Search results for "finite difference method"
showing 10 items of 63 documents
A generalized finite difference method using Coatmèlec lattices
2009
Generalized finite difference methods require that a properly posed set of nodes exists around each node in the mesh, so that the solution for the corresponding multivariate interpolation problem be unique. In this paper we first show that the construction of these meshes can be computerized using a relatively simple algorithm based on the concept of a Coatmelec lattice. Then, we present a generalized finite difference method which provides a numerical solution of a partial differential equation over an arbitrary domain, using the generated meshes. The accuracy and mesh adaptivity of the method is evaluated using elliptical equations in several domains.
Efficient finite-difference scheme for solving some heat transfer problems with convection in multilayer media
2000
Abstract An efficient finite-difference method for solving the heat transfer equation with piecewise discontinuous coefficients in a multilayer domain is developed. The method may be considered as a generalization of the finite-volumes method for the layered systems. We apply this method with the aim to reduce the 3D or 2D problem to the corresponding series of 2D or 1D problems. In the case of constant piecewise coefficients, we obtain the exact discrete approximation of the steady-state 1D boundary-value problem.
Introductory Quantum Physics Courses using a LabVIEW multimedia module
2007
We present the development of a LabVIEW multimedia module for introductory Quantum Physics courses and our experience in the use of this application as an educational tool in learning methodologies. The program solves the Time Dependent Schrodinger Equation for arbitrary potentials. We describe the numerical method used for solving this equation, as well as some mathematical tools employed to reduce the calculation time and to obtain more accurate results. As an illustration, we present the evolution of a wave packet for three different potentials: the repulsive barrier potential, the repulsive step potential, and the harmonic oscillator. This application has been successfully integrated in…
The Mathematical Modeling of Ca And Fe Distribution In Peat Layers
2015
Bogs have been formed by an accumulation of peat - a light brown-to-black organic material, built up from partial decomposition of mosses and other bryophytes, sedges, grasses, shrubs, or trees under waterlogged conditions. The total peatlands area in Latvia covers 698 918 ha or 10.7% of the entire territory. Knowledge’s of peat metals content are important for any kind of peat using. Experimental determination of metals in peat is very long and expensive work. Using experimental data mathematical model for calculation of concentrations of metals in different points for different layers can help to very easy and fast to find approximately concentration of metals or trace elements. The resul…
APPLICATION OF 3‐D FINITE DIFFERENCE METHOD FOR INDUCTANCE CALCULATION OF AIR‐CORE COILS SYSTEM
1994
The paper deals with the inductance calculation of air‐core coils system by means of 3‐D analysis of magnetic field of the coils with rectangular cross‐section. The possibility of mutual and self‐inductance calculation is presented. For magnetic field calculation, the Finite Difference Method with application of fast calculating procedures was applied. The method of calculation has been verified by experiments. The obtained difference between calculating and measurement results is equal to a few percent. The computer program is usefull especially for asymmetrical configuration of the coils.
A Comparison and Survey of Finite Difference Methods for Pricing American Options Under Finite Activity Jump-Diffusion Models
2012
Partial-integro differential formulations are often used for pricing American options under jump-diffusion models. A survey on such formulations and numerical methods for them is presented. A detailed description of six efficient methods based on a linear complementarity formulation and finite difference discretizations is given. Numerical experiments compare the performance of these methods for pricing American put options under finite activity jump models.
A Numerical Approach to Finite Journal Bearings Lubricated With Ferrofluid
1987
Several cases of cylindrical bearings lubricated with ferrofluid are examined by means of a finite-difference numerical procedure. The subregion of cavitation is determined by imposing mass conservation across the “rupture” and “reformation” boundaries of the complete film. The examined cases refer to bearings confined by sealing rings formed by the lubricant itself, for which there is no need of external supply. In each case the most significant parameters are calculated and it is possible to see that the use of these bearings is favorable when speeds are low, clearances large, and loads light, because in such conditions the magnetic effects are comparable with the pure hydrodynamic ones a…
Transmission properties at microwave frequencies of two-dimensional metallic lattices
1999
The transmission properties of different metallic photonic lattices (square and rectangular) have been experimentally studied. A numerical algorithm based on time domain finite differences has been used for simulating these photonic structures. The introduction of defects in the two-dimensional metallic lattice modifies its transmission spectrum. If metal rods are eliminated from (or added to) the lattice, extremely narrow peaks are observed at some particular frequencies below (or above) the band pass edge. Vicente.Such@uv.es ; Enrique.Navarro@uv.es
Finite difference analysis of the thermal behaviour of coated tools in orthogonal cutting of steels
2004
Abstract Temperature measurement and prediction have been a major focus of machining for several decades but now this problem became more important due to the wider use of advanced cutting tool coatings. Practically, there is a lack of simulation programs for prediction of the temperatures in the cutting zone when machining with differently coated cutting tools. In all literature items cited the finite difference methods (finite difference approaches) were used to find the distribution of temperature inside the uncoated tool body or along the tool–chip interface for continuous (turning) and interrupted (milling) machining processes. The algorithm applied overcomes this limit. In this study,…
FINITE DIFFERENCE METHOD-BASED SIMULATION OF TEMPERATURE FIELDS FOR APPLICATION TO ORTHOGONAL CUTTING WITH COATED TOOLS
2005
ABSTRACT A finite difference method was proposed to model the effect of a variety of tool coatings on the magnitude and distribution of temperatures through the tool-chip contact region and the coating/substrate boundaries. For each workpiece-tool pair tested the intensity of uniformly distributed heat flux and relevant analytically obtained values of the heat partition coefficient were assumed to change with variations of cutting speed and the corresponding friction. In this case the simulation of an orthogonal machining of AISI 1045 steel was performed using special computing algorithm with elementary balances of induced energies (MBE). It is concluded that the temperature contours obtain…