Add benchmark demonstrating Issue #78 fix

Benchmark results show:
- Broadcast operations: 224 bytes (down from >800MB)
- Consistent low allocations for 10x10 and 100x100 arrays
- Type stability confirmed

Author: hsugawa8651

benchmark/issue78_benchmark.jl

@@ -0,0 +1,83 @@
+#!/usr/bin/env julia
+# Broadcast operation benchmark for Issue #78
+
+using Pkg
+Pkg.activate(dirname(@__DIR__) * "/GreenFunc.jl")
+
+using GreenFunc
+using GreenFunc.MeshArrays
+using CompositeGrids
+
+println("Issue #78 - Broadcast Operation Benchmark")
+println("=" ^ 60)
+
+# Create grids for test
+k1 = CompositeGrids.SimpleG.Uniform([0.0, 1.0], 10)
+k2 = CompositeGrids.SimpleG.Uniform([0.0, 1.0], 10)
+
+# 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)...)
+
+println("\nTesting broadcast operations on 10x10 MeshArray:")
+println("-" ^ 40)
+
+# Warmup
+ma1 .+= ma2
+ma1 .*= 2.0
+
+# Reset
+ma1.data .= rand(size(ma1.data)...)
+
+# Measure broadcast allocations
+println("\nIn-place broadcast operations:")
+alloc_add = @allocated ma1 .+= ma2
+println("ma1 .+= ma2: $(alloc_add) bytes")
+
+alloc_mul = @allocated ma1 .*= 2.0
+println("ma1 .*= 2.0: $(alloc_mul) bytes")
+
+alloc_scalar = @allocated ma1 .+= 1.0
+println("ma1 .+= 1.0: $(alloc_scalar) bytes")
+
+# Test with larger arrays
+println("\nTesting with 100x100 MeshArray:")
+println("-" ^ 40)
+
+k1_large = CompositeGrids.SimpleG.Uniform([0.0, 1.0], 100)
+k2_large = CompositeGrids.SimpleG.Uniform([0.0, 1.0], 100)
+
+ma1_large = MeshArray(k1_large, k2_large; dtype=Float64)
+ma2_large = MeshArray(k1_large, k2_large; dtype=Float64)
+
+ma1_large.data .= rand(size(ma1_large.data)...)
+ma2_large.data .= rand(size(ma2_large.data)...)
+
+# Warmup
+ma1_large .+= ma2_large
+
+# Reset and measure
+ma1_large.data .= rand(size(ma1_large.data)...)
+
+alloc_add_large = @allocated ma1_large .+= ma2_large
+println("ma1 .+= ma2 (100x100): $(alloc_add_large) bytes")
+
+alloc_mul_large = @allocated ma1_large .*= 2.0
+println("ma1 .*= 2.0 (100x100): $(alloc_mul_large) bytes")
+
+println("\nConclusion:")
+if alloc_add == 0 && alloc_mul == 0
+    println("✓ Broadcast operations are allocation-free for small arrays")
+else
+    println("⚠ Broadcast operations still allocate for small arrays")
+end
+
+if alloc_add_large < 1000
+    println("✓ Large array broadcast allocations minimal: $(alloc_add_large) bytes")
+else
+    println("⚠ Large array broadcast allocations: $(round(alloc_add_large / 1024, digits=2)) KB")
+end