Search results for "finite difference"
showing 10 items of 122 documents
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…
Nonlinear System Response for Impulsive Parametric Input
1997
In engineering applications when the intensity of external forces depends on the response of the system, the input is called parametric. In this paper dynamical systems subjected to a parametric deterministic impulse are dealt with. Particular attention has been devoted to the evaluation of the discontinuity of the response when the parametric impulse occurs. The usual forward difference and trapezoidal integration schemes have been shown to provide only approximated solutions of the jump of the response; hence, the exact solution has been pursued and presented under the form of a numerical series. The impulse is represented throughout the paper by means of a classical Dirac’s delta functio…
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…
FDTD simulation for electromagnetic radiated emissions in 42 V vehicle electrical systems
2005
In this paper a full 3D approach, based on finite difference time domain method, is used to predict the electromagnetic radiated emissions from 42 V vehicle electrical loads. An experimental set-up has been arranged on purpose. A comparative analysis among measured and computed results is performed. The good agreement obtained among simulated and measured data enables to validate the numerical scheme. The proposed methodology contributes to predict electromagnetic emissions in the automotive environment since the design stage. Moreover, the proposed numerical tool can be used to define, for new vehicle electrical architectures, low cost test methods for electromagnetic compatibility and sui…
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.
Finite difference time domain simulation of earth electrodes soil ionisation under lightning surge condition
2008
The non linear effects of soil ionisation on the behaviour of earth electrodes are investigated by a finite difference time domain numerical scheme. A time variable soil resistivity is used in order to simulate the soil breakdown; step by step the resistivity value is controlled by the local instantaneous value of the electric field compared with the electrical strength, fixed for the soil. No a priori hypothesis about the geometrical shape of the ionised zone around the electrodes has to be enforced. Simulation results related to complex earth electrodes of limited extension are reported. The model has been validated by comparing the computed results with data available in technical litera…
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…
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.