Modified Born Series - MBS
Core Algorithm Behind WaveSim
The Modified Born Series (MBS) is the core algorithm powering WaveSim, an innovative solver for wave propagation problems. Designed to simulate full-wave solutions to the Maxwell and Helmholtz equations, MBS enables efficient and accurate modelling even in extremely large or complex media, with guaranteed convergence.
At its core, MBS provides a mathematically rigorous and computationally efficient framework, capable of handling 3D simulations with a vast number of variables.
Why Modified?
The traditional Born Series suffers from slow convergence and even divergence in strongly scattering or large-scale environments. MBS addresses these limitations through a convergence-accelerating preconditioner, significantly enhancing both robustness and speed. This innovation enables WaveSim to handle both low and high-contrast media with ease.
Modified Born Series is especially well-suited for applications where accurate wave modelling is critical, including:
Biomedical imaging
Photonics
Acoustics
Geophysics
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.
The Modified Born Series Approach for the Helmholtz Equation
Osnabrugge, G., Leedumrongwatthanakun, S., & Vellekoop, I. M. (2016). A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media.
Journal of Computational Physics, 322, 113-124. https://doi.org/10.1016/j.jcp.2016.06.034
The main reference for Wavesim, introducing the Modified Born Series approach for the Helmholtz equation, which was later generalized to vector fields.
Ultra-Thin Boundary Layer for Computational Efficiency
Osnabrugge, G., Benedictus, M., & Vellekoop, I. M. (2021). Ultra-thin boundary layer for high-accuracy simulations of light propagation.
Optics Express, 29(2), 1649-1658.
https://doi.org/10.1364/OE.412833
Introduced a modified fast Fourier transform that enabled having an ultra-thin boundary layer, significantly reducing the computational costs and memory requirements.
Domain Decomposition for Large-Scale Simulations
Mache, S., & Vellekoop, I. M. (2024). Domain decomposition of the modified born series approach for large-scale wave propagation simulations.
arXiv preprint. arXiv:2410.02395.
Introduced the domain decomposition of the Modified Born Series for the Helmholtz equation and the Python implementation of Wavesim.
WaveSim Seminar
World’s fastest full Maxwell & Helmholtz solver by Ivo Vellekoop
Learn about WaveSim in a seminar presented at IESL - FORTH on March 6, 2024
