arxiv: 2605.05469 · v1 · submitted 2026-05-06 · 💻 cs.CE · physics.comp-ph

Recognition: unknown

A Comparison of Massively Parallel Performance Portable Particle-in-Cell schemes for electrostatic kinetic plasma simulations

Sonali Mayani , Paul Fischill , Sriramkrishnan Muralikrishnan , Andreas Adelmann

Authors on Pith no claims yet

Pith reviewed 2026-05-08 15:19 UTC · model grok-4.3

classification 💻 cs.CE physics.comp-ph

keywords particle-in-cellpoisson solverperformance portabilityplasma simulationlandau dampinggpu computingvlasov-poissonparticle-in-fourier

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The pith

FFT solver is fastest in absolute time for electrostatic PIC simulations but limited in applicability, while PIF offers scalable high-fidelity alternative

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

The paper compares different Poisson solvers inside performance-portable Particle-in-Cell schemes for electrostatic Vlasov-Poisson plasma simulations, using the IPPL library. It benchmarks an FFT pseudo-spectral solver against matrix-free PCG and FEM solvers, plus a novel Particle-in-Fourier scheme that avoids a real-space grid, on the Landau damping test case with 512^3 and 1024^3 grids. Results are collected on AMD and Nvidia GPU platforms to measure absolute time, scaling, and portability. A sympathetic reader would care because large-scale kinetic plasma modeling on modern supercomputers requires choosing methods that balance speed, fidelity, and hardware independence. If the comparisons hold, they give concrete guidance on when to accept higher per-step cost for better applicability or scalability.

Core claim

In absolute time the FFT solver is advantageous, but is limited in its applicability. All other field solvers in the PIC scheme are an order-of-magnitude more expensive in terms of time, but scale similarly to the FFT case in the electrostatic PIC context. The PIF scheme serves as a high fidelity alternative to standard PIC, and while it is costlier than the FFT-based PIC scheme, it shows excellent scalability on all the architectures.

What carries the argument

The solve phase of the PIC loop comparing FFT pseudo-spectral, matrix-free PCG, matrix-free FEM, and non-uniform-FFT-based PIF Poisson solvers inside the IPPL library on the Landau damping benchmark.

If this is right

When the FFT solver applies, it should be selected to minimize wall-clock time per PIC step.
Matrix-free PCG and FEM solvers deliver comparable scaling to FFT at roughly ten times the cost.
The PIF scheme trades higher cost for high fidelity and strong scaling across GPU architectures.
The IPPL implementations achieve performance portability on both AMD and Nvidia GPUs.

Where Pith is reading between the lines

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

For problems with non-periodic boundaries where FFT cannot be used, PIF or the matrix-free solvers could substitute without large scalability penalties.
The observed scaling of PIF suggests it may enable higher-resolution or longer-time plasma simulations on exascale machines.
Benchmarking the same solvers on nonlinear or multi-scale plasma phenomena would test whether the reported performance ordering persists.

Load-bearing premise

The Landau damping test case with the chosen grid sizes and particle loading is representative enough to draw general conclusions about solver performance and portability for electrostatic kinetic plasma simulations.

What would settle it

Running the same solvers on a different electrostatic test problem such as two-stream instability and observing substantially different relative costs or scaling curves.

Figures

Figures reproduced from arXiv: 2605.05469 by Andreas Adelmann, Paul Fischill, Sonali Mayani, Sriramkrishnan Muralikrishnan.

**Figure 1.** Figure 1: The PIC loop starts with initialization of the particle view at source ↗

**Figure 2.** Figure 2: Energy of the electric field component in view at source ↗

**Figure 3.** Figure 3: Strong scaling study for case A ( view at source ↗

**Figure 4.** Figure 4: Strong scaling efficiency for case A (5123 and 8 particles per cell) for all presented solvers on all three architectures considered. 32 64 128 256 512 1024 2048 No. of total GPUs 10 0 10 1 10 2 Time [s] FFT ALPS FFT LUMI FFT Booster FEM ALPS FEM LUMI FEM Booster PCG ALPS PCG LUMI PCG Booster PIF ALPS PIF LUMI PIF Booster Ideal 1/N view at source ↗

