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This dissertation presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT) which are to be used for multiphysics, multidomain applications. As an introduction, we discuss grid generation on the sphere in a broad fashion. Next, we discuss the theory of CVTs in general, and specifically on the sphere. Subsequently we consider the iterative processes, such as Lloyd's algorithm, which are used to construct them. Following this, we describe a method for density functions via images so that we can shape generator density in an intuitive, yet arbitrary, manner, and then a method by which SCVTs can be easily adapted to conform to arbitrary sets of line segments, or shorelines. Then, we discuss sample meshes, used for various physical and nonphysical applications. Penultimately, we discuss two sample applications, as a proof of concept, where we adapt the Shallow Water Model from Model for Predictions Across Scales (MPAS) to use our grids for a more accurate border, and we also discuss elliptic interface problems both with and without hanging nodes. Finally, we share a few concluding remarks.
A Dissertation submitted to the Department of Scientiﬁc Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Max Gunzburger, Professor Co-Directing Dissertation; Janet Peterson, Professor Co-Directing Dissertation; Kyle Gallivan, University Representative; Gordon Erlebacher, Committee Member; Xiaoqiang Wang, Committee Member; Todd Ringler, Committee Member.
Florida State University
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