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David L. Darmofal. Yano, Masayuki, Ph. D. Massachusetts Institute of Technology Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program 2010-04-26T19:19:38Z 2010-04-26T19:19:38Z 2009 2009 http://hdl.handle.net/1721.1/54217 587602496 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. 85-91). A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the high-order interpolation. The Balancing Domain Decomposition by Constraints (BDDC) algorithm is applied to the linear systems arising from the two-dimensional, high-order discretization of the Poisson equation, the advection-diffusion equation, and the Euler equation. The Robin-Robin interface condition is extended to the Euler equation using the entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization for the diffusion-dominated flows. The Robin-Robin interface condition improves the performance of the method significantly for the advection-diffusion equation and the Euler equation. The BDDC method based on the inexact local solvers with incomplete factorization maintains the scalability of the exact counterpart with a proper reordering. by Masayuki Yano. S.M. 91 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. Massively parallel solver for the high-order Galerkin Least-Squares method Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="2d33e3f1-63aa-4cf0-9dcb-8b1b1e3b3f47"> <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>Massively parallel solver for the high-order Galerkin Least-Squares method</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2009</PublicationDate> <Authors> <Author> <DisplayName>Yano, Masayuki, Ph. D. Massachusetts Institute of Technology</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>A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the high-order interpolation. The Balancing Domain Decomposition by Constraints (BDDC) algorithm is applied to the linear systems arising from the two-dimensional, high-order discretization of the Poisson equation, the advection-diffusion equation, and the Euler equation. The Robin-Robin interface condition is extended to the Euler equation using the entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization for the diffusion-dominated flows. The Robin-Robin interface condition improves the performance of the method significantly for the advection-diffusion equation and the Euler equation. The BDDC method based on the inexact local solvers with incomplete factorization maintains the scalability of the exact counterpart with a proper reordering.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>