Applications of square-integrable basis functions for scattering problems: A comparison between approaches based on Toeplitz matrices and negative imaginary potentials

1994 ◽  
Vol 49 (6) ◽  
pp. 4549-4555 ◽  
Author(s):  
Shlomo Ron ◽  
Eli Eisenberg ◽  
Miquel Gilibert ◽  
Michael Baer
Keyword(s):  
Toeplitz Matrices ◽  
Basis Functions ◽  
Scattering Problems ◽  
Square Integrable Basis

scholarly journals Exact solvability of two new 3D and 1D non-relativistic potentials within the TRA framework

2018 ◽  
Vol 33 (32) ◽  
pp. 1850187 ◽  
Author(s):  
I. A. Assi ◽  
H. Bahlouli ◽  
A. Hamdan
Keyword(s):  
Wave Function ◽  
Orthogonal Polynomials ◽  
Jacobi Polynomials ◽  
Basis Functions ◽  
Exact Solvability ◽  
Analytical Properties ◽  
Expansion Coefficients ◽  
Potential Parameters ◽  
Square Integrable Basis

This work aims at introducing two new solvable 1D and 3D confined potentials and present their solutions using the Tridiagonal Representation Approach (TRA). The wave function is written as a series in terms of square integrable basis functions which are expressed in terms of Jacobi polynomials. The expansion coefficients are then written in terms of new orthogonal polynomials that were introduced recently by Alhaidari, the analytical properties of which are yet to be derived. Moreover, we have computed the numerical eigenenergies for both potentials by considering specific choices of the potential parameters.

Ultra-wideband characteristic basis function method merging the secondary level characteristic basis functions for rapid computation of wideband radar cross section problems from conducting targets

2020 ◽  
pp. 1-10
Author(s):  
Zhong-Gen Wang ◽  
Jun-Wen Mu ◽  
Wen-Yan Nie
Keyword(s):  
Basis Function ◽  
Function Method ◽  
Secondary Level ◽  
Singular Value ◽  
Basis Functions ◽  
Ultra Wideband ◽  
Scattering Problems ◽  
Wideband Radar ◽  
Value Decomposition ◽  
A Current

In this paper, a merged ultra-wideband characteristic basis function method (MUCBFM) is presented for high-precision analysis of wideband scattering problems. Unlike existing singular value decomposition (SVD) enhanced improved ultra-wideband characteristic basis function method (SVD-IUCBFM), the MUCBFM reduces the number of characteristic basis functions (CBFs) necessary to express a current distribution. This reduction is achieved by combining primary CBFs (PCBFs) with the secondary level CBFs (SCBFs) to form a single merged ultra-wideband characteristic basis function (MUCBF). As the MUCBF incorporates the effects of PCBFs and SCBFs, the accuracy does not change significantly compared to that obtained by the SVD-IUCBFM. Furthermore, the efficiencies of constructing the CBFs and filling the reduced matrix are improved. Numerical examples verify and demonstrate that the proposed method is credible both in terms of accuracy and efficiency.

scholarly journals Applying Loop-Flower Basis Functions to Analyze Electromagnetic Scattering Problems of PEC Scatterers

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Gaobiao Xiao
Keyword(s):  
Integral Equations ◽  
Electromagnetic Scattering ◽  
Basis Functions ◽  
Surface Integral ◽  
Scattering Problems ◽  
Low Frequencies ◽  
Electrically Conducting ◽  
Surface Integral Equations

This paper discusses the application of loop-flower basis functions for solving surface integral equations involved in electromagnetic scattering problems on perfectly electrically conducting surfaces. Flower-shaped basis functions are proposed to replace the conventional star basis functions. The flower basis functions are defined based on mesh nodes instead of surface triangles. It is shown that the loop-flower basis functions not only can be used to handle the electromagnetic scattering problems at very low frequencies, but also can be directly used to implement Calderon preconditioners for EFIEs.

The application of Toeplitz matrices to scattering problems

1993 ◽  
Vol 99 (5) ◽  
pp. 3503-3508 ◽  
Author(s):  
M. Gilibert ◽  
A. Baram ◽  
I. Last ◽  
H. Szichman ◽  
M. Baer
Keyword(s):  
Toeplitz Matrices ◽  
Scattering Problems
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