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Alan Edelman and Gilbert Strang. Persson, Per-Olof, 1973- Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Department of Mathematics 2008-02-28T16:03:44Z 2008-02-28T16:03:44Z 2005 2005 http://hdl.handle.net/1721.1/27866 60503856 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. Includes bibliographical references (p. 119-126). 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. by Per-Olof Persson. Ph.D. 126 p. eng Massachusetts Institute of Technology 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. http://dspace.mit.edu/handle/1721.1/7582 Mathematics. Mesh generation for implicit geometries Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="08385876-e0d1-4c5d-b793-ab01d72a100f"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Mesh generation for implicit geometries</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2005</PublicationDate> <Authors> <Author> <DisplayName>Persson, Per-Olof, 1973-</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Mathematics.</Keyword> <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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>