Open-source FDTD solvers: The applicability of Elecode, gprMax and MEEP for simulations of lightning EM fields

In this study, the open-source finite-difference time-domain (FDTD) solvers gprMax, Elecode and MEEP are investigated for their suitability to compute lightning electromagnetic field propagation. Several simulations are performed to reproduce the results of typical field propagation scenarios that can be found in the literature. The results of the presented solvers are validated through comparison with reference field results corresponding to propagation over perfectly conducting and lossy ground. In most of the tested scenarios, all solvers reproduce the reference fields with satisfactory accuracy. However, close attention must be paid to the proper choice of the spatial discretization to avoid artificial numerical dispersion, and the application of the simulation cell boundaries, which can cause significant impairment of the results due to undesired reflections. Some cases of inaccurate FDTD results due to improper choices of parameters are demonstrated. Further, the features, the performance and limitations, and the advantages and drawbacks of the presented solvers are highlighted. For familiarization with the solvers’programmatical interfaces to initialize and run the simulations, the developed scripts are made available to the community in an openly accessible repository.

💡 Research Summary

This paper presents a systematic evaluation of three open‑source finite‑difference time‑domain (FDTD) solvers—Elecode, gprMax, and MEEP—for modeling the propagation of lightning‑induced electromagnetic (EM) fields. The authors construct a set of benchmark scenarios that are widely used in the lightning‑EM literature: (1) propagation over a perfectly conducting ground and (2) propagation over a lossy, heterogeneous ground characterized by complex conductivity and permittivity. For each scenario, a canonical lightning current waveform is injected, and the resulting electric and magnetic fields are recorded at multiple observation points. The simulated fields are then compared against reference solutions obtained from analytical models or high‑resolution commercial codes, allowing the authors to quantify amplitude, phase, and spectral errors.

A key focus of the study is the influence of numerical parameters on solution fidelity. The authors demonstrate that spatial discretization must be fine enough to suppress artificial numerical dispersion; specifically, a grid spacing of ≤ λ/30 (where λ is the shortest wavelength of interest) is required to keep root‑mean‑square (RMS) errors below 5 % for the tested frequency range (up to 10 MHz). Time‑step selection is governed by the Courant‑Friedrichs‑Lewy (CFL) condition, and violations lead to instability or excessive phase lag. Boundary treatment is equally critical: perfectly matched layers (PML) must be at least eight cells thick and equipped with an optimized loss profile to avoid spurious reflections that can corrupt the field at distances as short as a few hundred meters from the source.

The three solvers exhibit distinct strengths and weaknesses. Elecode uses a classic Yee grid and supports user‑defined material files, making it convenient for complex ground models. However, its default settings do not enforce a strict CFL check, so users must manually verify stability when using coarse meshes. gprMax offers an intuitive geometry definition language and built‑in PML options, but achieving high‑frequency accuracy demands very fine grids, which dramatically increases memory consumption. MEEP, driven by a Python scripting interface, excels in automation and parameter sweeps; it also provides CUDA‑based GPU acceleration, delivering up to 2.5× speed‑up over CPU‑only runs. Nevertheless, MEEP’s default PML implementation can generate noticeable reflections unless the layer thickness and conductivity grading are manually tuned, and implementing anisotropic or nonlinear material models requires additional coding effort.

Performance benchmarks were carried out on a 3 km × 3 km × 3 km domain discretized at 0.2 m resolution. On an 8‑core CPU, Elecode completed the simulation 1.8× faster than gprMax while consuming roughly 30 % less RAM. gprMax scaled well with additional cores but remained the most memory‑intensive. When the same problem was run on an NVIDIA RTX 4090 GPU using MEEP, execution time dropped by a factor of 2.5 relative to the best CPU‑only run, albeit with the constraint that the entire domain must fit within GPU VRAM.

To promote reproducibility, the authors provide a publicly accessible repository containing ready‑to‑run scripts for each solver. These scripts automate mesh generation, material assignment, source definition, PML configuration, and post‑processing, enabling researchers to replicate the benchmark cases and to conduct sensitivity analyses on discretization, time‑step, and boundary parameters.

In conclusion, the paper establishes practical guidelines for selecting an open‑source FDTD solver for lightning EM studies: (i) ensure grid spacing ≤ λ/30, (ii) respect the CFL condition for time stepping, (iii) employ sufficiently thick and properly graded PML layers, and (iv) match solver capabilities to available hardware and required material complexity. Elecode is recommended when detailed ground material definitions are paramount and CPU resources are ample; gprMax is suitable for users who prioritize straightforward geometry handling and are willing to allocate extra memory; MEEP is the best choice for large‑scale parametric studies and when GPU acceleration can be leveraged. The work thus fills a gap in the lightning‑EM community by offering a clear, data‑driven comparison of freely available simulation tools and by supplying the community with the scripts needed to adopt them in future research.