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arxiv: 2606.19059 · v1 · pith:33A4MILInew · submitted 2026-06-17 · 🧮 math.NA · cs.DC· cs.NA· physics.comp-ph

A performance portable fast Ewald summation for Stokes flow

Gabriel Kosmacher , Ziyu Du , Joar Bagge , George Biros This is my paper

Pith reviewed 2026-06-26 20:06 UTC · model grok-4.3

classification 🧮 math.NA cs.DCcs.NAphysics.comp-ph
keywords Ewald summationStokes flowperformance portabilityGPU algorithmsN-body problemsparticle-to-gridperiodic domains
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0 comments X

The pith

A novel P2G algorithm delivers up to 16x speedup for Ewald summation in periodic Stokes flow on GPUs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops algorithms for Ewald summation to accelerate N-body Stokes flow simulations in periodic domains by splitting interactions into near-field particle-to-particle and far-field particle-to-grid plus grid-to-particle steps. It introduces a new particle-to-grid method to remove a common bottleneck in the far field and implements the full code with PyKokkos to run efficiently on NVIDIA and AMD GPUs as well as ARM and x86 CPUs. The result is high compute efficiency for the kernels and overall throughput of roughly 8 million particles per second on an H200 GPU at nine digits of accuracy. A multi-GPU test confirms scaling to 256 million particles on 64 GPUs with mostly bounded communication costs.

Core claim

We present GPU algorithms for Ewald summation methods for accelerating N-body Stokes flow problems in periodic domains. Like most N-body codes, Ewald sums use a near-field/far-field decomposition. The near field involves particle-to-particle (P2P) interactions. The far field primarily involves particle-to-grid (P2G) and grid-to-particle (G2P) interactions, as well as Fast Fourier Transforms. For each interaction, we investigate several algorithmic variants. Our implementation uses PyKokkos, a Python interface for the Kokkos C++ parallel programming framework, which supports portability to AMD/NVIDIA GPU and ARM/x86 CPU architectures. A novel P2G algorithm achieves up to 16× speedup compared

What carries the argument

The near-field/far-field decomposition of the Ewald sum, with a novel particle-to-grid (P2G) kernel that replaces the baseline far-field mapping step.

If this is right

  • The full Ewald sum code reaches 8 million particles per second on NVIDIA H200 GPUs and half a million on Grace CPUs at nine digits of accuracy.
  • P2P kernel compute efficiency reaches 84 percent on NVIDIA A100 and 73 percent on H200.
  • Weak scaling on up to 256 million particles across 64 GPUs keeps communication costs bounded except for the all-to-all particle sort.
  • The same code base runs on AMD GPUs, ARM CPUs, and x86 CPUs through the PyKokkos layer.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The P2G optimization may apply to other far-field summations if the underlying kernel structure is similar.
  • Switching the particle sort to neighbor-only communication in typical time-stepping loops could further improve large-scale runs.
  • Analytical performance models supplied in the paper can be used to predict runtimes on future hardware generations.

Load-bearing premise

The near-field/far-field decomposition and the specific algorithmic variants chosen for P2P, P2G, and G2P remain efficient and representative across the full range of target Stokes problems and particle distributions.

What would settle it

A measurement on a non-uniform particle distribution or different hardware showing that the novel P2G kernel does not reach the reported 16× speedup over baseline.

read the original abstract

We present GPU algorithms for Ewald summation methods for accelerating N-body Stokes flow problems in periodic domains. Like most N-body codes, Ewald sums use a near-field/far-field decomposition. The near field involves particle-to-particle (P2P) interactions. The far field primarily involves particle-to-grid (P2G) and grid-to-particle (G2P) interactions, as well as Fast Fourier Transforms. For each interaction, we investigate several algorithmic variants. Our implementation uses PyKokkos, a Python interface for the Kokkos C++ parallel programming framework, which supports portability to AMD/NVIDIA GPU and ARM/x86 CPU architectures. Double and single-precision numerical results, alongside analytical performance models, confirm the efficiency of our algorithms on AMD and NVIDIA GPU and on ARM and AMD CPU architectures. The P2P interaction achieves around 73% compute efficiency on NVIDIA H200, 84% on NVIDIA A100, 60% on AMD MI300, 52% on Grace CPU, and 68% on AMD Epyc CPU. A straightforward implementation of the P2G kernel can become a computational bottleneck. We introduce a novel P2G algorithm that achieves up to 16$\times$ speedup compared to a baseline GPU implementation. The overall Ewald sum code processes approximately 8 million particles per second on a H200 GPU, and about a half-million particles per second on a Grace CPU, for nine digits of accuracy. We also perform a multi-GPU weak scaling test on up to 256 million particles (64 GPUs) that shows bounded communication cost for all stages except the all-to-all particle sorting, which can be reduced to neighbor communication in the relevant time-stepping regime.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper presents GPU algorithms for Ewald summation in periodic Stokes flow N-body problems, employing a near-field/far-field split with P2P, P2G, and G2P interactions. Multiple algorithmic variants are explored for each, implemented via PyKokkos for portability across NVIDIA/AMD GPUs and ARM/x86 CPUs. Reported results include P2P compute efficiencies of 73% on H200, 84% on A100, 60% on MI300, 52% on Grace CPU, and 68% on Epyc CPU; a novel P2G algorithm yielding up to 16× speedup over a baseline GPU version; overall throughputs of ~8 million particles/sec on H200 and ~0.5 million on Grace CPU at 9-digit accuracy; and weak scaling to 256M particles on 64 GPUs with bounded communication except for all-to-all sorting.

Significance. If the measured throughputs and scaling hold, the work supplies a practical, architecture-portable implementation for large-scale Stokes flow simulations. The concrete efficiency percentages, analytical performance models, 16× P2G improvement, and 256M-particle weak-scaling test constitute reproducible evidence of utility for computational fluid dynamics and N-body codes.

minor comments (2)
  1. The abstract states 'nine digits of accuracy' without naming the error norm, tolerance definition, or reference solution used; add this detail in the results section for reproducibility.
  2. Clarify in the P2G section whether the 16× speedup baseline is a direct port of an existing CPU/GPU code or a naive Kokkos implementation, and list the exact particle counts and distributions for that measurement.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were raised.

Circularity Check

0 steps flagged

No significant circularity

full rationale

This is an implementation and benchmarking paper focused on GPU/CPU performance of Ewald summation variants for Stokes flow. All central claims (throughputs, 16× P2G speedup, 9-digit accuracy, scaling) are supported by direct measurements, analytical performance models, and empirical evaluation on specific hardware and particle distributions. No derivations, fitted parameters renamed as predictions, self-citations, or uniqueness theorems appear in the load-bearing steps; the near/far decomposition and kernel choices are presented as design decisions validated by timing data rather than reduced to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The contribution is algorithmic implementation and optimization; it rests on the standard mathematical validity of the Ewald decomposition for periodic Stokes problems but introduces no new fitted parameters, physical constants, or postulated entities.

axioms (1)
  • domain assumption The near-field/far-field split in Ewald summation remains computationally advantageous for the target particle counts and accuracies.
    Invoked in the opening description of the method and kernel design.

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