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 studies the PML method for wave scattering in a half space ofhomogeneous medium bounded by a two-dimensional, perfectly conducting, andlocally defected periodic surface, and develops a high-accuracyboundary-integral-equation (BIE) solver. Along the vertical direction, we placea PML to truncate the unbounded domain onto a strip and prove that the PMLsolution converges linearly to the true solution in the physical subregion ofthe strip with the PML thickness. Laterally, we divide the unbounded strip intothree regions: a region containing the defect and two semi-waveguide regions,separated by two vertical line segments. In both semi-waveguides, we prove thewell-posedness of an associated scattering problem so as to well define aNeumann-to-Dirichlet (NtD) operator on the associated vertical segment. The twoNtD operators, serving as exact lateral boundary conditions, reformulate theunbounded strip problem as a boundary value problem onto the defected region.Due to the periodicity of the semi-waveguides, both NtD operators turn out tobe closely related to a Neumann-marching operator, governed by a nonlinearRiccati equation. It is proved that the Neumann-marching operators arecontracting, so that the PML solution decays exponentially fast along bothlateral directions. The consequences culminate in two opposite aspects.Negatively, the PML solution cannot exponentially converge to the true solutionin the whole physical region of the strip. Positively, from a numericalperspective, the Riccati equations can now be efficiently solved by a recursivedoubling procedure and a high-accuracy PML-based BIE method so that theboundary value problem on the defected region can be solved efficiently andaccurately. Numerical experiments demonstrate that the PML solution convergesexponentially fast to the true solution in any compact subdomain of the strip.

PML and high-accuracy boundary integral equation solver for wave scattering by a locally defected periodic surface