Accession Number : ADA310499
Title : Anisotropic Mesh Generation with Particles.
Descriptive Note : Master's thesis,
Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
Personal Author(s) : Bossen, Frank
PDF Url : ADA310499
Report Date : 13 MAY 1996
Pagination or Media Count : 59
Abstract : Many important real world problems require meshing, that is the approximation of a given geometry by a set of simpler elements such as triangles or quadrilaterals in two dimensions, and tetrahedra or hexahedra in three dimensions. Applications include finite element analysis and computer graphics. This work focuses on the former. A physically based model of interacting 'particles' is introduced to uniformly spread points over a 2-dimensional polygonal domain. The set of points is triangulated to form a triangle mesh. Delaunay triangulation is used because it guarantees a low computational cost and reasonably well shaped elements. Several particle interaction (repulsion and attraction) models are investigated ranging from Gaussian energy potentials to Laplacian smoothing. Particle population control mechanisms are introduced to make the size of the mesh elements converge to the desired size. In most applications spatial mesh adaptivity is desirable. Triangles should not only adapt in size but also in shape, to better fit the function to approximate. Computational fluid dynamics simulations typically require triangles stretched in the direction of the flow. A metric tensor is introduced to quantify the stretching. The triangulation procedure is changed to generate 'Delaunay' meshes in the Riemannian space defined by the metric. This new approach to mesh generation appears quite promising.
Descriptors : *FINITE ELEMENT ANALYSIS, *COMPUTATIONAL FLUID DYNAMICS, SPATIAL DISTRIBUTION, INTERACTIONS, MESH, PARTICLES, COMPUTER GRAPHICS, TENSORS, TRIANGLES.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE