[Paper] Modeling the Effect of Data Redundancy on Speedup in MLFMA Near-Field Computation

Source: arXiv - 2511.21535v1

Overview

The paper investigates why the near‑field (particle‑to‑particle, or P2P) stage of the Multilevel Fast Multipole Algorithm (MLFMA) runs slowly on GPUs, and proposes a simple “data‑redundancy” trick to make memory accesses more cache‑friendly. By deliberately storing extra copies of data, the authors improve spatial locality, which translates into up to 7× faster kernels. The work also introduces an analytical “Locality” model that predicts how much speedup to expect without having to run costly hardware‑specific benchmarks.

Key Contributions

• Data‑redundancy technique for the P2P operator that reduces memory‑access dispersion on GPUs.
• Locality metric & analytical model that combines data volume and access dispersion to forecast speedup trends across problem sizes and densities.
• Empirical validation on two very different MLFMA‑based codes:
  1. DBIM‑MLFMA, an electromagnetic inverse‑scattering solver with a regular grid layout.
  2. PhotoNs‑2.0, a stellar‑dynamics simulation with highly irregular particle distributions.
• Quantitative results showing up to 7× kernel speedup (cache behavior) and a modest 1.04× end‑to‑end application speedup after accounting for the overhead of data restructuring.
• Low‑intrusiveness: the redundancy injection requires only minor code changes, making it easy to adopt in existing GPU‑accelerated MLFMA implementations.

Methodology

1. Identify the bottleneck – The P2P kernel suffers from scattered memory reads/writes because each particle interacts with a non‑contiguous set of neighbors.
2. Introduce redundancy – Duplicate particle data so that each thread block works on a locally contiguous chunk, even if it means storing extra copies.
3. Measure locality – Define a Locality metric = (data volume) × (access dispersion). Lower dispersion → higher locality.
4. Build an analytical model – Using the metric, derive a formula that predicts the relative speedup of the P2P kernel as a function of problem size, particle density, and redundancy factor. No actual GPU profiling is needed.
5. Validate – Run the modified kernels on two real‑world applications (one regular, one irregular) across a range of sizes, compare measured speedups to model predictions, and assess the overall impact on the full application runtime.

Results & Findings

• Cache behavior improves dramatically: fewer cache misses and higher L2 hit rates were observed after redundancy injection.
• Overhead matters: the extra time spent reshaping and copying data offsets most of the kernel gains, which is why the overall application speedup stays modest.
• Model accuracy: the analytical model does not nail the exact numeric speedup, but it reliably predicts whether a given redundancy level will help or hurt performance across different problem scales.

Practical Implications

• GPU‑accelerated MLFMA libraries (e.g., for computational electromagnetics, astrophysics, or acoustics) can adopt the redundancy pattern with minimal refactoring, gaining immediate kernel‑level speedups.
• Performance‑portability: because the model is hardware‑agnostic, developers can estimate the benefit on new GPU generations before writing any code.
• Trade‑off awareness: teams can decide how much extra memory they’re willing to allocate based on the expected locality gain, which is especially useful on memory‑constrained devices (e.g., embedded GPUs).
• Tooling opportunity: the Locality metric could be baked into profiling tools or autotuners that automatically pick the optimal redundancy factor for a given dataset.

Limitations & Future Work

• Memory overhead: the technique requires additional storage proportional to the redundancy factor, which may be prohibitive for extremely large simulations.
• End‑to‑end gains limited: restructuring costs dominate once the kernel is already fast, capping overall application speedup near 1.04× in the studied cases.
• Model granularity: the analytical model captures trends but not precise speedup numbers; extending it to include cache‑hierarchy specifics could improve accuracy.
• Broader applicability: future work could explore redundancy for other MLFMA stages (e.g., far‑field translations) or for different hierarchical algorithms such as Barnes‑Hut or FMM in fluid dynamics.

Bottom line: By deliberately trading a bit of extra memory for better data locality, developers can unlock significant GPU kernel speedups in MLFMA’s near‑field computation—provided they keep an eye on the restructuring overhead. The paper’s locality‑based model offers a practical way to gauge that trade‑off before committing to code changes.

Authors

• Morteza Sadeghi

Paper Information

• arXiv ID: 2511.21535v1
• Categories: cs.DC, cs.PF
• Published: November 26, 2025
• PDF: Download PDF