2026-09-24T01:37:48Zhttps://dspace.mit.edu/server/oai/request

oai:dspace.mit.edu:1721.1/80982022-01-13T07:54:11Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022

David Darmofal and Jaume Peraire. Okusanya, Tolulope Olawale, 1972 - Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics 2005-08-24T20:18:45Z 2005-08-24T20:18:45Z 2002 2002 http://hdl.handle.net/1721.1/8098 51278971 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2002. Includes bibliographical references (p. 141-152). A multilevel method for the solution of systems of equations generated by stabilized Finite Element discretizations of the Euler and Navier Stokes equations on generalized unstructured grids is described. The method is based on an elemental agglomeration multigrid which produces a hierarchical sequence of coarse subspaces. Linear combinations of the basis functions from a given space form the next subspace and the use of the Galerkin Coarse Grid Approximation (GCA) within an Algebraic Multigrid (AMG) context properly defines the hierarchical sequence. The multigrid coarse spaces constructed by the elemental agglomeration algorithm are based on a semi-coarsening scheme designed to reduce grid anisotropy. The multigrid transfer operators are induced by the graph of the coarse space mesh and proper consideration is given to the boundary conditions for an accurate representation of the coarse space operators. A generalized line implicit relaxation scheme is also described where the lines are constructed to follow the direction of strongest coupling. The solution algorithm is motivated by the decomposition of the system characteristics into acoustic and convective modes. Analysis of the application of elemental agglomeration AMG (AMGe) to stabilized numerical schemes shows that a characteristic length based rescaling of the numerical stabilization is necessary for a consistent multigrid representation. by Tolulope Olawale Okusanya. Ph.D. 152 p. 10046170 bytes 10045925 bytes application/pdf application/pdf 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 Aeronautics and Astronautics. Algebraic multigrid for stabilized finite element discretizations of the Navier Stokes equation Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="7d644968-586b-45c6-8945-34a283601292"> <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>Algebraic multigrid for stabilized finite element discretizations of the Navier Stokes equation</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2002</PublicationDate> <Authors> <Author> <DisplayName>Okusanya, Tolulope Olawale, 1972 -</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>Aeronautics and Astronautics.</Keyword> <Abstract>A multilevel method for the solution of systems of equations generated by stabilized Finite Element discretizations of the Euler and Navier Stokes equations on generalized unstructured grids is described. The method is based on an elemental agglomeration multigrid which produces a hierarchical sequence of coarse subspaces. Linear combinations of the basis functions from a given space form the next subspace and the use of the Galerkin Coarse Grid Approximation (GCA) within an Algebraic Multigrid (AMG) context properly defines the hierarchical sequence. The multigrid coarse spaces constructed by the elemental agglomeration algorithm are based on a semi-coarsening scheme designed to reduce grid anisotropy. The multigrid transfer operators are induced by the graph of the coarse space mesh and proper consideration is given to the boundary conditions for an accurate representation of the coarse space operators. A generalized line implicit relaxation scheme is also described where the lines are constructed to follow the direction of strongest coupling. The solution algorithm is motivated by the decomposition of the system characteristics into acoustic and convective modes. Analysis of the application of elemental agglomeration AMG (AMGe) to stabilized numerical schemes shows that a characteristic length based rescaling of the numerical stabilization is necessary for a consistent multigrid representation.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>