Automated Quadrilateral Coarsening by Ring Collapse

Abstract

BRIGHAM YOUNG UNIVERSITY As chair of the candidate's graduate committee, I have read the thesis of Mark W. Dewey in its final form and have found that (1) its format, citations, and bibliographical style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library. Date Steven E. Benzley Chair, Graduate Committee

Adaptive mesh coarsening for quadrilateral and hexahedral meshes

“…Dewey [31] outlines the complete procedure for collapsing coarsening rings, and is briefly presented here for clarity. The projected location of each of the node groups, the location of the nodes after they have been combined, is calculated to enable quality metric calculations for each of the coarsening rings.…”

Automatic All Quadrilateral Mesh Adaption through Refinement and Coarsening

“…While nine element quadtrees or 3-refinement (see figure 1(c)) are sometimes used to refine quadrilateral faces, 2-refinement was chosen because it offers more control over the number of elements added to the mesh. This adaptation algorithm uses the Automated Quadrilateral Coarsening by Ring Collapse (AQCRC) algorithm recently developed by Dewey [2]. This coarsening method provides completely localized coarsening by selecting and removing rings of adjacent faces from within a specified coarsening region as shown in figure 2.…”

“…This algorithm combines template-based quadrilateral refinement techniques [1] with recent developments in coarsening [2] and quadrilateral improvement [3] to adapt an existing mesh. Additionally, to provide an algorithm that will meet conformity and element type requirements of finite element solvers, this method guarantees a fully conformal, all-quadrilateral mesh.…”

Quadrilateral mesh simplification

“…That is, starting at a single edge on a closed quadrilateral mesh and traversing opposite edges on adjacent quadrilaterals, the traversal will always end at the starting edge. The polychord is a generalization of the ring structure constructed in related quadrilateral-based research [Bremer et al 2002;Dewey 2008]. …”

“…3). Related quadrilateral coarsening approaches have also exploited the ring structure, developing restructuring [Staten et al 2008] and localized deletion techniques [Dewey 2008]. …”