Generating geometric body shapes with electromagnetic source scattering techniques
type: Item
instance of: scholarly article
title: Generating geometric body shapes with electromagnetic source scattering techniques
zbMATH Open document ID: 1482.78008
author: D. Kharzeev
published in: Electronic Research Archive
publication date: 2020-07-14T00:00:00Z
review text: The authors consider the three-dimensional geometric body shape generation using characteristic values based on inverse scattering theory. Using the vector spherical harmonics expansion of the magnetic far field pattern, a one-to-one correspondence is built between the geometric body space and the multi-dimensional vector space. These coefficients serve as the shape generator. For a collection of geometric body shapes, the authors obtain the inputs (characteristic values of the body shapes) and the outputs (the coefficients of the spherical vector wave function expansion of the corresponding magnetic far field patterns). The multivariate Lagrange interpolation is used for new shapes, which are constructed using the multiple-frequency Fourier method. Numerical examples are presented.
reviewed by: Jiguang Sun
Mathematics Subject Classification ID: 78A46
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 78M22
zbMATH DE Number: 7220351
zbMATH Keywords: geometric body shape generation
zbMATH Keywords: far field pattern
zbMATH Keywords: characteristic values
describes a project that uses: SCAPE
MaRDI profile type: Publication
full work available at URL: era.2020061
OpenAlex ID: W3036794715
cites work: Inverse acoustic and electromagnetic scattering theory.
cites work: Two single-shot methods for locating multiple electromagnetic scatterers
cites work: An inverse scattering approach for geometric body generation: a machine learning perspective
cites work: Locating Multiple Multiscale Acoustic Scatterers
cites work: TE/TM decomposition of electromagnetic sources
cites work: A global uniqueness for formally determined inverse electromagnetic obstacle scattering
cites work: Mosco convergence for \(H(\text{curl})\) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
cites work: Reflection principle for the Maxwell equations and its application to inverse electromagnetic scattering
cites work: Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers
cites work: On Multivariate Lagrange Interpolation
cites work: Solving the multi-frequency electromagnetic inverse source problem by the Fourier method
cites work: Fourier method for identifying electromagnetic sources with multi-frequency far-field data
cites work: Fourier method for solving the multi-frequency inverse source problem for the Helmholtz equation
cites work: Retrieval of acoustic sources from multi-frequency phaseless data
cites work: Locating Multiple Multipolar Acoustic Sources Using the Direct Sampling Method
cites work: Unique determinations in inverse scattering problems with phaseless near-field measurements
DOI: 10.3934/ERA.2020061
description: scientific article; zbMATH DE number 7220351