Integral Equation Methods for Rough Surface Scattering Problems in three Dimensions

Heinemeyer, Eric

doi:10.53846/goediss-3461

Cited by 2 publications

References 32 publications

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Convergence and Numerics of a Multisection Method for Scattering by Three-Dimensional Rough Surfaces

Heinemeyer¹,

Lindner²,

Potthast³

2008

SIAM J. Numer. Anal.

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We introduce a novel multi-section 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 multi-section method is to solve an integral equation Aϕ = f by approximately solving the equation P AP τ ϕ = P f for some positive constants , τ. Here P is a projection operator that truncates a function to a ball with radius > 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 multi-section equation and that approximate solutions to the multi-section equation approximate the true solution ϕ 0 of the operator equation Aϕ = f. Finally, we describe a numerical implementation of the multi-section algorithm and provide numerical examples for the case of rough surface scattering in three dimensions.

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Convergence and Numerics of a Multisection Method for Scattering by Three-Dimensional Rough Surfaces

Heinemeyer¹,

Lindner²,

Potthast³

2008

SIAM J. Numer. Anal.

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A Collocation Method for Integral Equations with Super-Algebraic Convergence Rate

Arens¹,

Rösch²

2015

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Integral Equation Methods for Rough Surface Scattering Problems in three Dimensions

Cited by 2 publications

References 32 publications

Convergence and Numerics of a Multisection Method for Scattering by Three-Dimensional Rough Surfaces

Convergence and Numerics of a Multisection Method for Scattering by Three-Dimensional Rough Surfaces

A Collocation Method for Integral Equations with Super-Algebraic Convergence Rate

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