**Figure 7.** Figure 7: Breakdown of the total time of the Landau Damping view at source ↗

**Figure 8.** Figure 8: Weak scaling for the four solvers on all architec view at source ↗

**Figure 10.** Figure 10: The main bottleneck for FEM is the halo cell accumulation view at source ↗

**Figure 10.** Figure 10: Breakdown of the total time of the Landau Damp view at source ↗

**Figure 11.** Figure 11: CG iteration counts per time step with the FEM view at source ↗

**Figure 12.** Figure 12: Time spent per time step on the CG iterations view at source ↗

read the original abstract

We compare different Poisson solvers within the context of an electrostatic Vlasov-Poisson system. These schemes are implemented as part of the IPPL (Independent Parallel Particle Layer) library (Frey et al., 2024), which provides performance portable and dimension independent building blocks for scientific simulations requiring particle-mesh methods, with Eulerian (mesh-based) and Lagrangian (particle-based) approaches. The simulation used to compare the performance and portability of the schemes is Landau damping, part of a set of mini-applications implemented to benchmark and showcase the capabilities of the IPPL library (Muralikrishnan et al., 2024). We use grid-sizes of $512^3$ and $1024^3$ with 8 particles per cell, running with different algorithms in the solve phase of the Particle-in-Cell (PIC) loop: a Fast Fourier Transform (FFT) pseudo-spectral solver, a matrix-free finite difference Preconditioned Conjugate Gradient (PCG) solver, and a matrix-free Finite Element (FEM) solver. We also compare these PIC schemes to the novel Particle-in-Fourier (PIF) scheme, which performs interpolations using non-uniform FFTs thereby avoiding a grid in the real space. We obtain results on different computing architectures, such as AMD GPUs (LUMI at CSC), and Nvidia GPUs (Alps at CSCS and JUWELS Booster at J\"ulich Supercomputing Center), showcasing portability. In terms of absolute time the FFT solver is advantageous, but is limited in its applicability. All other field solvers in the PIC scheme are an order-of-magnitude more expensive in terms of time, but scale similarly to the FFT case in the electrostatic PIC context. The PIF scheme serves as a high fidelity alternative to standard PIC, and while it is costlier than the FFT-based PIC scheme, it shows excellent scalability on all the architectures.

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.

Desk Editor's Note private letter to a colleague

This is a straightforward GPU timing comparison of known PIC solvers in an existing library on one standard test case, with no new methods or broad validation.

read the letter

The paper's core contribution is a set of wall-clock measurements for FFT, matrix-free PCG, FEM, and PIF Poisson solvers inside the IPPL library, all applied to the same Landau damping run at 512^3 and 1024^3 grids with 8 particles per cell. It reports results on AMD and Nvidia GPUs and states that FFT is fastest in absolute time but limited in scope, the other PIC solvers are roughly ten times slower yet scale similarly, and PIF delivers high fidelity with good scalability. Those numbers and the cross-architecture portability data are the only concrete outputs. The work does a clean job of exercising the library's building blocks on real hardware and making the relative costs explicit for this setup. That kind of direct comparison can save time for groups deciding which solver to wire into a production code. The obvious soft spot is the single test problem. Landau damping is linear, periodic, and uniform, so the FFT enjoys global spectral advantages and low communication while iterative solvers stay cheap. Nothing in the abstract or the reported claims shows how the order-of-magnitude gap or the scaling similarity holds up once the problem becomes nonlinear, inhomogeneous, or non-periodic. Without those checks, the general statements about electrostatic kinetic plasma simulations rest on a narrow base. The absence of error bars or convergence checks in the summary also leaves the robustness of the timings unclear. This paper is aimed at people who run or maintain large-scale PIC codes on current GPU clusters and want practical guidance on solver choice within the IPPL framework. A reader already using that library or facing similar hardware decisions will get usable information. It deserves peer review because the measurements are hardware-grounded and the portability results are relevant, even though the authors would need to add at least one more demanding test case and quantitative validation to make the broader claims stick.

Referee Report

2 major / 1 minor

Summary. The manuscript compares the performance and portability of Poisson solvers (FFT pseudo-spectral, matrix-free finite-difference PCG, matrix-free FEM) inside standard electrostatic PIC schemes and a novel Particle-in-Fourier (PIF) scheme that uses non-uniform FFTs to avoid a real-space grid. All methods are implemented via the IPPL library and benchmarked on the Landau damping problem at 512^3 and 1024^3 grids with 8 particles per cell, run on AMD (LUMI) and Nvidia (Alps, JUWELS) GPUs. The central claims are that FFT is fastest in absolute wall-clock time but limited in applicability, the other PIC solvers are roughly an order of magnitude more expensive yet exhibit comparable strong scaling, and PIF offers higher fidelity at increased cost while maintaining excellent scalability across architectures.

