Mesh generation in four dimensions for adaptive refinement in space and time

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)

Abstract

This thesis presents the first known space-covering four-dimensional simplex mesh. An inductive algorithm for systematically covering space is provided, starting in one dimension and proceeding through two and three dimensions eventually to four dimensions. Human visualisation runs out of capacaity at three dimensions, so metrics of mesh quality are developed to objectively assess the meshses formed. Furthermore, a mesh distortion algorithm is demonstrated to provide adaptive refinement capability isotropically across four dimensions, which is ideal for the accuracy of the numerical PDE solvers envisaged to treat such a mesh as spanning space and time. This adaptation algorithm itself internally uses two PDE solvers modified from standard fluid dynamics applications to produce smoothly-varying mesh resolutions with well-formed cells, and without the combinatorical complexity of Delaunay triangulation in higher dimensions.
Date of Award7 May 2024
Original languageEnglish
Awarding Institution
  • University of Bristol
SupervisorAndrew G W Lawrie (Supervisor) & Alberto M Gambaruto (Supervisor)

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