A fast algorithm for the two-dimensional Helmholtz transmission problem with large multiple scattering...

Area of Science:

• Computational physics
• Acoustics
• Numerical methods

Background:

• Simulating acoustic scattering is computationally intensive, especially with numerous objects.
• Existing methods struggle with scalability for large configurations of penetrable scatterers.

Purpose of the Study:

• To develop an efficient and scalable algorithm for simulating multiple acoustic scattering.
• To handle complex interactions between a large number of penetrable scatterers in 2D configurations.

Main Methods:

• Reformulation of the Helmholtz transmission equation using boundary integral equations.
• Reduction of the boundary integral system for efficient wave interaction evaluation.
• Representation of scatterer interactions using cylindrical wavefunction expansions and the fast multipole method.

Main Results:

• The algorithm achieves linear complexity with respect to the number of scatterers.
• Demonstrated efficiency for simulating acoustic scattering in configurations from hundreds to hundreds of thousands of scatterers.
• Successful simulation of multiple acoustic scattering by large numbers of penetrable scatterers.

Conclusions:

• The developed three-stage algorithm is highly efficient for simulating acoustic scattering.
• The approach offers significant scalability for problems involving a vast number of scatterers.
• This method provides a powerful tool for analyzing complex acoustic wave phenomena.