An efficient spatial spectral integral-equation method for EM scattering from finite objects in layered media

2016 ◽  
Author(s):  
Roeland Johannes Dilz ◽  
Martijn Constant van Beurden
Keyword(s):  
Integral Equation ◽  
Layered Media ◽  
Integral Equation Method ◽  
Equation Method ◽  
Em Scattering ◽  
Spectral Integral

A new spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations via Chebyshev polynomials

2019 ◽  
Vol 36 (7) ◽  
pp. 2327-2368 ◽  
Author(s):  
Mohsen Hadadian Nejad Yousefi ◽  
Seyed Hossein Ghoreishi Najafabadi ◽  
Emran Tohidi
Keyword(s):  
Integral Equation ◽  
Chebyshev Polynomials ◽  
Integral Equation Method ◽  
Diffusion Equations ◽  
Equation Method ◽  
Two Dimensional ◽  
Content Type ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Spectral Integral

Purpose The purpose of this paper is to develop an efficient and reliable spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations. Design/methodology/approach In this study, the considered two-dimensional unsteady advection-diffusion equations are transformed into the equivalent partial integro-differential equations via integrating from the considered unsteady advection-diffusion equation. After this stage, by using Chebyshev polynomials of the first kind and the operational matrix of integration, the integral equation would be transformed into the system of linear algebraic equations. Robustness and efficiency of the proposed method were illustrated by six numerical simulations experimentally. The numerical results confirm that the method is efficient, highly accurate, fast and stable for solving two-dimensional unsteady advection-diffusion equations. Findings The proposed method can solve the equations with discontinuity near the boundaries, the advection-dominated equations and the equations in irregular domains. One of the numerical test problems designed specially to evaluate the performance of the proposed method for discontinuity near boundaries. Originality/value This study extends the intention of one dimensional Chebyshev approximate approaches (Yuksel and Sezer, 2013; Yuksel et al., 2015) for two-dimensional unsteady advection-diffusion problems and the basic intention of our suggested method is quite different from the approaches for hyperbolic problems (Bulbul and Sezer, 2011).

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