2026-09-19T00:24:27Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/166572022-01-13T07:54:11Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
David L. Darmofal.
Fidkowski, Krzysztof J., 1981-
Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2005-05-17T14:49:19Z
2005-05-17T14:49:19Z
2004
2004
http://hdl.handle.net/1721.1/16657
56526253
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.
Includes bibliographical references (p. 87-90).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Results are presented from the development of a high-order discontinuous Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing algorithm is presented for unstructured meshes, and p-multigrid is outlined for the nonlinear Euler equations of gas dynamics. Analysis of 2-D advection shows the improved performance of line implicit versus block implicit relaxation. Through a mesh refinement study, the accuracy of the discretization is determined to be the optimal O(h[superscript]P+l) for smooth problems in 2-D and 3-D. The multigrid convergence rate is found to be independent of the interpolation order but weakly dependent on the grid size. Timing studies for each problem indicate that higher order is advantageous over grid refinement when high accuracy is required. Finally, parallel versions of the 2-D and 3-D solvers demonstrate close to ideal coarse-grain scalability.
by Krzysztof J. Fidkowski.
S.M.
90 p.
1069914 bytes
1093802 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.
A high-order discontinuous Galerkin multigrid solver for aerodynamic applications
Thesis
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<Abstract>Results are presented from the development of a high-order discontinuous Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing algorithm is presented for unstructured meshes, and p-multigrid is outlined for the nonlinear Euler equations of gas dynamics. Analysis of 2-D advection shows the improved performance of line implicit versus block implicit relaxation. Through a mesh refinement study, the accuracy of the discretization is determined to be the optimal O(h[superscript]P+l) for smooth problems in 2-D and 3-D. The multigrid convergence rate is found to be independent of the interpolation order but weakly dependent on the grid size. Timing studies for each problem indicate that higher order is advantageous over grid refinement when high accuracy is required. Finally, parallel versions of the 2-D and 3-D solvers demonstrate close to ideal coarse-grain scalability.</Abstract>
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