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Scattering And Absorption of Light in Planetary Regoliths

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Calculating multiple scattering by circular cylinders using the multipole method: A comparative study on numerical

Tatsuhiro Tanaka¹

¹Graduate School of Engineering, Kyoto University, Kyoto 615-8540, Japan.

JASA Express Letters

|March 19, 2026

Summary

This study analyzes multiple scattering calculations for cylinders using the multipole method. It reveals that specific system formulations enhance stability and accuracy, offering computational advantages for complex scattering problems.

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Area of Science:

Electromagnetics and Optics
Computational Physics
Wave Scattering

Background:

Multiple scattering calculations are essential for understanding wave interactions with complex geometries.
The multipole method is a common technique for solving scattering problems, but its stability is formulation-dependent.
Truncating infinite systems in the multipole method can lead to numerical inaccuracies or instability.

Purpose of the Study:

To investigate the impact of different linear system formulations on the stability and accuracy of the multipole method for calculating multiple scattering.
To identify formulations that offer computational advantages for scattering by infinitely long circular cylinders.

Main Methods:

The study employed the multipole method to calculate multiple scattering by infinitely long circular cylinders.
Four algebraically equivalent formulations of the linear system were derived and compared.
Numerical experiments were conducted to assess the stability and accuracy of each formulation under varying truncation numbers.

Main Results:

Commonly used formulations of the linear system exhibit instability at high truncation numbers.
Less common formulations demonstrate superior stability due to well-conditioned system matrices.
The choice of formulation significantly impacts the reliability of multipole method calculations.

Conclusions:

The stability of the multipole method is critically dependent on the chosen linear system formulation.
Well-conditioned formulations provide a more stable and accurate approach for multiple scattering calculations.
This research highlights the importance of selecting appropriate formulations for computational efficiency and reliability in wave scattering problems.