English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper is concerned with direct and inverse scattering by a locallyperturbed infinite plane (called a locally rough surface in this paper) onwhich a Neumann boundary condition is imposed. A novel integral equationformulation is proposed for the direct scattering problem which is defined on abounded curve (consisting of a bounded part of the infinite plane containingthe local perturbation and the lower part of a circle) with two corners andsome closed smooth artificial curve. It is a nontrivial extension of ourprevious work on direct and inverse scattering by a locally rough surface fromthe Dirichlet boundary condition to the Neumann boundary condition [{\em SIAMJ. Appl. Math.}, 73 (2013), pp. 1811-1829]. In this paper, we make us of therecursively compressed inverse preconditioning (RCIP) method developed byHelsing to solve the integral equation which is efficient and capable ofdealing with large wave numbers. For the inverse problem, it is proved that thelocally rough surface is uniquely determined from a knowledge of the far-fieldpattern corresponding to incident plane waves. Further, based on the novelintegral equation formulation, a Newton iteration method is developed toreconstruct the locally rough surface from a knowledge of multiple frequencyfar-field data. Numerical examples are also provided to illustrate that thereconstruction algorithm is stable and accurate even for the case ofmultiple-scale profiles.

A novel integral equation for scattering by locally rough surfaces and application to the inverse problem: the Neumann case