The Floquet-Bloch Transform and Scattering from Locally Perturbed\n Periodic Surfaces

2016/02/10 by Armin Lechleiter, Lechleiter, Armin · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Electromagnetic Scattering and Analysis

paper · pdf · doi:10.48550/arxiv.1602.03349

Abstract

We use the Floquet-Bloch transform to reduce variational formulations of\nsurface scattering problems for the Helmholtz equation from periodic and\nlocally perturbed periodic surfaces to equivalent variational problems\nformulated on bounded domains. To this end, we establish various mapping\nproperties of that transform between suitable weighted Sobolev spaces on\nperiodic strip-like domains and coupled families of quasiperiodic Sobolev\nspaces. Our analysis shows in particular that the decay of solutions to surface\nscattering problems from locally perturbed periodic surfaces is precisely\ncharacterized by the smoothness of its Bloch transform in the quasiperiodicity.\n

Cited by

• A boundary integral equation method for wave scattering in periodic structures via the Floquet-Bloch transform

Related

• Scattering problems from slightly perturbed periodic surfaces: Part I. regularity of the Bloch transformed fields
• A Floquet-Bloch transform based numerical method for scattering from locally perturbed periodic surfaces
• A Convergent Numerical Scheme for Scattering of Aperiodic Waves from Periodic Surfaces Based on the Floquet-Bloch Transform
• The Study of the Bloch Transformed Fields Scattered by Locally Perturbed Periodic Surfaces
• The radiation condition for Helmholtz equations above (locally perturbed) periodic surfaces