Search results for "finite difference method"
showing 10 items of 63 documents
Smoothed Particle ElectroMagnetics: A mesh-free solver for transients
2006
AbstractIn this paper an advanced mesh-free particle method for electromagnetic transient analysis, is presented. The aim is to obtain efficient simulations by avoiding the use of a mesh such as in the most popular grid-based numerical methods. The basic idea is to obtain numerical solutions for partial differential equations describing the electromagnetic problem by using a set of particles arbitrarily placed in the problem domain. The mesh-free smoothed particle hydrodynamics method has been adopted to obtain numerical solution of time domain Maxwell's curl equations. An explicit finite difference scheme has been employed for time integration. Details about the numerical treatment of elec…
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.
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
Weighted Extrapolation Techniques for Finite Difference Methods on Complex Domains with Cartesian Meshes
2016
The design of numerical boundary conditions in high order schemes is a challenging problem that has been tackled in different ways depending on the nature of the problem and the scheme used to solve it numerically. In this paper we propose a technique to extrapolate the information from the computational domain to ghost cells for schemes with structured Cartesian Meshes on complex domains. This technique is based on the application of Lagrange interpolation with weighted filters for the detection of discontinuities that permits a data dependent extrapolation, with high order at smooth regions and essentially non oscillatory properties near discontinuities. This paper is a sequel of Baeza et…
Qualitative Analysis of Differential, Difference Equations, and Dynamic Equations on Time Scales
2015
and Applied Analysis 3 thank Guest Editors Josef Dibĺik, Alexander Domoshnitsky, Yuriy V. Rogovchenko, Felix Sadyrbaev, and Qi-Ru Wang for their unfailing support with editorial work that ensured timely preparation of this special edition. Tongxing Li Josef Dibĺik Alexander Domoshnitsky Yuriy V. Rogovchenko Felix Sadyrbaev Qi-Ru Wang
Anharmonic force fields from analytic CCSD(T) second derivatives: HOF and F2O
1999
The recent implementation of analytic second derivatives for CCSD(T) (coupled cluster theory with single and double excitations augmented by a perturbational treatment of connected triple excitations) has been combined with a numerical finite difference procedure to calculate cubic and semidiagonal quartic force fields. Computational details of this approach are outlined. Applications are reported for HOF and F2O. The CCSD(T) results are in excellent agreement with experiment and represent a substantial improvement over the results obtained from MP2 (Mo/ller–Plesset second-order perturbation theory).
Determination of Torsional Stresses in Shafts: From Physical Analogies to Mathematical Models
2015
This paper presents the historical development of methods used for the study of torsional stresses in shafts. In particular, the paper covers both analog methods, especially those based on electrical analogies proposed circa 1925, and numerical methods, especially finite difference methods (FDM), finite element methods (FEM) and boundary element methods (BEM).
Finite-Difference Time-Domain Simulation of Towers Cascade Under Lightning Surge Conditions
2015
In this paper, the simulation of towers cascade under lightning surge conditions is presented. Finite-difference time-domain method is used to solve both the Maxwell's and telegraph equations. Maxwell's equations and the time-domain resistivity model of Darveniza are used to simulate the nonlinear behavior of the grounding system. Telegraph equations are used to describe the propagation in the overhead lines. Multiple ionizations, on different grounding electrodes belonging to various towers, can be implemented simultaneously, without making assumptions on the shape of the ionized areas.
A Non-Local Two Dimensional Foundation Model
2012
Classical foundation models such as the Pasternak and the Reissner models have been recently reformulated within the framework of non-local mechanics, by using the gradient theory of elasticity. To contribute to the research effort in this field, this paper presents a two-dimensional foundation model built by using a mechanically based non-local elasticity theory, recently proposed by the authors. The foundation is thought of as an ensemble of soil column elements resting on an elastic base. It is assumed that each column element is acted upon by a local Winkler-like reaction force exerted by the elastic base, by contact shear forces and volume forces due, respectively, to adjacent and non-…
Iterative Methods for Pricing American Options under the Bates Model
2013
We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG meth…