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

TL;DR

This paper introduces data redundancy techniques to improve GPU performance in MLFMA near-field computations by enhancing data locality, validated through an analytical model and real-world applications, achieving significant kernel speedups.

Contribution

It presents a novel data redundancy approach to improve spatial locality in MLFMA P2P kernels and an analytical model to predict performance trends without hardware profiling.

Findings

Up to 7X kernel speedup due to better cache behavior

End-to-end speedup limited to 1.04X because of data restructuring overheads

Model reliably captures performance trends despite not predicting exact speedups

Abstract

The near-field (P2P) operator in the Multilevel Fast Multipole Algorithm (MLFMA) is a performance bottleneck on GPUs due to poor memory locality. This work introduces data redundancy to improve spatial locality by reducing memory access dispersion. For validation of results, we propose an analytical model based on a Locality metric that combines data volume and access dispersion to predict speedup trends without hardware-specific profiling. The approach is validated on two MLFMA-based applications: an electromagnetic solver (DBIM-MLFMA) with regular structure, and a stellar dynamics code (PhotoNs-2.0) with irregular particle distribution. Results show up to 7X kernel speedup due to improved cache behavior. However, increased data volume raises overheads in data restructuring, limiting end-to-end application speedup to 1.04X. While the model cannot precisely predict absolute speedups, it reliably captures performance trends across different problem sizes and densities. The technique is injectable into existing implementations with minimal code changes. This work demonstrates that data redundancy can enhance GPU performance for P2P operator, provided locality gains outweigh data movement costs.