On the convergence rate of a parallel nonoverlapping domain decomposition method

In recent years,a nonoverlapping domain decomposition iterative procedure,which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces,has been developed and analyzed.It is known that the convergence rate of this method is 1-O(h),where h is mesh size.In this paper,the convergence rate is improved to be 1-O(h1/2 H-1/2)sometime by choosing suitable parameter,where H is the subdomain size.Counter examples are constructed to show that our convergence estimates are sharp,which means that the convergence rate cannot be better than 1-O(h1/2H-1/2)in a certain case no matter how parameter is chosen.

NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS

In this paper we consider the nonoverlapping domain decomposition method based on mixed element approximation for elliptic problems in two dimentional space. We give a kind of discrete domain decomposition iterative algorithm using mixed finite element, the subdomain problems of which can be implemented parallelly. We also give the existence, uniqueness and convergence of the approximate solution.

Simulation and computational heat transfer in the human eye with Dirichlet–Neumann domain decomposition approximation

In this paper,a bioheat model of temperature distribution in the human eye is studied,the mathematical formulation of this model is described using adequate mathematical tools.The existence and the uniqueness of the solution of this problem is proven and four algorithms based on finite element method approximation and domain decomposition methods are presented in details.The validation of all algorithm is done using a numerical application for an example where the analytical solution is known.The properties and parameters reported in the open literature for the human eye are used to approximate numerically the temperature for bioheat model by finite element approximation and nonoverlapping domain decomposition method.The obtained results that are verified using the experimental results recorded in the literature revealed a better accuracy by the use of algorithm proposed.

Nonoverlapping Dirichlet-Neumann method for transient bioheat transfer in the human eye

This paper presents a 2D simulation of transient heat transfer in the human eye using appropriate boundary conditions.The mathematical model governing bioheat transfer in the human eye is discussed and the existence and uniqueness of the solution are proven.Four methods based on finite element method and nonoverlapping domain decomposition method to obtain transient heat transfer in the human eye are presented and described in details.After conducting numerous simulations using realistic parameters obtained from the open literature and after comparison with measurements reported by previous experimental studies,all proposed methods gave an accurate representation of transient heat transfer in the human eye.The results obtained by the domain decomposition of the human eye into four subdomains are found to be the closest to reality.