Features

Integration Schemes

• Centroid: Single point at element center (fastest)
• Gauss Quadrature: 1, 4, or 10-point rules for tetrahedra (most accurate)
• Dense Sampling: Adaptive grid sampling (good for large elements)

Integration Methods

Multiple integration schemes are offered:

• Dense Stepping: Uniform grid sampling within elements (default)
• Voxel-Based: Sample at voxel intersections (faster for large elements)

Performance Optimisations

LUMA has undergone a lot of work to try and be efficient. If you find something that does not perform as well as you expect, or you think I have implimented something wrong, please let me know.

The current optimisation steps are:

• Parallel material assignment: Elements processed in parallel across CPU cores
• Direct buffer writing: Manual formatting bypasses standard library overhead
• Pre-computed lookups: Material ID vectors eliminate HashMap lookups
• Large buffer batches: 1MB+ string buffers minimise I/O operations
• Batch processing: 5000 elements per batch reduces syscall overhead
• Single write operations: Replace many small writes with bulk operations
• Spatial acceleration: Efficient voxel lookup with bounds checking
• SIMD utilisation: Vectorised mathematical operations where possible