Foundational Publications
The development of MBS is underpinned by three foundational research articles that describe the algorithm’s convergence properties and its advanced boundary handling techniques. These papers have significantly advanced the state-of-the-art in wave simulation.
Journal of Computational Physics
Volume 322, 1 October 2016, Pages 113-124
A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media
Osnabrugge, G., Leedumrongwatthanakun, S., & Vellekoop, I. M.
The main reference for Wavesim, introducing the Modified Born Series approach for the Helmholtz equation, which was later generalized to vector fields. https://doi.org/10.1016/j.jcp.2016.06.034
@article{osnabrugge2016convergent,
author={Osnabrugge, Gerwin and Leedumrongwatthanakun, Saroch and Vellekoop, Ivo M},
title="{A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media}",
journal="{Journal of Computational Physics}",
year={2016},
volume={322},
pages={113-124},
publisher={Elsevier}
}
Optics Express
Volume 29, Issue 2, 2021, Pages 1649-1658
Ultra-thin boundary layer for high-accuracy simulations of light propagation
Osnabrugge, G., Benedictus, M., & Vellekoop, I. M.
Introduced a modified fast Fourier transform that enabled having an ultra-thin boundary layer, significantly reducing the computational costs and memory requirements. https://doi.org/10.1364/OE.412833
@article{osnabrugge2021ultra,
author={Osnabrugge, Gerwin and Benedictus, Maaike and Vellekoop, Ivo M},
title={Ultra-thin boundary layer for high-accuracy simulations of light propagation},
journal="{Optics Express}",
year={2021},
volume={29},
number={2},
pages={1649-1658},
publisher={Optica Publishing Group}
}
Journal of Computational Physics
Volume 550, 1 April 2026, 114619
Domain decomposition of the modified Born series approach for large-scale wave propagation simulations
Mache, S., & Vellekoop, I. M.
Introduced the domain decomposition of the Modified Born Series for the Helmholtz equation and the Python implementation of Wavesim. https://doi.org/10.1016/j.jcp.2025.114619
@article{mache2024domain,
author = {Swapnil Mache and Ivo M. Vellekoop},
title = {Domain decomposition of the modified Born series approach for large-scale wave propagation simulations},
journal = {Journal of Computational Physics},
year = {2026},
volume = {550},
pages = {114619},
issn = {0021-9991},
doi = {https://doi.org/10.1016/j.jcp.2025.114619},
url = {https://www.sciencedirect.com/science/article/pii/S0021999125009015},
keywords = {Helmholtz equation, Born series, Domain decomposition},
}