EffectiveTMatrix.jl

EffectiveTMatrix.jl is a Julia package for simulating wave scattering in media composed of randomly packed particles. It implements the Effective Waves Method as described in Napal et al. (2024), enabling efficient computation of the scattering after ensemble averaging over particles configurations.

The package also includes brute-force Monte Carlo simulations to validate the accuracy and convergence of the effective model against direct ensemble averages.

Beyond numerical validation, there are industrial applications that need a method to calculate waves scattered from a cylinder with particles. Examples of cylinders filled with cylindrical particles include concrete beams reinforced with iron, cables filled with wires or fibre-reinforced composite. Applications include designing cylinders with exotic effective properties or developing methods to measure the cylindrical particles.

Reference:

[Napal et al. (2024)] K. K. Napal, P. S. Piva, and A. L. Gower. Effective T-matrix of a cylinder filled with a random two-dimensional particulate. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2292):20230660, 2024.

Figure 1. Incident plane wave scattering.

Figure 1. Modal source scattering.

Features

• Compute effective T-matrices for 2D particle-filled domains
• Implement the Effective Waves Method for wave scattering
• Run Monte Carlo simulations for validation and benchmarking
• Designed with extensibility for future wave scattering models

Installation

Install Julia v1.6.1 or later then run in the Julia REPL:

using Pkg

Then type ] to enter the Pkg REPL mode and run

pkg> add https://github.com/Kevish-Napal/EffectiveTMatrix.jl.git

Learn through examples

Example 1: compute the coefficients of the effective T-matrix and the resulting averaged scattered field from a given incident field.

--> examples/pressure_field/pressure_field.ipynb

Example 2: covers the main functionality of the package. That is validation of the Effective Waves Method (fast computation of the effective T-matrix) against the Monte Carlo method (slow computation of the effective T-matrix based on averaging of simulated scattering data).

--> examples/monte_carlo_validation/monte_carlo_validation.ipynb

Example 3: attempts to clarify the theory by exhibiting the "mode to mode scattering" of the averaged cylinder.

--> examples/modal_scattering/modal_scattering.ipynb