A tutorial on wavelets from an electrical engineering perspective.I. Discrete wavelet techniques

The objective of this paper is to present the subject of wavelets from a filter-theory perspective, which is quite familiar to electrical engineers. Such a presentation provides both physical and mathematical insights into the problem. It is shown that taking the discrete wavelet transform of a function is equivalent to filtering it by a bank of constant-Q filters, the non-overlapping bandwidths of which differ by an octave. The discrete wavelets are presented, and a recipe is provided for generating such entities. One of the goals of this tutorial is to illustrate how the wavelet decomposition is carried out, starting from the fundamentals, and how the scaling functions and wavelets are generated from the filter-theory perspective. Examples (including image compression) are presented to illustrate the class of problems for which the discrete wavelet techniques are ideally suited. It is interesting to note that it is not necessary to generate the wavelets or the scaling functions in order to implement the discrete wavelet transform. Finally, it is shown how wavelet techniques can be used to solve operator/matrix equations. It is shown that the “orthogonal-transform property” of the discrete wavelet techniques does not hold in numerical computations     

Efficient solution of the differential form of Maxwell's equationsin rectangular regions

One of the problems of the finite element and the finite difference method is that as the dimension of the problem increases, the condition number of the system matrix increases as Θ(1/h² ) (of the order of h², where h is the subsection length). Through the use of a suitable basis function tailored for rectangular regions, it is shown that the growth of the condition number can be checked while still retaining the sparsity of the system matrix. This is achieved through a proper choice of entire domain basis functions. Numerical examples have been presented for efficient solution of waveguide problems with rectangular regions utilizing this approach     

On the use of many-core machines for the acceleration of a mesh truncation technique for FEM

The Journal of Supercomputing - Finite element method (FEM) has been used for years for radiation problems in the field of electromagnetism. To tackle problems of this kind, mesh truncation...     

Green's function analysis of single and stacked rectangularmicrostrip patch antennas enclosed in a cavity

A rigorous Green's function analysis of rectangular microstrip patch antennas enclosed in a rectangular cavity is described. The formulation makes use of a frequency-independent preprocessing (image extraction) on the spectral domain representation of the Green's function. Measured and simulated results are shown for both single and stacked-patch antennas enclosed in a cavity     

Experimental study of the impact behavior of repaired thin laminates with double composite patch

Abstract

The aim of this article is to present a study of the behavior of patch-repaired laminates subjected to low-velocity impacts. A broad range of impact energies was selected. Results for repaired laminates in terms of contact load, damage and absorbed energy were compared to those obtained from intact specimens. At impact energies below 10?J, energy absorption in repaired specimens was higher than the one given in intact laminates, although the measured damage area was found to be greater in the former configuration. For higher impact energies, both damage area and energy absorption in intact specimens were greater than in repaired laminates.     

Fully Coupled Hybrid FEM-UTD Method Using NURBS for the Analysis of Radiation Problems

A novel hybrid finite element method (FEM) -uniform theory of diffraction (UTD) method for the analysis of radiating structures in the presence of electrically large objects is presented. The hybridization is done in a fully coupled way taking into account mutual interactions between the FEM and UTD regions. The UTD objects are modeled using non-uniform rational B-spline (NURBS) surfaces. Ray acceleration techniques and simple clustering strategies are used to speed up the computation time. Numerical results are presented showing the validity of the method.