DOMAIN DECOMPOSITION METHODS FOR SOLVING PDE's ON MULTI-PROCESSORS

In this paper, we discuss the parallel domain decomposition method(DDM)for solving PDE's on parallel computers. Three types of DDM: DDM with overlapping, DDM without overlapping and DDM with fictitious component are discussed in a uniform framework. The eonvergence of the asynchronous parallel algorithms based on DDM are discussed.

Effect of Viscous Dissipation (Φ) on Temperature Distribution of Blood Plasma in Presence of a Magnetic Field

Applications of heat transfer show the variations in temperature of the body which is helpful for the purpose of thermal therapy in the treatment of tumor glands. This study considered theoretical approaches in analyzing the effect of viscous dissipation on temperature distribution on the flow of blood plasma through an asymmetric arterial segment. The plasma was considered to be unsteady, laminar and an incompressible fluid through non-uniform arterial segment in a two-dimensional flow. Numerical schemes developed for the coupled partial differential equations governing blood plasma were solved using Finite Difference scheme (FDS). With the aid of the finite difference approach and the related boundary conditions, results for temperature profiles were obtained. The study determined the effect of viscous dissipation on temperature of blood plasma in arteries. The equations were solved using MATLAB softwares and results were presented graphically and in tables. The increase in viscous dissipation tends to decrease blood plasma heat distribution. This study will find important application in hospitals.

Pricing Stochastic Barrier Options under Hull-White Interest Rate Model

A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.

A DUAL COUPLED METHOD FOR BOUNDARY VALUE PROBLEMS OF PDE WITH COEFFICIENTS OF SMALL PERIOD

In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.

Newton-Multigrid for Biological Reaction-Diffusion Problems with Random Coefficients

An algebraic Newton-multigrid method is proposed in order to efficiently solve systems of nonlinear reaction-diffusion problems with stochastic coefficients.These problems model the conversion of starch into sugars in growing apples.The stochastic system is first converted into a large coupled system of deterministic equations by applying a stochastic Galerkin finite element discretization.This method leads to high-order accurate stochastic solutions.A stable and high-order time discretization is obtained by applying a fully implicit Runge-Kutta method.After Newton linearization,a point-based algebraic multigrid solution method is applied.In order to decrease the computational cost,alternative multigrid preconditioners are presented.Numerical results demonstrate the convergence properties,robustness and efficiency of the proposed multigrid methods.

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems

We propose a new semi-implicit level set approach to a class of curvature dependent flows.The method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi(ROF)model for image regularization.Our proposal is general enough so that one can easily extend and apply the method to other curvature dependent motions.Since the derivation is based on a semi-implicit time discretization,this suggests that the numerical scheme is stable even using a time-step significantly larger than that of the corresponding explicit method.As an interesting application of the numerical approach,we propose a new variational approach for extracting limit cycles in dynamical systems.The resulting algorithm can automatically detect multiple limit cycles staying inside the initial guess with no condition imposed on the number nor the location of the limit cycles.Further,we also propose in this work an Eulerian approach based on the level set method to test if the limit cycles are stable or unstable.

Mathematical modeling of atmospheric internal waves phenomenon and its solution by Elzaki Adomian decomposition method

This article involves the study of atmospheric internal waves phenomenon,also referred to as gravity waves.This phenomenon occurs inside the fluid,not on the surface.The model is based on a shallow fluid hypothesis represented by a system of nonlinear partial differential equations.The basic assumption of the shallow flow model is that the horizontal size is much larger than the vertical size.Atmospheric internal waves can be perfectly represented by this model as the waves are spread over a large horizontal area.Here we used the Elzaki Adomian Decomposition Method(EADM)to obtain the solution for the considered model along with its convergence analysis.The Adomian decomposition method together with the Elzaki transform gives the solution in a convergent series without any linearization or perturbation.Comparisons are built between the results obtained by EADM and HAM to examine the accuracy of the proposed method.