Browsing by Subject "Convergence"

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Direct serendipity and mixed finite elements on polygons and cuboidal hexahedra
(2023-07-25) Wang, Chuning; Arbogast, Todd James, 1957-; Demkowicz, Leszek; Martinsson, Per-Gunnar; Tsai, Yen-Hsi
In recent years, there has been a lot of interest in defining finite elements on nonstandard, polytopal elements, i.e., on polygons and polyhedra. Inspired by Arnold and Awanou's serendipity family of finite elements on cuboidal meshes, the dissertation generalizes the construction of direct serendipity and mixed finite elements to general planar, strictly convex polygons. This work also gives an explicit construction of direct serendipity finite elements on convex cuboidal hexahedra. Direct serendipity and mixed finite elements are H1 and H(div) conforming, respectively, and possess optimal order of accuracy for any order. They have a minimal number of degrees of freedom subject to conformity and accuracy constraints. The finite element shape functions are defined to be the full spaces of scalar or vector polynomials plus a space of supplemental functions, of which the choice is not unique. The direct serendipity elements are the precursors of the direct mixed elements in a de Rham complex. The convergence properties of these new families of finite elements are shown under the assumption of shape regularity, as well as some mild restrictions on the choice of supplemental functions. Numerical experiments on various meshes exhibit their performance, especially their potential value in applications where flexible polytopal meshes are advantageous.
Enhancing the practical usability of dynamic traffic assignment
(2012-12) Pool, Christopher Matthew; Boyles, Stephen David, 1982-; Bhat, Chandra
A general framework is presented for replacing static traffic assignment with dynamic traffic assignment within the standard four step transportation planning model. Issues including model consistency and the implementation of a proper feedback loop are explored. The new model is compared with the standard four step model in order to highlight the benefits of using dynamic traffic assignment rather than static. The model is then extended to include a term for the difference between experienced and free-flow travel times, which can be used as a proxy for travel time reliability and highlights the benefits of time-dependent DTA. Additionally, a study on improving the quality of convergence for dynamic traffic assignment is conducted in order to help facilitate the usefulness of this modeling approach in practice. A variety of equilibration techniques are tested, and analysis is performed to contrast these techniques with the method of successive averages.
Working for the competition : an analysis of the local news pool
(2012-05) West, Katharine Elizabeth; Coleman, Renita; Poindexter, Paula; Browning, Larry; Strover, Sharon; Chyi, Iris
The Local News Pool or “LNP” as it’s referred to concerns competing television news stations within a single market forming a cooperative partnership in order to share content such as video and interviews. This study used depth interviews with assignment editors, producers, and photographers in Austin, Texas, Tampa, Florida, and Denver, Colorado, and incorporated a quantitative content analysis of news stories assigned to the LNP in Austin to discover how this convergence model operates, its effects on workers, and the potential for homogenization. This study discovered that by incorporating this convergence model into a newsroom and categorizing certain stories as “shared” it altered the level of importance photographers and producers placed on the story. By these journalists having prior knowledge that the competition might use or have an interest in a certain story, it altered the value placed on it to one of something “extra” or “filler” and not highly desired for the news broadcast. In addition, this study provides an updated look at the multilayer gatekeeping process by incorporating competing organizations within this decision making process. This study found gatekeepers cooperate on stories each find would produce similar content if their station were to send their own crews. The aspect of competition becomes present when gatekeepers request stories not intended for the LNP such as breaking news. The level of cooperation is often based on ratings and perception of one’s willingness to reciprocate if needed.