Search results for "finite difference method"
showing 10 items of 63 documents
Generalized finite difference schemes with higher order Whitney forms
2021
Finite difference kind of schemes are popular in approximating wave propagation problems in finite dimensional spaces. While Yee’s original paper on the finite difference method is already from the sixties, mathematically there still remains questions which are not yet satisfactorily covered. In this paper, we address two issues of this kind. Firstly, in the literature Yee’s scheme is constructed separately for each particular type of wave problem. Here, we explicitly generalize the Yee scheme to a class of wave problems that covers at large physics field theories. For this we introduce Yee’s scheme for all problems of a class characterised on a Minkowski manifold by (i) a pair of first ord…
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…
A Mesh-free Particle Method for Transient Full-wave Simulation
2007
A mesh-free particle method is presented for electromagnetic (EM) transient simulation. The basic idea is to obtain numerical solutions for the partial differential equations describing the EM problem in time domain, by using a set of particles, considered as spatial interpolation points of the field variables, arbitrarily placed in the problem domain and by avoiding the use of a regular mesh. Irregular problems geometry with diffused non-homogeneous media can be modeled only with an initial set of arbitrarily distributed particles. The time dependence is accounted for with an explicit finite difference scheme. Moreover the particle discretization can be improved during the process time ste…
Controllability method for acoustic scattering with spectral elements
2007
We formulate the Helmholtz equation as an exact controllability problem for the time-dependent wave equation. The problem is then discretized in time domain with central finite difference scheme and in space domain with spectral elements. This approach leads to high accuracy in spatial discretization. Moreover, the spectral element method results in diagonal mass matrices, which makes the time integration of the wave equation highly efficient. After discretization, the exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method. We illustrate the method with some numerical experiments, which demonstrate the significant improveme…
Method of Lines and Finite Difference Schemes with Exact Spectrum for Solving Some Linear Problems of Mathematical Physics
2013
In this paper linear initial-boundary-value problems of mathematical physics with different type boundary conditions BCs and periodic boundary conditions PBCs are studied. The finite difference scheme FDS and the finite difference scheme with exact spectrum FDSES are used for the space discretization. The solution in the time is obtained analytically and numerically, using the method of lines and continuous and discrete Fourier methods.
Swing options in commodity markets: a multidimensional Lévy diffusion model
2013
Author's version of an article in the journal: Mathematical Methods of Operations Research. Also available from the publisher at: http://dx.doi.org/10.1007/s00186-013-0452-7 We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constraint. We analyze some general properties of the model and study the solution by analyzing the associated HJB-equation. Furthermo…
On the Efficacy of PCM to Shave Peak Temperature of Crystalline Photovoltaic Panels: An FDM Model and Field Validation
2013
The exploitation of renewable energy sources and specifically photovoltaic (PV) devices have been showing significant growth; however, for a more effective development of this technology it is essential to have higher energy conversion performances. PV producers often declare a higher efficiency respect to real conditions and this deviation is mainly due to the difference between nominal and real temperature conditions of the PV. In order to improve the solar cell energy conversion efficiency many authors have proposed a methodology to keep the temperature of a PV system lower: a modified crystalline PV system built with a normal PV panel coupled with a Phase Change Material (PCM) heat stor…
Finite difference thermal model of a latent heat storage system coupled with a photovoltaic device: Description and experimental validation
2014
Abstract The use of photovoltaic (PV) systems has been showing a significant growth trend but for a more effective development of this technology it is essential to have higher energy conversion performances. Producers of PV often declare an higher efficiency respect to real conditions and this deviation is mainly due to the difference between nominal and real temperature conditions of the PV. To improve the solar cell energy conversion efficiency many authors have proposed a methodology to keep lower the temperature of a PV system: a modified PV system built with a normal PV panel coupled with a Phase Change Material (PCM) heat storage device. In this paper is described a thermal model ana…
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.
Simple algorithms for calculation of the axial‐symmetric heat transport problem in a cylinder
2001
The approximation of axial‐symmetric heat transport problem in a cylinder is based on the finite volume method. In the classical formulation of the finite volume method it is assumed that the flux terms in the control volume are approximated with the finite difference expressions. Then in the 1‐D case the corresponding finite difference scheme for the given source function is not exact. There we propose the exact difference scheme. In 2‐D case the corresponding integrals are approximated using different quadrature formulae. This procedure allows one to reduce the heat transport problem described by a partial differential equation to an initial‐value problem for a system of two ordinary diff…