High performance computing for solving large sparse systems. Optical diffraction tomography as a case of study (Tesis Doctorales (Edición Electrónica))

High performance computing for solving large sparse systems.

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Imosver
(PONTECALDELAS, España)

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Descripción Condición: Nuevo. This thesis, entitled ÇHigh Performance Computing for solving large sparse systems. Optical Diffraction Tomography as a case of studyÇ investigates the computational issues related to the resolution of linear systems of equations which come from the discretization of physical models described by means of Partial Differential Equations (PDEs). These physical models are conceived for the description of the space-temporary behavior of some physical phenomena f(x, y, z, t) in terms of their variations (partial derivative) with respect to the dependent variables of the phenomena. There is a wide variety of discretization methods for PDEs. Two of the most well-known methods are the Finite Difference Method (FDM) and the Finite Element Method (FEM). Both methods result in an algebraic description of the model that can be translated into the approach of a linear system of equations of type (Ax = b), where A is a sparse matrix (a high percentage of zero elements) whose size depends on the required accuracy of the modeled phenomena. This thesis begins with the algebraic description of the model associated with the physical phenomena, and the work herein has been focused on the design of techniques and computational models that allow the resolution of these linear systems of equations. The main interest of this study is specially focused on models which require a high level of discretization and usually generate sparse matrices, A, which have a highly sparse structure and large size. Literature characterizes these types of problems by their high demanding computational requirements (because of their fine degree of discretization) and the sparsity of the matrices involved, suggesting that these kinds of problems can only be solved using High Performance Computing techniques and architectures. One of the main goals of this thesis is the research of the possible alternatives which allow the implementation of routines to solve large and sparse linear sys. Nº de ref. del artículo: AGP0012401

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