Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Thu, 24 Oct 2019 02:34:31 GMT2019-10-24T02:34:31Z10401COMPUTATIONAL ASPECTS OF PSEUDOSPECTRAL LAGUERRE APPROXIMATIONShttp://hdl.handle.net/11380/761489Titolo: COMPUTATIONAL ASPECTS OF PSEUDOSPECTRAL LAGUERRE APPROXIMATIONS
Abstract: Pseudospectral approximations in unbounded domains by Laguerre polynomials lead to ill-conditioned algorithms. We introduce a scaling function and appropriate numerical procedures to limit these phenomena.
Mon, 01 Jan 1990 00:00:00 GMThttp://hdl.handle.net/11380/7614891990-01-01T00:00:00ZHigh Frequency Electrical Oscillations in Cavitieshttp://hdl.handle.net/11380/1171952Titolo: High Frequency Electrical Oscillations in Cavities
Abstract: If the interior of a conducting cavity (such as a capacitor or a coaxial cable) is supplied with a very high-frequency electric signal, the information between the walls propagates with an appreciable delay, due to the ﬁniteness of the speed of light. The conﬁguration is typical of cavities having size larger than the wavelength of the injected signal. Such a non rare situation, in practice, may cause a break down of the performances of the device. We show that the classical Coulomb’s law and Maxwell’s equations do not correctly predict this behavior. Therefore, we provide an extension of the modeling equations that allows for a more reliable determination of the electromagnetic ﬁeld during the evolution process. The main issue is that, even in vacuum (no dielectric inside the device), the fast variation of the signal produces sinks and sources in the electric ﬁeld, giving rise to zones where the divergence is not zero. These regions are well balanced, so that their average in the domain is zero. However, this behavior escapes the usual treatment with classical electromagnetism.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11380/11719522018-01-01T00:00:00ZTrapping Electromagnetic Solitons in Cylindershttp://hdl.handle.net/11380/1057914Titolo: Trapping Electromagnetic Solitons in Cylinders
Abstract: Electromagnetic waves in vacuum or dielectrics can be confined in unbounded cylinders in such a way that they turn around the main axis. For particular choices of the cylinder's section, interesting stationary configurations may be assumed. By refining some results obtained in previous papers, additional more complex situations are examined here. For such peculiar guided waves an explicit expression is given in terms of Bessel's functions. Possible applications are in the development of whispering gallery resonators.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10579142014-01-01T00:00:00ZSimulation of Electromagnetic Scattering with Stationary or Accelerating Targetshttp://hdl.handle.net/11380/1057917Titolo: Simulation of Electromagnetic Scattering with Stationary or Accelerating Targets
Abstract: The scattering of electromagnetic waves by an obstacle is analyzed
through a set of partial differential equations combining the Maxwell's
model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be modeled in this context since they turn out
to be explicit solutions. From the numerical viewpoint, the interaction of
these waves with a material body is examined. Computations are carried
out via a parallel high-order finite-differences code. Due to the presence of
a gradient of pressure in the model equations, waves hitting the obstacle
may impart acceleration to it. Some explicative 2D dynamical configurations are then studied, enabling the study of photon-particle iterations
through classical arguments.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10579172014-01-01T00:00:00ZA note on second-order finite-difference schemes on uniform meshes for advection-diffusion equationshttp://hdl.handle.net/11380/7674Titolo: A note on second-order finite-difference schemes on uniform meshes for advection-diffusion equations
Abstract: An artificial-viscosity finite-difference scheme is introduced for stabilizing the solutions of advection-diffusion equations. Although only the linear one-dimensional case is discussed, the method is easily susceptible to generalization. Some theory and comparisons with other well-known schemes are carried out. The aim is, however, to explain the construction of the method, rather than considering sophisticated applications.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/11380/76741999-01-01T00:00:00ZSome remarks about the collocation method on a modified Legendre gridhttp://hdl.handle.net/11380/9211Titolo: Some remarks about the collocation method on a modified Legendre grid
Abstract: We compare the results obtained by applying the standard collocation method at the Legendre Gauss-Lobatto nodes, for a model problem simulating a steady advection-diffusion equation, with those obtained by collocating at a new set of nodes. These nodes are derived from a suitable modification of the Legendre grid, according to the magnitude of the ratio between the advective and the diffusive parts of the differential operator.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11380/92111997-01-01T00:00:00ZFinite-difference schemes for transport-dominated equations using special collocation nodeshttp://hdl.handle.net/11380/306527Titolo: Finite-difference schemes for transport-dominated equations using special collocation nodes
Abstract: We introduce finite-difference schemes based on a special upwind-type collocation grid, in order to obtain approximations of the solution of linear transport-dominated advection-diffusion problems. The method is well suited when the diffusion parameter is very small compared to the discretization parameter. A theory is developed and many numerical experiments are shown.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11380/3065272005-01-01T00:00:00ZA Model for Ball Lightning Derived from an Extension of the Electrodynamics Equationshttp://hdl.handle.net/11380/1168646Titolo: A Model for Ball Lightning Derived from an Extension of the Electrodynamics Equations
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11380/11686462018-01-01T00:00:00ZPolynomial Approximation of Differential Equationshttp://hdl.handle.net/11380/743618Titolo: Polynomial Approximation of Differential Equations
Abstract: This book is a basic and comprehensive introduction to the use of spectral methods for the approximation of the solution to ordinary differential equations and time-dependent boundary-value problems. The algorithms are presented and studied both from the point of view of the theoreticalanalysis of convergence and the numerical implementation. Unlike other texts devoted to the subject this is a concise introduction that is ideally suited to the novice and practitioner alike, enabling them to assimilate themethods quickly and efficiently.
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/11380/7436181992-01-01T00:00:00ZSpectral Elements for Transport-Dominated Equationshttp://hdl.handle.net/11380/743620Titolo: Spectral Elements for Transport-Dominated Equations
Abstract: The book deals with the numerical approximation of various PDEs using the spectral element method, with particular emphasis for elliptic equations dominated by first-order terms. It provides a simple introduction to spectral elements with additional new tools (upwind grids and preconditioners). Applications to fluid dynamics and semiconductor devices are considered, as well as in other models were transport-diffusion equations arise. The aim is to provide the reader with both introductive and more advanced material on spectral Legendre collocation methods. The book however does not cover all the aspects of spectral methods. Engineers, physicists and applied mathematicians may study how to implement the collocation method and use the results to improve their computational codes.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11380/7436201997-01-01T00:00:00Z