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Kanaun S.,ITESM CEM | Levin V.,Mexican Institute of Petroleum
Wave Motion | Year: 2013

The problem of scattering of plane monochromatic elastic waves on an isolated heterogeneous inclusion of arbitrary shape is considered. Volume integral equations for elastic displacements in heterogeneous media are used for reducing this problem to the region occupied by the inclusion. Discretization of this equation is carried out by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms. For regular grids of approximating nodes, the matrix of the discretized problem has the Toeplitz properties, and the matrix-vector products can be calculated by the Fast Fourier Transform technique. The latter strongly accelerates the process of the iterative solution of the discretized problem. Elastic displacements and differential cross-sections of a homogeneous spherical inclusion are calculated for longitudinal and transversal incident waves of various wave lengths. The numerical results are compared with exact solutions. The displacement fields and differential cross-sections of a cylindrical inclusion are calculated for incident fields of different directions with respect to the cylinder axis. © 2013. Source


Garcia Garcia J.F.,ITESM CEM | Venegas-Andraca S.E.,Monterrey Institute of Technology
Machine Vision and Applications | Year: 2015

Image segmentation methods based on spectral graph theory, although capable of overcoming some of the drawbacks of the so-called “central”-grouping methods, are computationally expensive and quickly become infeasible to solve as the size of the image grows. As a counter measure, the Nyström approximation allows to extrapolate the complete grouping solution for these methods using only a proportionally smaller set of samples instead of the whole pixels that compose the image. In this correspondence, we further explore the Nyström approximation by taking the concept of “regions”, pixels of the image previously grouped by a central method, to both reduce the computational resources required and provide a finer segmentation of the image by combining the strengths of both methods. We apply the proposed approach to the segmentation of images of burns where we attempt to extract regions that would roughly correspond to the different degrees of the lesion. © 2015, Springer-Verlag Berlin Heidelberg. Source


Kanaun S.,ITESM CEM
Progress In Electromagnetics Research B | Year: 2010

The work is devoted to the problem of scattering of monochromatic electromagnetic waves on heterogeneous dielectric inclusions of arbitrary shapes. For the numerical solution of the problem, the volume integral equation for the electric field in the region occupied by the inclusion is used. Discretization of this equation is carried out by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms. For a regular grid of approximating nodes, the matrix of the discretized problem proves to have the Toeplitz structure, and the matrix-vector product with such matrices can be carried out by the Fast Fourier Transform technique. The latter strongly accelerates the process of the iterative solution of the discretized problem. Electric fields inside a spherical inclusion and its differential cross-sections are calculated and compared with the exact (Mie) solution for various wave lengths of the incident field. Internal electric fields and the differential cross-sections of a cylindrical inclusion are calculated for the incident fields of various directions and wave lengths. Source


Kanaun S.,ITESM CEM | Pervago E.,Mexican Institute of Petroleum
International Journal of Engineering Science | Year: 2011

The work is devoted to the calculation of static elastic fields in 3D-composite materials consisting of a homogeneous host medium (matrix) and an array of isolated heterogeneous inclusions. A self-consistent effective field method allows reducing this problem to the problem for a typical cell of the composite that contains a finite number of the inclusions. The volume integral equations for strain and stress fields in a heterogeneous medium are used. Discretization of these equations is performed by the radial Gaussian functions centered at a system of approximating nodes. Such functions allow calculating the elements of the matrix of the discretized problem in explicit analytical form. For a regular grid of approximating nodes, the matrix of the discretized problem has the Toeplitz properties, and matrix-vector products with such matrices may be calculated by the fast fourier transform technique. The latter accelerates significantly the iterative procedure. First, the method is applied to the calculation of elastic fields in a homogeneous medium with a spherical heterogeneous inclusion and then, to composites with periodic and random sets of spherical inclusions. Simple cubic and FCC lattices of the inclusions which material is stiffer or softer than the material of the matrix are considered. The calculations are performed for cells that contain various numbers of the inclusions, and the predicted effective constants of the composites are compared with the numerical solutions of other authors. Finally, a composite material with a random set of spherical inclusions is considered. It is shown that the consideration of a composite cell that contains a dozen of randomly distributed inclusions allows predicting the composite effective elastic constants with sufficient accuracy.. © 2010 Elsevier Ltd. All rights reserved. Source


Kanaun S.,ITESM CEM
International Journal of Engineering Science | Year: 2011

In the work, a numerical method for calculation of electro and thermo static fields in matrix composite materials is considered. Such materials consist of a regular or random set of isolated inclusions embedded in a homogeneous background medium (matrix). The proposed method is based on fast calculation of fields in a homogeneous medium containing a finite number of isolated inclusions. By the solution of this problem, the volume integral equations for the fields in heterogeneous media are used. Discretization of these equations is carried out by Gaussian approximating functions that allow calculating the elements of the matrix of the discretized problem in explicit analytical forms. If the grid of approximating nodes is regular, the matrix of the discretized problem proves to have the Toeplitz structure, and the matrix-vector product with such matrices can be calculated by the Fast Fourier Transform technique. The latter strongly accelerates the process of iterative solution of the discretized problem. In the case of an infinite medium containing a homogeneous in space random set of inclusions, our approach combines a self-consistent effective field method with the numerical solution of the conductivity problem for a typical cell. The method allows constructing detailed static (electric or temperature) fields in the composites with inclusions of arbitrary shapes and calculating effective conductivity coefficients of the composites. Results are given for 2D and 3D-composites and compared with the existing exact and numerical solutions. © 2010 Elsevier Ltd. All rights reserved. Source

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