A volume integral method for solving scattering problems from locally perturbed infinite periodic layers

Houssem Haddar; Thi Phong Nguyen

doi:10.1080/00036811.2016.1221942

A volume integral method for solving scattering problems from locally perturbed infinite periodic layers

Houssem Haddar, Thi Phong Nguyen

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We investigate the scattering problem for the case of locally perturbed periodic layers in ℝ^d, d = 2, 3. Using the Floquet–Bloch transform in the periodicity direction, we reformulate this scattering problem as an equivalent system of coupled volume integral equations. We then apply a spectral method to discretize the obtained system after periodization in the direction orthogonal to the periodicity directions of the medium. The convergence of this method is established and validating numerical results are provided.

Original language	English (US)
Pages (from-to)	130-158
Number of pages	29
Journal	Applicable Analysis
Volume	96
Issue number	1
DOIs	https://doi.org/10.1080/00036811.2016.1221942
State	Published - Jan 2 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

Scattering problems

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10.1080/00036811.2016.1221942

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abstract = "We investigate the scattering problem for the case of locally perturbed periodic layers in ℝd, d = 2, 3. Using the Floquet–Bloch transform in the periodicity direction, we reformulate this scattering problem as an equivalent system of coupled volume integral equations. We then apply a spectral method to discretize the obtained system after periodization in the direction orthogonal to the periodicity directions of the medium. The convergence of this method is established and validating numerical results are provided.",

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AU - Nguyen, Thi Phong

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N2 - We investigate the scattering problem for the case of locally perturbed periodic layers in ℝd, d = 2, 3. Using the Floquet–Bloch transform in the periodicity direction, we reformulate this scattering problem as an equivalent system of coupled volume integral equations. We then apply a spectral method to discretize the obtained system after periodization in the direction orthogonal to the periodicity directions of the medium. The convergence of this method is established and validating numerical results are provided.

AB - We investigate the scattering problem for the case of locally perturbed periodic layers in ℝd, d = 2, 3. Using the Floquet–Bloch transform in the periodicity direction, we reformulate this scattering problem as an equivalent system of coupled volume integral equations. We then apply a spectral method to discretize the obtained system after periodization in the direction orthogonal to the periodicity directions of the medium. The convergence of this method is established and validating numerical results are provided.

KW - Scattering problems

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JF - Applicable Analysis

IS - 1

ER -

A volume integral method for solving scattering problems from locally perturbed infinite periodic layers

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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