Multipoint formulas for scattered far field in multidimensions

R. G. Novikov

doi:10.1088/1361-6420/aba891

Multipoint formulas for scattered far field in multidimensions

R. G. Novikov

Institute of Bioorganic Chemistry

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

Abstract

We give asymptotic formulas for finding the scattering amplitude at fixed frequency and angles (scattered far field) from the scattering wave function given at n points in dimension d 2. These formulas are explicit and their precision is proportional to n. To our knowledge these formulas are new for n 2; whereas they reduce to a classical result for n = 1.

Original language	English
Article number	095001
Journal	Inverse Problems
Volume	36
Issue number	9
DOIs	https://doi.org/10.1088/1361-6420/aba891
Publication status	Published - 1 Sept 2020

Keywords

Helmholtz equation
Inverse scattering problems
Scattered far field
Scattered near field
SchrÃdinger equation
Vandermonde matrix

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10.1088/1361-6420/aba891

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title = "Multipoint formulas for scattered far field in multidimensions",

abstract = "We give asymptotic formulas for finding the scattering amplitude at fixed frequency and angles (scattered far field) from the scattering wave function given at n points in dimension d 2. These formulas are explicit and their precision is proportional to n. To our knowledge these formulas are new for n 2; whereas they reduce to a classical result for n = 1.",

keywords = "Helmholtz equation, Inverse scattering problems, Scattered far field, Scattered near field, Schr{\~A}dinger equation, Vandermonde matrix",

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N2 - We give asymptotic formulas for finding the scattering amplitude at fixed frequency and angles (scattered far field) from the scattering wave function given at n points in dimension d 2. These formulas are explicit and their precision is proportional to n. To our knowledge these formulas are new for n 2; whereas they reduce to a classical result for n = 1.

AB - We give asymptotic formulas for finding the scattering amplitude at fixed frequency and angles (scattered far field) from the scattering wave function given at n points in dimension d 2. These formulas are explicit and their precision is proportional to n. To our knowledge these formulas are new for n 2; whereas they reduce to a classical result for n = 1.

KW - Helmholtz equation

KW - Inverse scattering problems

KW - Scattered far field

KW - Scattered near field

KW - SchrÃdinger equation

KW - Vandermonde matrix

UR - https://www.scopus.com/pages/publications/85092300737

U2 - 10.1088/1361-6420/aba891

DO - 10.1088/1361-6420/aba891

M3 - Article

AN - SCOPUS:85092300737

SN - 0266-5611

VL - 36

JO - Inverse Problems

JF - Inverse Problems

IS - 9

M1 - 095001

ER -

Multipoint formulas for scattered far field in multidimensions

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Keywords

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