Boundary perturbation methods for high-frequency acoustic scattering: shallow periodic gratings.
Despite significant recent advances in numerical methodologies for simulating rough-surface acoustic scattering, their applicability has been constrained by the limitations of state-of-the-art computational resources. This has been particularly true in high-frequency applications where the sheer size of the full-wave simulations render them impractical, and engineering processes must therefore rely on asymptotic models [e.g., Kirchhoff approximation (KA)]. However, the demands for high precision can make the latter inappropriate, thus efficient, error-controllable methodologies must be devised. This paper presents a computational strategy that combines the virtues of rigorous solvers (error control) with those of high-frequency asymptotic models (frequency-independent computational costs). These methods are based on high-order "boundary perturbations," which display high precision and unparalleled efficiency. This is accomplished by incorporating asymptotic phase information to effect a significant decrease in computational effort, simultaneously retaining the full-wave nature of the approach. The developments of this contribution are constrained to configurations that preclude multiple scattering; it is further explained how the schemes can be made applicable to general scattering scenarios, though implementation details are left for future work. Even for single-scattering configurations, the approach presented here gives significant gains in accuracy when compared to asymptotic theories (e.g., KA) with modest additional computational cost.
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607, USA. nicholls@math.uic.edu
David P
DP
Nicholls
Fernando
F
Reitich
D000162:Acoustics; D000465:Algorithms; D003198:Computer Simulation; D004548:Elasticity; D008433:Mathematics; D015233:Models, Statistical; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D014465:Ultrasonics