scholarly journals Tailored finite point method for steady-state reaction-diffusion equations

2010 ◽  
Vol 8 (4) ◽  
pp. 887-899 ◽  
Author(s):  
Houde Han ◽  
Zhongyi Huang
Keyword(s):  
Steady State ◽  
Reaction Diffusion ◽  
Point Method ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Finite Point ◽  
Finite Point Method ◽  
Tailored Finite Point Method ◽  
Tailored Finite Point

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.

An Equation Decomposition Based Tailored Finite Point Method for Linearized Incompressible Flow in Two-Dimensional Space

2015 ◽  
Vol 15 (1) ◽  
pp. 39-58
Author(s):  
Ye Li ◽  
Houde Han ◽  
Zhongyi Huang
Keyword(s):  
Incompressible Flow ◽  
Stokes Problem ◽  
Two Dimensions ◽  
Point Method ◽  
Computational Domain ◽  
Finite Point ◽  
Finite Point Method ◽  
Tailored Finite Point Method ◽  
Tailored Finite Point ◽  
Interior Domain

AbstractIn this paper, we propose a tailored finite point method for linearized incompressible flow (Oseen equations) in two dimensions based on the equation decomposition technique. Unlike the usual vorticity-stream function formulation, the velocities are decomposed to irrotational and rotational parts. We only need to solve a system of two elliptic equations which are decoupled in the interior domain. They are only coupled in boundary conditions. When the domain is unbounded, we use the artificial boundary method to reduce the original problem to a problem on a bounded computational domain. Our finite point method has been tailored to some particular properties of the problem. Therefore, our scheme satisfies the discrete maximum principle in the interior domain automatically. We also give some remarks on more generally linearized incompressible flow, and it can be considered as the first step to solve the incompressible Navier–Stokes problem. Finally, several numerical examples show the efficiency and feasibility of our method whatever the Reynolds number is small or large.

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