Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems
Journal of Scientific Computing, cilt.83, sa.1, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 83 Sayı: 1
- Basım Tarihi: 2020
- Doi Numarası: 10.1007/s10915-020-01189-x
- Dergi Adı: Journal of Scientific Computing
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
- Anahtar Kelimeler: Galerkin boundary element method, High-frequency, Multiple-scattering
- Boğaziçi Üniversitesi Adresli: Evet
Özet
We consider high-frequency multiple-scattering problems in the exterior of two-dimensional smooth scatterers consisting of finitely many compact, disjoint, and strictly convex obstacles. To deal with this problem, we propose Galerkin boundary element methods, namely the frequency-adapted Galerkin boundary element methods and Galerkin boundary element methods generated using frequency-dependent changes of variables. For both of these new algorithms, in connection with each multiple-scattering iterate, we show that the number of degrees of freedom needs to increase as O(kϵ) (for any ϵ> 0) with increasing wavenumber k to attain frequency-independent error tolerances. We support our theoretical developments by a variety of numerical implementations.