.5× speedup, Red: <0.8× (slower than baseline)
Times measured using BenchmarkTools.jl @belapsed