A low-dispersive padé approximation method for wave propagation in isotropic and anisotropic poroelastic medium

2021 ◽  
pp. 1-16
Author(s):  
Fan Lu ◽  
Yanjie Zhou ◽  
Xijun He ◽  
Xueyuan Huang ◽  
Yanan Zhang
Keyword(s):  
Wave Propagation ◽  
Approximation Method ◽  
Padé Approximation ◽  
Poroelastic Medium ◽  
Pade Approximation

Padé Approximation Method for FDTD Modeling of Wave Propagation in Dispersive Media

2012 ◽  
Vol 268-270 ◽  
pp. 1585-1588
Author(s):  
Wei Chen
Keyword(s):  
Wave Propagation ◽  
Approximation Method ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Padé Approximation ◽  
Fdtd Method ◽  
Dispersive Media ◽  
Pade Approximation ◽  
Air Muscle ◽  
Difference Time

A finite-difference time-domain (FDTD) method for simulating wave propagation in Cole-Cole dispersive media was presented. The main difficulty of the proposed way was the appearance of fractional time derivatives in the FDTD equation. The Padé approximation method was employed to solve this problem. The expansion of the fractional time derivatives could deal with this model. The comparison of analytical and calculated the reflection of a plasma proves the validity of the method. Then apply this method to calculate the reflection of the air-muscle interface.

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

Improved bounds on the conductivity of composites by interpolation

1994 ◽  
Vol 444 (1921) ◽  
pp. 363-374 ◽  
Keyword(s):  
Composite Material ◽  
Lower Bounds ◽  
Approximation Method ◽  
Interpolation Method ◽  
Padé Approximation ◽  
Upper Bounds ◽  
Pade Approximation ◽  
Two Component ◽  
Null Lagrangian

Different bounds on the conductivity of a composite material may improve on each other in different conductivity régimes. If so, the question arises of how to efficiently interpolate between the bounds. In this paper I show how to do an interpolation with a two-point Padé approximation method. For bounds on two-component composites the interpolation method is shown to be, in a sense, the best possible. The method is discussed in the context of equiaxed polycrystals where the classic Hashin-Shtrikman bounds and the more recent null-lagrangian bounds, partly improve on each other. Denoting the principal conductivities of the crystallite σ 1 ≼ σ 2 ≼ σ 3 , the method gives improved lower bounds for equiaxed polycrystals which have σ 2 (0.77σ 1 + 0.23σ 3 ) ≽ σ 1 σ 3 . The method also gives improved upper bounds.

scholarly journals On application of the finite-difference Padé approximation of the pseudo-differential parabolic equation to the tropospheric radio wave propagation problem

2020 ◽  
pp. 405-419
Author(s):  
М.С. Лытаев
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Electromagnetic Wave Propagation ◽  
Padé Approximation ◽  
Fourier Method ◽  
Geometric Theory ◽  
Wide Angle ◽  
Pade Approximation ◽  
Propagation Angle ◽  
Wave Propagation Problem

Рассматривается задача численного моделирования распространения электромагнитных волн в неоднородной тропосфере на основе широкоугольных обобщений метода параболического уравнения. Используется конечно-разностная аппроксимация Паде оператора распространения. Существенно, что в предлагаемом подходе указанная аппроксимация осуществляется одновременно по продольной и поперечной координатам. При этом допускается моделирование произвольного коэффициента преломления тропосферы. Метод не накладывает ограничений на максимальный угол распространения. Для различных условий распространения радиоволн проведено сравнение с методом расщепления Фурье и методом геометрической теории дифракции. Показаны преимущества предлагаемого подхода. This paper is devoted to the numerical simulation of electromagnetic wave propagation in an inhomogeneous troposphere. The study is based on the wide-angle generalizations of the parabolic wave equation. The finite-difference Padé approximation is used to approximate the propagation operator. It is important that, within the proposed approach, the Padé approximation is carried out simultaneously along with the longitudinal and transverse coordinates. At the same time, the proposed approach gives an opportunity to model an arbitrary tropospheric refractive index. The method does not impose restrictions on the maximum propagation angle. The comparison with the split-step Fourier method and the geometric theory of diffraction is discussed. The advantages of the proposed approach are shown.

scholarly journals New Refinements for the Error Function with Applications in Diffusion Theory

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2017
Author(s):  
Gabriel Bercu
Keyword(s):  
Fourier Series ◽  
Approximation Method ◽  
Diffusion Theory ◽  
Error Function ◽  
Padé Approximation ◽  
Absolute Error ◽  
Series Method ◽  
Pade Approximation ◽  
Fourier Series Method ◽  
The Absolute

In this paper we provide approximations for the error function using the Padé approximation method and the Fourier series method. These approximations have simple forms and acceptable bounds for the absolute error. Then we use them in diffusion theory.

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