We suggest an approach to grid optimization for a second order finite-difference scheme for elliptic equations. A model problem corresponding to the three-point finite-difference semidiscretization of the Laplace equation on a semi-infinite strip is considered. We relate the approximate boundary Neumann-to-Dirichlet map to a rational function and calculate steps of our finite-difference grid us...

We consider discretization of the planar convection of the incompressible fluid in a porous medium filling rectangular enclosure. This problem belongs to the class of cosymmetric systems and admits an existence of a continuous family of steady states in the phase space. Mimetic finite-difference schemes for the primitive variables equation are developed. The connection of a derived staggered di...

We consider finite difference approximations of solutions of inverse Sturm-Liouville problems in bounded intervals. Using three-point finite difference schemes, we discretize the equations on so-called optimal grids constructed as follows: For a staggered grid with 2k points, we ask that the finite difference operator (a k ×k Jacobi matrix) and the Sturm-Liouville differential operator share th...

An algorithm for the generation of hexahedral element meshes is demonstrated. The algorithm starts by creating a structured grid in the interior of an object. Then the boundary region is meshed by means of an isomorphism technique that uses basically 2D-operations. Examples are given that demonstrate the quality of the algorithm.

The method of difference potentials was originally proposed by Ryaben’kii, and is a generalized discrete version of the method of Calderon’s operators. It handles non-conforming curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity of the solver at the level of a finite-difference scheme on a regular structured grid. Compact finite diff...

design of bridge deck with long-term strength, durability and permanence is a significant interest for engineers. one applicable solution to this challenge could be via using hybrid system consisting of conventional materials such as concrete and steel with frp plates which is also known as composite deck. since these deck are relatively new so their performance is not completely known. the pre...