Surface and bulk moving mesh methods based on equidistribution and alignment
Issue Date
2019-05-31Author
Kolasinski, Avary Justice
Publisher
University of Kansas
Format
147 pages
Type
Dissertation
Degree Level
Ph.D.
Discipline
Mathematics
Rights
Copyright held by the author.
Metadata
Show full item recordAbstract
In this dissertation, we first present a new functional for variational mesh generation and adaptation that is formulated by combining the equidistribution and alignment conditions into a single condition with only one dimensionless parameter. The functional is shown to be coercive which, when employed with the moving mesh partial differential equation method, allows various theoretical properties to be proved. Numerical examples for bulk meshes demonstrate that the new functional performs comparably to a similar existing functional that is known to work well but contains an additional parameter. Variational mesh adaptation for bulk meshes has been well developed however, surface moving mesh methods are limited. Here, we present a surface moving mesh method for general surfaces with or without explicit parameterization. The development starts with formulating the equidistribution and alignment conditions for surface meshes from which, we establish a meshing energy functional. The moving mesh equation is then defined as the gradient system of the energy functional, with the nodal mesh velocities being projected onto the underlying surface. The analytical expression for the mesh velocities is obtained in a compact, matrix form, which makes the implementation of the new method on a computer relatively easy and robust. Moreover, it is analytically shown that any mesh trajectory generated by the method remains nonsingular if it is so initially. It is emphasized that the method is developed directly on surface meshes, making no use of any information on surface parameterization. A selection of two-dimensional and three-dimensional examples are presented.
Collections
- Dissertations [4660]
- Mathematics Dissertations and Theses [179]
Items in KU ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
We want to hear from you! Please share your stories about how Open Access to this item benefits YOU.