0000000000132970
AUTHOR
A. Tortorici
Wavelet-like bases for thin-wire integral equations in electromagnetics
AbstractIn this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis trans…
Regularization of optical flow with M-band wavelet transform
The optical flow is an important tool for problems arising in the analysis of image sequences. Flow fields generated by various existing solving techniques are often noisy and partially incorrect, especially near occlusions or motion boundaries. Therefore, the additional information on the scene gained from a sequence of images is usually worse. In this paper, discrete wavelet transform has been adopted in order to enhance the reliability of optical flow estimation. A generalization of the well-known dyadic orthonormal wavelets to the case of the dilation scale factor M > 2 with N vanishing moments has been used, and it has proved to be a useful regularizing tool. The advantages in the comp…
An advanced variant of an interpolatory graphical display algorithm
In this paper an advanced interpolatory graphical display algorithm based on cardinal B-spline functions is provided. It is well-known that B-spline functions are a flexible tool to design various scale rapresentations of a signal. The proposed method allows to display without recursion a function at any desiderable resolution so that only initial data and opportune vectors weight are involved. In this way the structure of the algorithm is independent across the scale and a computational efficiency is reached. In this paper mono and bi-dimensional vectors weight generated by means of centered cubic cardinal B-spline functions have been supplied. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Wei…
A Smoothed Particle Interpolation Scheme for Transient Electromagnetic Simulation
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…
An Advanced Numerical Model in Solving Thin-Wire Integral Equations by Using Semi-Orthogonal Compactly Supported Spline Wavelets
Abstract—In this paper, the semi-orthogonal compactly sup- ported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computation- ally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze elec…
Iterative moment method for electromagnetic transients in grounding systems on CRAY T3D
In this paper the parallel aspects of an electromagnetic model for transients in grounding systems based on an iterative scheme are investigated in a multiprocessor environment. A coarse and fine grain parallel solutions have been developed on the CRAY T3D, housed at CINECA, equipped with 64 processors working in space sharing modality. The performances of the two parallel approaches implemented according to the work sharing parallel paradigm have been evaluated for different problem sizes employing variable number of processors.
A Mesh-free Particle Method for Transient Full-wave Simulation
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…
Corrective meshless particle formulations for time domain Maxwell's equations
AbstractIn this paper a meshless approximation of electromagnetic (EM) field functions and relative differential operators based on particle formulation is proposed. The idea is to obtain numerical solutions for EM problems by passing up the mesh generation usually required to compute derivatives, and by employing a set of particles arbitrarily placed in the problem domain. The meshless Smoothed Particle Hydrodynamics method has been reformulated for solving the time domain Maxwell's curl equations. The consistency of the discretized model is investigated and improvements in the approximation are obtained by modifying the numerical process. Corrective algorithms preserving meshless consiste…
On the use of a meshless solver for PDEs governing electromagnetic transients
In this paper some key elements of the Smoothed Particle Hydrodynamics methodology suitably reformulated for analyzing electromagnetic transients are investigated. The attention is focused on the interpolating smoothing kernel function which strongly influences the computational results. Some issues are provided by adopting the polynomial reproducing conditions. Validation tests involving Gaussian and cubic B-spline smoothing kernel functions in one and two dimensions are reported.
The Poisson problem: A comparison between two approaches based on SPH method
Abstract In this paper two approaches to solve the Poisson problem are presented and compared. The computational schemes are based on Smoothed Particle Hydrodynamics method which is able to perform an integral representation by means of a smoothing kernel function by involving domain particles in the discrete formulation. The first approach is derived by means of the variational formulation of the Poisson problem, while the second one is a direct differential method. Numerical examples on different domain geometries are implemented to verify and compare the proposed approaches; the computational efficiency of the developed methods is also studied.
Smoothed Particle ElectroMagnetics: A mesh-free solver for transients
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…
Wavelet-based efficient simulation of electromagnetic transients in a lightning protection system
In this paper, a wavelet-based efficient simulation of electromagnetic transients in a lightning protection systems (LPS) is presented. The analysis of electromagnetic transients is carried out by employing the thin-wire electric field integral equation in frequency domain. In order to easily handle the boundary conditions of the integral equation, semiorthogonal compactly supported spline wavelets, constructed for the bounded interval [0,1], have been taken into account in expanding the unknown longitudinal currents. The integral equation is then solved by means of the Galerkin method. As a preprocessing stage, a discrete wavelet transform is used in order to efficiently compress the Fouri…
Exploiting Numerical Behaviors in SPH.
Smoothed Particle Hydrodynamics is a meshless particle method able to evaluate unknown field functions and relative differential operators. This evaluation is done by performing an integral representation based on a suitable smoothing kernel function which, in the discrete formulation, involves a set of particles scattered in the problem domain. Two fundamental aspects strongly characterizing the development of the method are the smoothing kernel function and the particle distribution. Their choice could lead to the so-called particle inconsistency problem causing a loose of accuracy in the approximation; several corrective strategies can be adopted to overcome this problem. This paper focu…
A Smoothed Particle Image Reconstruction method
Many image processing techniques work with scattered data distribution usually employing grid based methods leading to numerical problems. To address this issue, a numerical method avoiding mesh generation can be used. Such a method performs an integral representation by means of a smoothing kernel function and, in the discrete formulation, involves domain particles. In this paper the meshless Smoothed Particle Hydrodynamics method is proposed in the Image Reconstruction context and a new computational strategy called Smoothed Particle Image Reconstruction is presented; the new method is based on a scatter approach and several innovative ideas are introduced in order to improve the computat…
A Meshless Approach for Electromagnetic Simulation of Metallic Carbon Nanotubes
In this paper, a study on the electromagnetic behaviour of a single wall carbon nanotube model is described. The electrons available for conduction are treated as a thin cylindrical layer fluid and their motion is described by means of classical hydrodynamics equations in linearized form. These equations are solved in time domain using the Smoothed Particle Hydrodynamics method. The method suitably handled runs on GRID environment.
Exploring parallel capabilities of an innovative numerical method for recovering image velocity vectors field
In this paper an efficient method devoted to estimate the velocity vectors field is investigated. The method is based on a quasi-interpolant operator and involves a large amount of computation. The operations characterizing the computational scheme are ideal for parallel processing because they are local, regular and repetitive. Therefore, the spatial parallelism of the process is studied to rapidly proceed in the computation on distributed multiprocessor systems. The process has shown to be synchronous, with good task balancing and requiring a small amount of data transfer.