Abstract
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.
Original language | English (US) |
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Article number | 1 |
Journal | Journal of Scientific Computing |
Volume | 83 |
Issue number | 1 |
DOIs | |
State | Published - Apr 1 2020 |
All Science Journal Classification (ASJC) codes
- Software
- Theoretical Computer Science
- Numerical Analysis
- Engineering(all)
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics
Keywords
- Galerkin boundary element method
- High-frequency
- Multiple-scattering