2019/03/11 by Andrew Gibbs, Simon N. Chandler‐Wilde, Gibbs, Andrew +5
Engineering · Physics and Astronomy · #35J05 #65N38 #65R20 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Geophysical Methods and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1903.04449
openalex publication_date 2019/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a boundary element method for problems of time-harmonic acoustic scattering by multiple obstacles in two dimensions, at least one of which is a convex polygon. By combining a Hybrid Numerical Asymptotic (HNA) approximation space on the convex polygon with standard polynomial-based approximation spaces on each of the other obstacles, we show that the number of degrees of freedom required in the HNA space to maintain a given accuracy needs to grow only logarithmically with respect to the frequency, as opposed to the (at least) linear growth required by standard polynomial-based schemes. This method is thus most effective when the convex polygon is many wavelengths in diameter and the small obstacles have a combined perimeter comparable to the problem wavelength.