Search results for "difference [momentum]"
showing 10 items of 141 documents
Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian
2017
Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.
Multi-level contrast filtering in image difference metrics
2013
In this paper, we present a new metric to estimate the perceived difference in contrast between an original image and a reproduction. This metric, named weighted-level framework Δ E E (WLF-DEE), implements a multilevel filtering based on the difference of Gaussians model proposed by Tadmor and Tolhurst (2000) and the new Euclidean color difference formula in log-compressed OSA-UCS space proposed by Oleari et al. (2009). Extensive tests and analysis are presented on four different categories belonging to the well-known Tampere Image Database and on two databases developed at our institution, providing different distortions directly related to color and contrast. Comparisons in performance wi…
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…
Sub-wavelength imaging of light confinement and propagation in SOI based photonic crystal devices
2006
A light source is coupled into photonic crystal devices and a near field optical probe is used to observe the electromagnetic field propagation and distribution at a sub-wavelength scale. Bloch modes are clearly observed.
A Smoothed Particle Interpolation Scheme for Transient Electromagnetic Simulation
2006
In this paper, the fundamentals of a mesh-free particle numerical method for electromagnetic transient simulation are presented. The smoothed particle interpolation methodology is used by considering the particles as interpolation points in which the electromagnetic field components are computed. The particles can be arbitrarily placed in the problem domain: No regular grid, nor connectivity laws among the particles, have to be initially stated. Thus, the particles can be thickened only in distinct confined areas, where the electromagnetic field rapidly varies or in those regions in which objects of complex shape have to be simulated. Maxwell’s equations with the assigned boundary and initi…