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Furthermore, we propose a modification of the Newton-type algorithm to recover a real-valued surface impedance from phase-less far field data.
This indicates the near field data will have more influence on the result than the far field data when the covariance function is changed.
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Although far-field data was seen to be comparable the near-field discrepancies resulted in variable overall accuracy in the model.
It is found that allowing for this experimentally observed dependence markedly improves the agreement of the model's prediction with experimental far-field data.
Our tool is designed according to an object-oriented paradigm and provides a rapid visualization of the objects profile from noisy far-field data in the case of both inhomogeneous and impenetrable objects.
Our detailed numerical experiments demonstrate that this nonlinear field projection method (NFPM) is well-suited for extracting the interfacial tractions from the far-field data of any nonlinear elastic or elasto-plastic material with known constitutive laws.
Furthermore, a recursive Newton-type iteration algorithm in frequencies is also developed to numerically recover both the location and the shape of the obstacle simultaneously from multi-frequency phaseless far-field data.
Various results of numerical simulations performed on the far-field data affected by large amounts of random noise are similar to the analytical results derived in this study, and they provide a direction for future studies.
In this paper, direct sampling method is considered for determining the location of a set of small, linear perfectly conducting cracks from the collected far-field data corresponding to an incident field.
We express the unknown normal and shear tractions along the interface in terms of the Fourier series, and use specially constructed analytical auxiliary fields in the reciprocal theorem to extract the unknown Fourier coefficients from far-field data; the reciprocity gap in the formulation is iteratively determined with a set of numerical algorithms.
It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location of the obstacle can be recovered from the phaseless far-field data.
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