Mesh generation for implicit geometries
Name
60503856-MIT.pdf
Description
Full printable version
Size
27.01 MB
Format
Adobe PDF
Checksum (MD5)
1b3901934609a8d582af514f7414d997
Author(s)
Persson, Per-Olof, 1973-
Advisor(s)
Alan Edelman and Gilbert Strang.
Date Issued
2005
Publisher
Massachusetts Institute of Technology
Abstract
We present new techniques for generation of unstructured meshes for geometries specified by implicit functions. An initial mesh is iteratively improved by solving for a force equilibrium in the element edges, and the boundary nodes are projected using the implicit geometry definition. Our algorithm generalizes to any dimension and it typically produces meshes of very high quality. We show a simplified version of the method in just one page of MATLAB code, and we describe how to improve and extend our implementation. Prior to generating the mesh we compute a mesh size function to specify the desired size of the elements. We have developed algorithms for automatic generation of size functions, adapted to the curvature and the feature size of the geometry. We propose a new method for limiting the gradients in the size function by solving a non-linear partial differential equation. We show that the solution to our gradient limiting equation is optimal for convex geometries, and we discuss efficient methods to solve it numerically. The iterative nature of the algorithm makes it particularly useful for moving meshes, and we show how to combine it with the level set method for applications in fluid dynamics, shape optimization, and structural deformations. It is also appropriate for numerical adaptation, where the previous mesh is used to represent the size function and as the initial mesh for the refinements. Finally, we show how to generate meshes for regions in images by using implicit representations.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 119-126).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
Persistent DSpace Link
