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

This study focuses on calculating multiple scattering by infinitely long circular cylinders using the multipole method. The multipole method requires truncating an infinite-dimensional linear system to a finite system, but selecting inappropriate truncation numbers may lead to inaccuracy or instability. Interestingly, the system's stability depends crucially on its formulation. Here, to demonstrate this, four (algebraically equivalent) formulations of the linear system are considered and compared through numerical experiments. The experimental results indicate that commonly used formulations become unstable with high truncation numbers, whereas less common formulations remain stable because of their well-conditioned system matrices, suggesting their computational advantage.