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David L. Darmofal. Sun, Huafei Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program 2010-04-26T19:19:26Z 2010-04-26T19:19:26Z 2009 2009 http://hdl.handle.net/1721.1/54215 587498193 Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Cataloged from student submitted PDF version of thesis. Includes bibliographical references (p. 95-101). The impact of triangle shapes, including angle sizes and aspect ratios, on accuracy and stiffness is investigated for simulations of highly anisotropic problems. The results indicate that for high-order discretizations, large angles do not have an adverse impact on solution accuracy. However, a correct aspect ratio is critical for accuracy for both linear and high-order discretizations. In addition, large angles are not problematic for the conditioning of the linear systems arising from discretization. They can be overcome through small increases in preconditioning costs. A direct adaptation scheme that controls the output error via mesh operations and mesh smoothing is also developed. The decision of mesh operations is solely based on output error distribution without any a priori assumption on error convergence rate. Anisotropy is introduced by evaluating the error changes due to potential edge split, and thus the anisotropies of both primal and dual solutions are taken into account. This scheme is demonstrated to produce grids with fewer degrees of freedom for a specified error level than the existing metric-based approach. by Huafei Sun. S.M. 101 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Computation for Design and Optimization Program. Impact of triangle shapes using high-order discretizations and direct mesh adaptation for output error Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="a67cdbf0-fd95-45e2-a207-5d93e6eec053"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Impact of triangle shapes using high-order discretizations and direct mesh adaptation for output error</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2009</PublicationDate> <Authors> <Author> <DisplayName>Sun, Huafei</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Computation for Design and Optimization Program.</Keyword> <Abstract>The impact of triangle shapes, including angle sizes and aspect ratios, on accuracy and stiffness is investigated for simulations of highly anisotropic problems. The results indicate that for high-order discretizations, large angles do not have an adverse impact on solution accuracy. However, a correct aspect ratio is critical for accuracy for both linear and high-order discretizations. In addition, large angles are not problematic for the conditioning of the linear systems arising from discretization. They can be overcome through small increases in preconditioning costs. A direct adaptation scheme that controls the output error via mesh operations and mesh smoothing is also developed. The decision of mesh operations is solely based on output error distribution without any a priori assumption on error convergence rate. Anisotropy is introduced by evaluating the error changes due to potential edge split, and thus the anisotropies of both primal and dual solutions are taken into account. This scheme is demonstrated to produce grids with fewer degrees of freedom for a specified error level than the existing metric-based approach.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>