High-frequency asymptotic expansions for multiple scattering problems with Neumann boundary conditions
Journal of Mathematical Analysis and Applications, cilt.544, sa.1, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 544 Sayı: 1
- Basım Tarihi: 2025
- Doi Numarası: 10.1016/j.jmaa.2024.129047
- Dergi Adı: Journal of Mathematical Analysis and Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Anahtar Kelimeler: Helmholtz equation, High-frequency scattering, Asymptotic expansion, Neumann boundary condition
- Boğaziçi Üniversitesi Adresli: Evet
Özet
We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth (C∞), strictly convex obstacles with Neumann boundary conditions. Using integral equation formulations, we determine the Hörmander classes and derive Melrose-Taylor type high-frequency asymptotic expansions of the total fields corresponding to multiple scattering iterations on the boundaries of the scattering obstacles. These asymptotic expansions are used to obtain sharp wavenumber dependent estimates on the derivatives of multiple scattering total fields. Numerical experiments supporting the validity of these expansions are presented.