Modified Rayleigh Conjecture and applications
A.G. Ramm
TL;DR
This paper introduces the Modified Rayleigh Conjecture (MRC), a new approach in scattering theory that enables numerical solutions for acoustic wave scattering problems and shape reconstruction of obstacles.
Contribution
The paper proposes and justifies the MRC, providing a new numerical method for solving direct scattering problems and reconstructing obstacle shapes from scattering data.
Findings
MRC allows accurate numerical solutions for scattering problems.
Provides error estimates for the direct scattering problem.
Introduces a method for shape reconstruction of obstacles.
Abstract
Modified Rayleigh conjecture (MRC) in scattering theory is proposed and justified. MRC allows one to develop numerical algorithms for solving direct scattering problems related to acoustic wave scattering by soft and hard obstacles of arbitrary shapes. It gives an error estimate for solving the direct scattering problem. It suggests a numerical method for finding the shape of a starshaped obstacle from the scattering data.
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