Show simple item record

dc.contributor.advisorDavid L. Darmofal.en_US
dc.contributor.authorYano, Masayuki, Ph. D. Massachusetts Institute of Technologyen_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.en_US
dc.date.accessioned2013-01-07T21:19:45Z
dc.date.available2013-01-07T21:19:45Z
dc.date.copyright2012en_US
dc.date.issued2012en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/76090
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (p. 271-281).en_US
dc.description.abstractImproving the autonomy, efficiency, and reliability of partial differential equation (PDE) solvers has become increasingly important as powerful computers enable engineers to address modern computational challenges that require rapid characterization of the input-output relationship of complex PDE governed processes. This thesis presents work toward development of a versatile PDE solver that accurately predicts engineering quantities of interest to user-prescribed accuracy in a fully automated manner. We develop an anisotropic adaptation framework that works with any localizable error estimate, handles any discretization order, permits arbitrarily oriented anisotropic elements, robustly treats irregular features, and inherits the versatility of the underlying discretization and error estimate. Given a discretization and any localizable error estimate, the framework iterates toward a mesh that minimizes the error for a given number of degrees of freedom by considering a continuous optimization problem of the Riemannian metric field. The adaptation procedure consists of three key steps: sampling of the anisotropic error behavior using element-wise local solves; synthesis of the local errors to construct a surrogate error model based on an affine-invariant metric interpolation framework; and optimization of the surrogate model to drive the mesh toward optimality. The combination of the framework with a discontinuous Galerkin discretization and an a posteriori output error estimate results in a versatile PDE solver for reliable output prediction. The versatility and effectiveness of the adaptive framework are demonstrated in a number of applications. First, the optimality of the method is verified against anisotropic polynomial approximation theory in the context of L2 projection. Second, the behavior of the method is studied in the context of output-based adaptation using advection-diffusion problems with manufactured primal and dual solutions. Third, the framework is applied to the steady-state Euler and Reynolds-averaged Navier-Stokes equations. The results highlight the importance of adaptation for high-order discretizations and demonstrate the robustness and effectiveness of the proposed method in solving complex aerodynamic flows exhibiting a wide range of scales. Fourth, fully-unstructured space-time adaptivity is realized, and its competitiveness is assessed for wave propagation problems. Finally, the framework is applied to enable spatial error control of parametrized PDEs, producing universal optimal meshes applicable for a wide range of parameters.en_US
dc.description.statementofresponsibilityby Masayuki Yano.en_US
dc.format.extent281 p.en_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectAeronautics and Astronautics.en_US
dc.titleAn optimization framework for adaptive higher-order discretizations of partial differential equations on anisotropic simplex meshesen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics
dc.identifier.oclc820205006en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record