With Heterogeneous Exascale Particle-In-Cell (HEXAPIC) project, we intend to significantly shorten the simulation time of the fully kinetic approach and, at the same time, increase the level of complexity of plasma processes’ description to enable high-fidelity kinetic simulations of various technological processes involving plasma on reasonable time scales.

The bilateral partnership with the University of Luxembourg (uni.lu) is tackling the R&D withing several work packages (WPs) equally divided in workloads and reported as results and realization in sequel.

WP1 Project management

Both uni.lu and uni-lj.si partners contribute their extensive knowledge and experience to ensure effective project management.

Project established a website for the project [1] and for the HEXAPIC code [2] on Github. Regular meetings and working groups per WP were established as planned. At uni.lu and at uni-lj.si some postdoc researchers were hired during the project that started in September 2024 as agreed with uni.lu.

WP2 Plasma Physics Modules

WP2 develops a versatile and efficient kinetic plasma code by implementing algorithmic improvements and optimizations that build on the advancements from the other work packages.

We have developed a Particle-In-Cell (PIC) code for plasma physics simulations that consists of several modules: i) particle mover (Boris algorithm) for charged and neutral particles, ii) electrostatic field solver (HYPRE multigrid) with different boundary conditions (absorbing, reflective and periodic for particle, Dirichlet, Neumann and periodic for fields), iii) sources and sinks for particles and energy (planar and volumetric), iv) Monte-Carlo collisional module for interactions of charged and neutral particles (elastic, excitation, ionization and charge-exchange), and v) module for plasma-surface interactions (electron-impact and ion-impact secondary electron emission, ion recycling into neutrals) [2]. 

In this work package, all tasks have been completed and all milestones have been achieved.

WP3 Plasma Physics Use Cases

WP3 develops representative use cases from various plasma physics fields to demonstrate the HEXAPIC code’s capability to simulate large systems with complex boundary conditions, while serving as a development driver for WP2 and a performance benchmark for WP4 and WP5

We have established a PIC model of tokamak SOL with a divertor for HEXAPIC (milestone M3.1) and tests are underway on VEGA HPC.

WP4 Plasma Simulations on Heterogeneous Architecture

WP4 investigates the efficient use of complex heterogeneous HPC architectures (pre-exascale and exascale) by selecting and adapting suitable programming models, with special focus on multi-node scalability as well as adaptivity, geometry, and solvers. 

We have investigated the use of Alpaka3 library (Abstraction Library for Parallel Kernel Acceleration) into HEXAPIC. We have developed a basic PIC workflow that is platform-independent and supports the concurrent and cooperative use of multiple devices, including host CPUs (x86, ARM, RISC-V, and Power8+) and GPUs from different vendors (NVIDIA, AMD, and Intel). A variety of accelerator backends—CUDA, HIP, SYCL, OpenMP, and serial execution—are available and can be selected based on the target device. Only a single implementation of a user kernel is required, expressed as a function object with a standardized interface, which eliminates the need to write specialized CUDA, HIP, SYCL, OpenMP, or threading code.

Our partner, University of Luxembourg, has investigated and developed a plug-in GPU variant of the HYPRE field solver (using CUDA/OpenACC) to be used with the CPU-only MPI version of HEXAPIC. 

No milestones nor deliverables are due for the current reporting period, except for the general scientific publications.

WP5 Plasma Simulations on Exascale HPC Machines 

WP5 enables scalable and portable plasma simulations on pre-exascale and exascale systems by addressing portability, data partitioning, communication, I/O challenges, and integration of the programming model developed in WP4, with particular attention to geometry, adaptivity, solvers, and MPI.

We have improved the PIC parallel I/O (Task 5.1) by using openPMD (Open Standard for Particle-Mesh Data) with ADIOS2 (Adaptable Input Output System version 2) backend. This approach focuses on performance I/O scalability in high performance computing (HPC) applications and adaptability from unified interfaces that allow for several modes of transport (files, memory-to-memory).

We have conducted strong and weak scaling tests on VEGA HPC using the CPU-only MPI version of HEXAPIC [8].  The strong scaling test is limited by the amount of memory a single HPC node can have; therefore, the weak scaling is more representative for PIC codes. The weak scaling unveils parallel efficiency >85% at 32768 CPU cores.

No milestones nor deliverables are due for the current reporting period, except for the general scientific publications.

[1] HEXAPIC project website https://hexapic.github.io/project-website/  
[2] Heterogenous EXAscale Particle- In-Cell source code https://github.com/LeCAD-PEG/hexapic  
[3] S. Costea et al. Heterogeneous exascale Particle-in-Cell, ASHPC (2025), COBISS.SI-ID – 270248963 
[4] I. Vasileska et al. Accelerating sheath particle-in-cell simulations with StarPU, MIPRO (2025) COBISS.SI-ID – 244993795 
[5] N.Vukašinović, U.Urbas, L.Kos, I.Vasileska, Accelerating Particle-in-Cell simulations in Tokamak Scrape-off Layer using segmented surrogate models, EngAppAI (2026) COBISS.SI-ID – 270229507 
[6] I. Vasileska et al. Unveiling performance insights and portability achievements between CUDA and SYCL for particle-in-cell codes on different GPU architectures, MIPRO (2024), COBISS.SI-ID – 245014531 
[7] Unveiling performance insights and portability achievements between CUDA and SYCL for particle-in-cell codes on different GPU architectures, MIPRO (2024), COBISS.SI-ID – 245014531 
[8] HEXAPIC scaling documentation:  https://lecad-peg.github.io/hexapic/scaling/