Preconditioned iterative methods and finite difference schemes for convection–diffusion

2000 ◽  
Vol 109 (1) ◽  
pp. 11-30 ◽  
Author(s):  
Jun Zhang
Keyword(s):  
Finite Difference ◽  
Iterative Methods ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Convection Diffusion ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

Spectral analysis of finite difference schemes for convection diffusion equation

2017 ◽  
Vol 150 ◽  
pp. 95-114 ◽  
Author(s):  
V.K. Suman ◽  
Tapan K. Sengupta ◽  
C. Jyothi Durga Prasad ◽  
K. Surya Mohan ◽  
Deepanshu Sanwalia
Keyword(s):  
Spectral Analysis ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

scholarly journals Iterative Methods for Obtaining Energy-Minimizing Parametric Snakes with Applications to Medical Imaging

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Alexandru Ioan Mitrea ◽  
Radu Badea ◽  
Delia Mitrea ◽  
Sergiu Nedevschi ◽  
Paulina Mitrea ◽  
...  
Keyword(s):  
Medical Imaging ◽  
Numerical Methods ◽  
Finite Difference ◽  
Iterative Method ◽  
Iterative Methods ◽  
Approximation Error ◽  
Deformable Models ◽  
Difference Schemes ◽  
Finite Difference Schemes

After a brief survey on the parametric deformable models, we develop an iterative method based on the finite difference schemes in order to obtain energy-minimizing snakes. We estimate the approximation error, the residue, and the truncature error related to the corresponding algorithm, then we discuss its convergence, consistency, and stability. Some aspects regarding the prosthetic sugical methods that implement the above numerical methods are also pointed out.

scholarly journals Iterative realization of finite difference schemes in the fictitious domain method for elliptic problems with mixed derivatives

2019 ◽  
pp. 69-76 ◽  
Author(s):  
Vasily M. Volkov ◽  
Alena V. Prakonina
Keyword(s):  
Finite Difference ◽  
Small Parameter ◽  
Iterative Methods ◽  
Difference Schemes ◽  
Fictitious Domain ◽  
Finite Difference Schemes ◽  
Fictitious Domain Method ◽  
Step Size ◽  
Asymptotic Dependence ◽  
Domain Method

Development of efficient finite difference schemes and iterative methods for solving anisotropic diffusion problems in an arbitrary geometry domain is considered. To simplify the formulation of the Neumann boundary conditions, the method of fictitious domains is used. On the example of a two-dimensional model problem of potential distribution in an isolated anisotropic ring conductor a comparative efficiency analysis of some promising finite-difference schemes and iterative methods in terms of their compatibility with the fictitious domain method is carried out. On the basis of numerical experiments empirical estimates of the asymptotic dependence of the convergence rate of the biconjugate gradient method with Fourier – Jacobi and incomplete LU factorization preconditioners on the step size and the value of the small parameter determining the continuation of the conductivity coefficient in the fictitious domain method are obtained. It is shown, that for one of the considered schemes the Fourier – Jacobi preconditioner is spectrally optimal and allows to eliminate the asymptotical dependence of the iterations number to achieve a given accuracy both on the value of the step size and the value of the small parameter in the fictitious domain method.

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