Numerical modeling of heat transfer during solidification has become widespread in the foundry industry. This is because it is possible to investigate the effects of adjustment to the casting variables on final casting quality, without having to do costly trial-and-error experiments. After selecting a suitable mathematical model, one has to choose an appropriate discretization method. If the gr...

abstract: The PCD (piecewise constant distributions) method is a discretization technique of the boundary value problems in which the unknown distribution and its derivatives are represented by piecewise constant distributions but on distinct meshes. It has the advantage of producing the most sparse stiffness matrix resulting from the approximate problem. In this contribution, we propose a gene...

A three-dimensional unstructured mesh discretization of the rotational from of the incompressible Navier–Stokes is presented. The method uses novel and highly efficient algorithms for interpolating the velocity vector and constructing the convention term. The resulting discretization is shown to conserve mass, kinetic energy, and vorticity to machine precision both locally and globally. The spa...

The linear systems with separable matrices arising from the nite diierence discretization of constant-coeecient elliptic equations in rectangles are considered. A new direct method is proposed and analyzed for the approximate solution of general partial solution problems for such systems of grid equations. This method can be used also with quasiuniform discretization grids, whereas the earlier ...

Abstract. In this paper we present a hybrid finite difference scheme on a piecewise uniform mesh for a class of Black-Scholes equations governing option pricing which is path-dependent. In spatial discretization a hybrid finite difference scheme combining a central difference method with an upwind difference method on a piecewise uniform mesh is used. For the time discretization, we use an impl...

We present a numerical scheme for an efficient discretization of nonlinear systems of differential equations subjected to highly oscillatory perturbations. This method is superior to standard ODE numerical solvers in the presence of high frequency forcing terms, and is based on asymptotic expansions of the solution in inverse powers of the oscillatory parameter ω, featuring modulated Fourier se...

The main aim of this paper is to examine the effectiveness of the Half-Sweep Arithmetic Mean (HSAM) iterative method in solving dense linear systems generated from the discretization of the first and second kind linear Fredholm integral equations. The formulation and implementation of the proposed method is also presented. Numerical tests and comparisons with other existing methods are given to...

We propose a finite element discretization of a problem issued from the fictitious domain technique. We prove a priori error estimates for the discrete problem and present numerical experiments which are in good agreement with the analysis. Résumé: Nous proposons une discrétisation par éléments finis d’un problème lié à la technique de domaine fictif. Nous prouvons des estimations d’erreur a pr...

In this work, numerical solution of 3D-integral equations of electro-static theory for an infinite homogeneous medium with a heterogeneous isolated inclusion is considered. Gaussian approximating functions are used for discretization of the integral equations of the problem. These functions essentially simplify construction of the matrix of the system of linear algebraic equations to which the ...

This paper is concerned with the design of a spatial discretization method for polar and nonpolar parabolic equations in one space variable. A new spatial discretization method suitable for use in a library program is derived. The relationship to other methods is explored. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithm and to compare it...