Multimodal-PE (v1.0.0): Paper code release for "Wide-angle multimodal parabolic equations: modeling of directional sound propagation in stratified range-dependent fluid waveguides." (Proc. R. Soc. A)

This release provides the paper-version implementation of the Wide-angle Multimodal Parabolic Equation (Multimodal-PE) method described in: "Wide-angle multimodal parabolic equations: modeling of directional sound propagation in stratified range-dependent fluid waveguides" (Proceedings A), . What this release contains A MATLAB implementation of the Multimodal-PE solver for directional sound propagation in stratified and range-dependent fluid waveguides. The method projects the acoustic pressure field onto a set of basis modes (sine functions satisfying boundary conditions at z = 0 and z = H) and advances the modal coefficients along range using a split-step Padé wide-angle approximation. Six demos are provided: Demos 1–5: reproduce the key numerical results reported in Figs. 3, 6, 9, 12, and 13 of the paper. Demo 6: demonstrates the computational efficiency for environments containing range-independent segmented regions. Reproducibility Each demo includes the corresponding environment input (*.env) and can be run to regenerate the associated paper figure(s). The read_env.m parser and README.md document the *.env format, including parameter definitions and units. How to run Clone/download this repository: https://github.com/TengjiaoHE/Multimodal-PE. Open MATLAB and add the repository root to your path. Run the scripts demo (demo 1–6). Each demo prints key settings and produces the corresponding figure(s). Notes This release is intended as a research code provided "as is", to support transparency and reproducibility of the published results. Please cite the Proceedings A article and this software release (Zenodo DOI, if applicable) when using this code.