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Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data

Peng Gao, Heping Dong, Fuming Ma (2018)

Applications of Mathematics

We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...

Numerical solution of Cauchy type singular integral equations by use of the Lobatto-Jacobi numerical integration rule

Nikolaos I. Ioakimidis, Pericles S. Theocaris (1978)

Aplikace matematiky

The Lobatto-Jacobi numerical integration rule can be extended so as to apply to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauchy type kernels by reduction to systems of linear equations. To this end, the integrals in such a singular integral equation are replaced by sums, as if they were regular integrals, after the singular integral equation is applied at appropriately selected points of the integration interval....

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