Finite Point Method for the Time Fractional Convection-Diffusion Equation

2018 ◽  
pp. 28-36 ◽  
Author(s):  
Junchan Li ◽  
Xinqiang Qin
Keyword(s):  
Diffusion Equation ◽  
Point Method ◽  
Finite Point ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Finite Point Method

scholarly journals Finite point method of nonlinear convection diffusion equation

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1517-1533
Author(s):  
Xinqiang Qin ◽  
Gang Hu ◽  
Gaosheng Peng
Keyword(s):  
Diffusion Equation ◽  
Domain Size ◽  
Nonlinear Flow ◽  
Step Size ◽  
Finite Point ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Numerical Oscillations ◽  
The One

Aiming at the nonlinear convection diffusion equation with the numerical oscillations, a numerical stability algorithm is constructed. The basic principle of the finite point algorithm is given and the computational scheme of the nonlinear convection diffusion equation is deduced. Then, the numerical simulation of the one-dimensional and two-dimensional nonlinear convection-dominated diffusion equation is carried out. The relationship between the calculation result and the support domain size, step size and time is discussed. The results show that the algorithm has the characteristics of simplicity, stability and efficiency. Compared with the traditional finite element method and finite difference method, the new algorithm can attain a higher calculation accuracy. Simultaneously, it proves that the method given in this paper is effective to solve the nonlinear flow diffusion equation and can eliminate the numerical oscillations.

An Anisotropic Convection-Diffusion Model Using Tailored Finite Point Method for Image Denoising and Compression

2016 ◽  
Vol 19 (5) ◽  
pp. 1357-1374
Author(s):  
Yu-Tuan Lin ◽  
Yin-Tzer Shih ◽  
Chih-Ching Tsai
Keyword(s):  
Image Denoising ◽  
Diffusion Model ◽  
Point Method ◽  
Grid Structure ◽  
Finite Point ◽  
Convection Diffusion ◽  
Finite Point Method ◽  
Tailored Finite Point Method ◽  
Tailored Finite Point ◽  
Salt And Pepper

AbstractIn this paper we consider an anisotropic convection-diffusion (ACD) filter for image denoising and compression simultaneously. The ACD filter is discretized by a tailored finite point method (TFPM), which can tailor some particular properties of the image in an irregular grid structure. A quadtree structure is implemented for the storage in multi-levels for the compression. We compare the performance of the proposed scheme with several well-known filters. The numerical results show that the proposed method is effective for removing a mixture of white Gaussian and salt-and-pepper noises.

A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers

2011 ◽  
Vol 10 (1) ◽  
pp. 161-182 ◽  
Author(s):  
Po-Wen Hsieh ◽  
Yintzer Shih ◽  
Suh-Yuh Yang
Keyword(s):  
Hartmann Number ◽  
Difference Operator ◽  
Point Method ◽  
Duct Flow ◽  
Finite Point ◽  
Convection Diffusion ◽  
Flow Problems ◽  
Finite Point Method ◽  
Tailored Finite Point Method ◽  
Tailored Finite Point

AbstractIn this paper we propose a development of the finite difference method, called the tailored finite point method, for solving steady magnetohydrodynamic (MHD) duct flow problems with a high Hartmann number. When the Hartmann number is large, the MHD duct flow is convection-dominated and thus its solution may exhibit localized phenomena such as the boundary layer. Most conventional numerical methods can not efficiently solve the layer problem because they are lacking in either stability or accuracy. However, the proposed tailored finite point method is capable of resolving high gradients near the layer regions without refining the mesh. Firstly, we devise the tailored finite point method for the scalar inhomogeneous convection-diffusion problem, and then extend it to the MHD duct flow which consists of a coupled system of convection-diffusion equations. For each interior grid point of a given rectangular mesh, we construct a finite-point difference operator at that point with some nearby grid points, where the coefficients of the difference operator are tailored to some particular properties of the problem. Numerical examples are provided to show the high performance of the proposed method.

Tailored Finite Point Method for Parabolic Problems

2016 ◽  
Vol 16 (4) ◽  
pp. 543-562 ◽  
Author(s):  
Zhongyi Huang ◽  
Yi Yang
Keyword(s):  
Diffusion Problem ◽  
Point Method ◽  
Parabolic Problems ◽  
Finite Difference Schemes ◽  
Finite Point ◽  
Convection Diffusion ◽  
Finite Point Method ◽  
Tailored Finite Point Method ◽  
Uniformly Convergent ◽  
Tailored Finite Point

AbstractIn this paper, we propose a class of new tailored finite point methods (TFPM) for the numerical solution of parabolic equations. Our finite point method has been tailored based on the local exponential basis functions. By the idea of our TFPM, we can recover all the traditional finite difference schemes. We can also construct some new TFPM schemes with better stability condition and accuracy. Furthermore, combining with the Shishkin mesh technique, we construct the uniformly convergent TFPM scheme for the convection-dominant convection-diffusion problem. Our numerical examples show the efficiency and reliability of TFPM.

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