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# Convergence and numerics of a multisection method for scattering by three-dimensional rough surfaces

Publikationstyp

Journal Article

Publikationsdatum

2008-11-10

Sprache

English

Enthalten in

Volume

46

Issue

4

Start Page

1780

End Page

1798

Citation

SIAM Journal on Numerical Analysis 46 (4): 1780-1798 (2008-11-10)

Publisher DOI

Scopus ID

We introduce a novel multisection method for the solution of integral equations on unbounded domains. The method is applied to the rough surface scattering problem in three dimensions, in particular to a Brakhage-Werner-type integral equation for acoustic scattering by an unbounded rough surface with Dirichlet boundary condition, where the fundamental solution is replaced by some appropriate half-space Green's function. The basic idea of the multisection method is to solve an integral equation Aφ = f by approximately solving the equation PρAPτφ = Pρf for some positive constants ρ, τ. Here Pρ is a projection operator that truncates a function to a ball with radius ρ > 0. For a very general class of operators A, for which the Brakhage-Werner equation from acoustic scattering is a particular example, we will show existence of approximate solutions to the multisection equation and show that approximate solutions to the multisection equation approximate the true solution φ0 of the operator equation Aφ = f. Finally, we describe a numerical implementation of the multisection algorithm and provide numerical examples for the case of rough surface scattering in three dimensions. © 2008 Society for Industrial and Applied Mathematics.