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Your search keyword '"LINEAR systems"' showing total 2 results
Start Over Descriptor "LINEAR systems" Topic numerical analysis Language spanish
2 results on '"LINEAR systems"'

1. Método EBE de los elementos finitos para sistemas de gran tamaño y su aplicación en la Física Digital de Rocas.

Author

Benavides Murillo, Francisco José

Subjects
*FINITE element method, *SPARSE matrices, *PARTIAL differential equations, *LINEAR equations, *LINEAR systems, *DATA structures
Abstract

The finite element method (FEM) is a numerical technique that estimates solutions of partial differential equations on arbitrary domains. It has been widely used to solve problems in Physics and Engineering. In general, the final step of this technique consists of a linear system of equations Ax=b in which the matrix A is sparse and its bandwidth depends on the finite element shape functions support. When the number of elements is large, even the efficient data structure sparse matrix representations can consume the entire computer memory. In this article, we describe a technique to solve these large-scale problems without explicitly representing this matrix. This computational trick is known as EBE (Element By Element). We also describe an application in which such kind of implementation is necessary, in the field of digital rock physics, to estimate the elastic coefficient of rock samples using micro-tomographic images. [ABSTRACT FROM AUTHOR]

Published
2019
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2. Solución Numérica de los Estados Base y Primer Excitado de Condensados de Bose-Einstein 1D y 2D Usando los Métodos de BESP Y BFSP.

Author

Uribe Laverde, M. A.

Subjects
*BOSE-Einstein condensation, *QUANTUM theory, *NUMERICAL analysis, *EQUATIONS, *LINEAR systems, *WAVE functions
Abstract

Within this report we are describing the treatment made to the Gross-Pittaevsky equation, which describes the behavior of Bose-Einstien condensates, in order to be normalized and nondimensionalized. We show that the condensate solutions are those normalized functions for which the energy functional minimices. In order to solve the problem the equation is discretized by means of a gradient flow (GFDN) which, under certain circumstances, is energy diminishing and therefore appropriate to find ground and first excited states under proper initial conditions. To discretize completely the GFDN two algorithms known as Backward Euler sine-pseudospectral method (BESP) and Backward/Forward Euler sine-pseudospectral method (BFSP) are proposed. In the framework of this methods the spacial derivatives of the wave function can be written in terms of sine transforms which make easier the solution of the linear system appearing when the iteration is carried out. Finally we report the results obtained by the simulations of condensates and we find some properties of the dependence of the wave function and its response to different potentials with respect to the condensate interaction parameter. [ABSTRACT FROM AUTHOR]

Published
2008

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