A domain integral equation approach for simulating two dimensional transverse electric scattering in a layered medium with a Gabor frame discretization.

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
103 Downloads (Pure)

Abstract

We solve the 2D transverse-electrically polarized domain-integral equation in a layered background medium by applying a Gabor frame as a projection method. This algorithm employs both a spatial and a spectral discretization of the electric field and the contrast current in the direction of the layer extent. In the spectral domain we use a representation on the complex plane that avoids the poles and branchcuts found in the Green function. Because of the special choice of the complex-plane path in the spectral domain and because of the choice to use a Gabor frame to represent functions on this path, fast algorithms based on FFTs are available to transform to and from the spectral domain, yielding an O(Nlog⁡N)O(Nlog⁡N) scaling in computation time.
Original languageEnglish
Pages (from-to)528-542
Number of pages15
JournalJournal of Computational Physics
Volume345
Issue number1
Early online date22 May 2017
DOIs
Publication statusPublished - 15 Sep 2017

Fingerprint

Gabor Frames
Layered Media
Integral equations
integral equations
Integral Equations
Transverse
Discretization
Scattering
scattering
Green's function
Fast Fourier transforms
Argand diagram
Poles
Electric fields
Path
fast Fourier transformations
Projection Method
Fast Algorithm
Pole
Electric Field

Cite this

@article{221624ee472a4c83b358c829b63830ef,
title = "A domain integral equation approach for simulating two dimensional transverse electric scattering in a layered medium with a Gabor frame discretization.",
abstract = "We solve the 2D transverse-electrically polarized domain-integral equation in a layered background medium by applying a Gabor frame as a projection method. This algorithm employs both a spatial and a spectral discretization of the electric field and the contrast current in the direction of the layer extent. In the spectral domain we use a representation on the complex plane that avoids the poles and branchcuts found in the Green function. Because of the special choice of the complex-plane path in the spectral domain and because of the choice to use a Gabor frame to represent functions on this path, fast algorithms based on FFTs are available to transform to and from the spectral domain, yielding an O(Nlog⁡N)O(Nlog⁡N) scaling in computation time.",
keywords = "Gabor frame, Integral equation, electromagnetic scattering, Green function",
author = "R.J. Dilz and {van Beurden}, M.C.",
year = "2017",
month = "9",
day = "15",
doi = "10.1016/j.jcp.2017.05.034",
language = "English",
volume = "345",
pages = "528--542",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - A domain integral equation approach for simulating two dimensional transverse electric scattering in a layered medium with a Gabor frame discretization.

AU - Dilz, R.J.

AU - van Beurden, M.C.

PY - 2017/9/15

Y1 - 2017/9/15

N2 - We solve the 2D transverse-electrically polarized domain-integral equation in a layered background medium by applying a Gabor frame as a projection method. This algorithm employs both a spatial and a spectral discretization of the electric field and the contrast current in the direction of the layer extent. In the spectral domain we use a representation on the complex plane that avoids the poles and branchcuts found in the Green function. Because of the special choice of the complex-plane path in the spectral domain and because of the choice to use a Gabor frame to represent functions on this path, fast algorithms based on FFTs are available to transform to and from the spectral domain, yielding an O(Nlog⁡N)O(Nlog⁡N) scaling in computation time.

AB - We solve the 2D transverse-electrically polarized domain-integral equation in a layered background medium by applying a Gabor frame as a projection method. This algorithm employs both a spatial and a spectral discretization of the electric field and the contrast current in the direction of the layer extent. In the spectral domain we use a representation on the complex plane that avoids the poles and branchcuts found in the Green function. Because of the special choice of the complex-plane path in the spectral domain and because of the choice to use a Gabor frame to represent functions on this path, fast algorithms based on FFTs are available to transform to and from the spectral domain, yielding an O(Nlog⁡N)O(Nlog⁡N) scaling in computation time.

KW - Gabor frame

KW - Integral equation

KW - electromagnetic scattering

KW - Green function

U2 - 10.1016/j.jcp.2017.05.034

DO - 10.1016/j.jcp.2017.05.034

M3 - Article

VL - 345

SP - 528

EP - 542

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -