The Factorization Method for the β-Difference Hypergeometric Equation

2019 ◽  
Author(s):  
Gaspard Bangerezako
Keyword(s):  
Factorization Method ◽  
Hypergeometric Equation

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

The inverse elastic scattering by an impenetrable obstacle and a crack

2020 ◽  
Author(s):  
Jianli Xiang ◽  
Guozheng Yan
Keyword(s):  
Mixed Type ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Integral Equation Method ◽  
Factorization Method ◽  
Boundary Integral ◽  
Far Field ◽  
Direct Scattering ◽  
Time Harmonic

Abstract This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

scholarly journals An out-of-core sparse symmetric-indefinite factorization method

2006 ◽  
Vol 32 (3) ◽  
pp. 445-471 ◽  
Author(s):  
Omer Meshar ◽  
Dror Irony ◽  
Sivan Toledo
Keyword(s):  
Factorization Method

On some generalizations of the factorization method

1997 ◽  
Vol 110 (3) ◽  
pp. 267-276 ◽  
Author(s):  
I. Z. Golubchik ◽  
V. V. Sokolov
Keyword(s):  
Factorization Method
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