Significance. If the reported cost ratios and scaling behaviors prove robust, the work supplies concrete, hardware-grounded guidance for selecting field solvers in performance-portable particle-mesh codes for electrostatic plasma simulations. Direct timings on multiple GPU platforms and the use of an open library (IPPL) constitute practical strengths that could help practitioners weigh the trade-off between spectral accuracy, iterative solver overhead, and portability.

major comments (2)

Abstract: the statements that 'All other field solvers in the PIC scheme are an order-of-magnitude more expensive' and 'scale similarly to the FFT case' are presented without tabulated timings, speed-up factors, iteration counts, or error bars, rendering the quantitative claims difficult to verify or reproduce.
Abstract and Landau-damping benchmark description: the generalization to 'electrostatic kinetic plasma simulations' rests on a single linear, periodic, uniform-density test; in nonlinear or inhomogeneous regimes the iteration counts of PCG/FEM and the communication pattern of PIF NUFFTs can increase substantially, so the claimed order-of-magnitude cost ratio and scaling similarity lack a secure anchor for the broader class named in the title.

minor comments (1)

A compact table listing absolute wall-clock times, strong-scaling efficiencies, and solver iteration counts for each architecture and grid size would improve readability and allow direct comparison of the reported order-of-magnitude difference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive evaluation of the practical value of our performance-portability study. We address each major comment below, proposing targeted revisions where appropriate while defending the manuscript's scope and claims on the basis of the presented evidence.

read point-by-point responses

Referee: Abstract: the statements that 'All other field solvers in the PIC scheme are an order-of-magnitude more expensive' and 'scale similarly to the FFT case' are presented without tabulated timings, speed-up factors, iteration counts, or error bars, rendering the quantitative claims difficult to verify or reproduce.

Authors: We agree that the abstract would benefit from greater quantitative grounding to improve verifiability. The full manuscript already reports detailed wall-clock timings, strong-scaling efficiencies, and iteration counts for the PCG and FEM solvers in the results section (Figures 3–5 and associated text for the 512³ and 1024³ cases on LUMI, Alps, and JUWELS). In the revised manuscript we will update the abstract to include representative quantitative statements (e.g., “approximately 8–12× higher wall-clock time” and “strong-scaling efficiencies above 80 % up to full machine scale”) while explicitly referencing the benchmark data and tables in the main text. This change preserves abstract length while making the claims directly traceable to the reported measurements. revision: yes
Referee: Abstract and Landau-damping benchmark description: the generalization to 'electrostatic kinetic plasma simulations' rests on a single linear, periodic, uniform-density test; in nonlinear or inhomogeneous regimes the iteration counts of PCG/FEM and the communication pattern of PIF NUFFTs can increase substantially, so the claimed order-of-magnitude cost ratio and scaling similarity lack a secure anchor for the broader class named in the title.

Authors: Landau damping is a standard, widely adopted benchmark precisely because it isolates the essential kinetic and electrostatic features of the Vlasov–Poisson system while remaining computationally tractable for large-scale performance studies. The observed cost ratios and scaling behaviors arise from fundamental properties of the solvers (direct FFT versus matrix-free iterative methods) and the NUFFT communication pattern in PIF, which are implemented in the performance-portable IPPL library; these algorithmic traits are expected to govern relative performance even when iteration counts rise in more demanding regimes. Nevertheless, we acknowledge that the single-test scope limits the strength of the generalization. In the revised manuscript we will add an explicit limitations paragraph in the discussion section that (i) qualifies the claims to the tested linear periodic regime, (ii) notes that iteration counts and NUFFT overhead may increase in nonlinear or inhomogeneous cases, and (iii) recommends future benchmarks (e.g., two-stream instability or density-gradient problems) to extend the comparison. This revision anchors the title and abstract more securely without altering the reported results. revision: partial

Circularity Check

0 steps flagged

No circularity: performance claims rest on direct hardware timings for a fixed test case

full rationale

The paper reports empirical wall-clock timings and scaling behavior obtained by executing the IPPL-based PIC and PIF codes on AMD and Nvidia GPUs for the Landau damping problem at 512^3 and 1024^3 grids with 8 ppc. No equations, fitted parameters, or predictions are derived; the central statements (FFT fastest but limited, other solvers ~10x slower yet similarly scaling, PIF high-fidelity with good scalability) are direct summaries of measured run times. Self-citations to the IPPL library (Frey et al. 2024) and mini-applications (Muralikrishnan et al. 2024) supply only the implementation framework and test definition; they do not supply the numerical results or the cost-ratio claims. Because the load-bearing content is fresh benchmark data rather than a closed derivation or self-referential fit, the analysis contains no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard assumptions of the electrostatic Vlasov-Poisson system and the Landau damping test; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (1)

domain assumption Landau damping is a representative test for electrostatic kinetic plasma behavior
Invoked when using the simulation to compare solver performance and portability

pith-pipeline@v0.9.0 · 5670 in / 1320 out tokens · 41044 ms · 2026-05-08T15:19:32.845293+00:00 · methodology

discussion (0)

Reference graph

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