2D shallow water equations with depth-averaged k−εmodel is considered. A meshless method based on multiquadric radial basis functions isdescribed. This methods is based on the collocation formulation and does not require thegeneration of a grid and any integral evaluation. The application of this method to a flowin horizontal channel, taken as an experimental device, is presented. The results ofcomputations are compared with experimental data and are found to be satisfactory

Plant growth depends essentially on nutrients coming from the roots and metabolitesproduced by the plant. Appearance of new branches is determined by concentrations ofcertain plant hormones. The most important of them are Auxin and Cytokinin. Auxin isproduced in the growing, Cytokinin in either roots or in growing parts. Many dynamicalmodels of this phenomena have been studied in [1]. In [5], the authors deal with onebranch model. In this work, we focus our interest on a multiple branch model. We deal withthe transport equation in domains of different sizes. A variational reduction type method[3] based on asymptotic partial decomposition introduced in [2] (see also [4]) is used. Inthis work we consider the transport equation in decomposed domain with a general righthand side

The Asymptotic Numerical Method (ANM) is a family of algorithms, based on computation oftruncated vectorial series, for path following problems [2]. In this paper, we present anddiscuss some techniques to define local parameterization [4, 6, 7] in the ANM. We givesome numerical comparisons of pseudo arc-length parameterization and localparameterization on non-linear elastic shells problems

We present in this work a numerical study of a problem governed by Navier-Stokesequations and heat equation. The mathematical problem under consideration is obtained bymodelling the natural convection of an incompressible fluid, in laminar flow between twohorizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposedto be greater than the outer one. The numerical simulation of the flow is carried out bycollocation-Legendre method. The influence of Prandtl and Rayleigh numbers isinvestigated

This paper is devoted to the study of global existence of periodic solutions of a delayedtumor-immune competition model. Also some numerical simulations are given to illustratethe theoretical results

Propagation of polymerization fronts with liquid monomer and liquid polymer is consideredand the influence of vibrations on critical conditions of convective instability isstudied. The model includes the heat equation, the equation for the concentration and theNavier-Stokes equations considered under the Boussinesq approximation. Linear stabilityanalysis of the problem is fulfilled, and the convective instability boundary is founddepending on the amplitude and on the frequency of vibrations

Evolution of cell populations can be described with dissipative particle dynamics, whereeach cell moves according to the balance of forces acting on it, or with partialdifferential equations, where cell population is considered as a continuous medium. Wecompare these two approaches for some model examples

It is shown that a real Hankel matrix admits an approximate block diagonalization inwhich the successive transformation matrices are upper triangular Toeplitz matrices. Thestructure of this factorization was first fully discussed in [1]. This approach isextended to obtain the quotients and the remainders appearing in the Euclidean algorithmapplied to two polynomials u(x) andv(x) of degree n andm, respectively, whith m <n

In this paper, we will discuss the meshless polyharmonic reconstruction of vector fieldsfrom scattered data, possibly, contaminated by noise. We give an explicit solution of theproblem. After some theoretical framework, we discuss some numerical aspect arising in theproblems related to the reconstruction of vector fields

We present an iterative method based on an infinite dimensional adaptation of thesuccessive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation.In a wide range of application, the neutron transport operator admits a Self-Adjoint andm-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method whichconverges unconditionally and is equivalent to a fixed point problem where the operator isa 2 by 2 matrix of operators. An infinite dimensional adaptation of a SOR algorithm isthen applied to solve the matrix operator equation. Theoretical and numerical results ofconvergence are given

In this paper, a new a posteriori error estimator for nonconforming convection diffusionapproximation problem, which relies on the small discrete problems solution in stars, hasbeen established. It is equivalent to the energy error up to data oscillation without anysaturation assumption nor comparison with residual estimator

We derive a residual a posteriori error estimates for the subscales stabilization ofconvection diffusion equation. The estimator yields upper bound on the error which isglobal and lower bound that is local

Anisotropic adaptive methods based on a metric related to the Hessian of the solution areconsidered. We propose a metric targeted to the minimization of interpolation errorgradient for a nonconforming linear finite element approximation of a given piecewiseregular function on a polyhedral domain Ω ofℝ d , d ≥ 2. We alsopresent an algorithm generating a sequence of asymptotically quasi-optimal meshes relativeto such a nonconforming discretization and give numerical asymptotic behavior of the errorreduction produced by the generated mesh

We consider the problem of frictional contact between an piezoelectric body and aconductive foundation. The electro-elastic constitutive law is assumed to be nonlinear andthe contact is modelled with the Signorini condition, nonlocal Coulomb friction law and aregularized electrical conductivity condition. The existence of a unique weak solution ofthe model is established. The finite elements approximation for the problem is presented,and error estimates on the solutions are derived

We present a new method for generating a d-dimensional simplicial meshthat minimizes the L p -norm,p > 0, of the interpolation error or its gradient. The methoduses edge-based error estimates to build a tensor metric. We describe and analyze thebasic steps of our method

In this paper, a new hybrid simulated annealing algorithm for constrained globaloptimization is proposed. We have developed a stochastic algorithm called ASAPSPSA thatuses Adaptive Simulated Annealing algorithm (ASA). ASA is a series of modifications to thebasic simulated annealing algorithm (SA) that gives the region containing the globalsolution of an objective function. In addition, Simultaneous Perturbation StochasticApproximation (SPSA) method, for solving unconstrained optimization problems, is used torefine the solution. We also propose Penalty SPSA (PSPSA) for solving constrainedoptimization problems. The constraints are handled using exterior point penalty functions.The combination of both techniques ASA and PSPSA provides a powerful hybrid optimizationmethod. The proposed method has a good balance between exploration and exploitation withvery fast computation speed, its performance as a viable large scale optimization methodis demonstrated by testing it on a number of benchmark functions with 2 - 500 dimensions.In addition, applicability of the algorithm on structural design was tested and successfulresults were obtained

In this paper we present a new hybrid method, called SASP method. We propose thehybridization of two methods, the simulated annealing (SA), which belong to the class ofglobal optimization based on the principles of thermodynamics, and the descent method werewe estimate the gradient using the simultaneous perturbation. This hybrid method givesbetter results. We use the Normal Boundary Intersection approach (NBI) based on the SASPmethod to solve a portfolio optimization problem. Such problem is a multi-objectiveoptimization problem, in order to solve this problem we use three statistical quantities:the expected value, the variance and the Conditional Value-at-Risk (CVaR). The purpose ofthis work is to find the efficient boundary of the considered multi-objective problemusing the NBI method based on the SASP method

The goal of this paper is to apply the Continuous Hopfield Networks (CHN) to thePlacement of Electronic Circuit Problem (PECP). This assignment problem has been expressedas Quadratic Knapsack Problem (QKP). To solve the PECP via the CHN, we choose an energyfunction which ensures an appropriate balance between minimization of the cost functionand simultaneous satisfaction of the PECP constraints. In addition, the parameters of thisfunction must avoid some bad local minima. Finally, some computational experiments solvingthe PECP are included

The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which thefeasible set is determined by the set of optimal solutions of parametric Knapsack Problem.In this paper, we propose two stages exact method for solving the BKP. In the first stage,a dynamic programming algorithm is used to compute the set of reactions of the follower.The second stage consists in solving an integer program reformulation of BKP. We show thatthe integer program reformulation is equivalent to the BKP. Numerical results show theefficiency of our method compared with those obtained by the algorithm of Moore andBard