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| Author(s): |
Alexandre de Lacassa
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2007-04-20 |
| Examining board members: |
Antonio Castelo Filho;
Maurilio Boaventura;
Luis Gustavo Nonato
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| Advisor: | Antonio Castelo Filho |
| Abstract | |
The use of polygonal meshes for numerical simulation of physical problems is a well known component. Mesh is an piecewise approximation from a given geometry defined by a set of simpler elements, such as triangles and quadrilaterals (two-dimensional case) or tetrahedra, prisms, pyramid and hexahedra (three-dimensional case). In this work, the interest is unstructured meshes of triangles. The choice of a mesh is aimed at the performance and the precision of the simulation results. The performance depends of the number of elements that will be processed, i.e., the larger is the covered area for each mesh element, the less element is needed, therefore the simulation is faster performed. The simulation precision is related with the shape and the size of the elements. On the other hand, the smaller the elements are, the more precise are the results. The shape of the elements also influences on precision, generally, equilateral elements are preferred. It is worth to mention that performance and precision are opposite requirements and it is important to ponder between them. For a group of applications, the best commitment between performance and precision is obtained with thin and long elements correctly aligned on the domain where the mesh is defined. These meshes are named anisotropic meshes. Furthermore, a method of anisotropic refinement can even improve the precision. We aim at developing anisotropic mesh methods based on isotropic properties from well known Delaunay refinement methods, viz., the Delaynay refinement methods by Jim Ruppert [13] and Paul Chew [6], and performing a Delaunay simplification proposed by Olivier Devillers [8] (AU) | |