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| Author(s): |
Lucas Batista Freitas
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Computação |
| Defense date: | 2010-12-17 |
| Examining board members: |
Jorge Stolfi;
Maria Cristina de Castro Cunha;
Philippe Remy Bernard Devloo;
Eduardo Fiilpo Ferreira da Silva;
Jessé Carvalho Costa
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| Advisor: | Martin Tygel; Jorge Stolfi |
| Abstract | |
The exploration and monitoring of a hydrocarbon reservoir demand a very detailed knowledge about the geological structures of the target area. The mathematical and computation representation of this knowledge is a geophysical model. In this thesis, we describe a general system for geophysical modeling based on polynomial finite elements of arbitrary degree. We adopted an approach that is popular in industry, whereby both the geometry and the physical properties of the geological formations are represented by piecewise-defined functions, or splines, that are obtained by the assembly of many such elements. In this context, we present both theoretical and computational contributions. The main theoretical contribution is a unified theory of simploidal Bézier elements, which include the element types most common in mesh based modeling - such as Bézier arcs, triangular and rectangular Bézier patches, tetrahedral, prismatic and hexahedral Bézier blocks, and their generalizations to arbitrary dimensions with independent degrees on each axis and each component. As part of this theory, we developed general explicit formulas for the conversion between these various block types, as well as differentiation, affine reparametrization and degree raising. The computational contributions of this thesis include the implementation of this theory as a library (BezEl) that allows efficient representation and manipulation of meshes of simploidal Bézier elements with arbitrary dimension and degree. Another original contribution of this thesis is a methodology for performing efficient ray tracing in meshes of such simploidal elements (AU) | |