Characteristic Tailored Finite Point Method for Convection-Dominated Convection-Diffusion-Reaction Problems

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.

Download Full-text

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

Communications in Computational Physics ◽

10.4208/cicp.070110.020710a ◽

2011 ◽

Vol 10 (1) ◽

pp. 161-182 ◽

Cited By ~ 13

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.

Download Full-text

Tailored Finite Point Method for Parabolic Problems

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2016-0017 ◽

2016 ◽

Vol 16 (4) ◽

pp. 543-562 ◽

Cited By ~ 4

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.

Download Full-text