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Adaptive unstructured spacetime meshing for four-dimensional spacetime discontinuous Galerkin finite element methods

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Title: Adaptive unstructured spacetime meshing for four-dimensional spacetime discontinuous Galerkin finite element methods
Author(s): Mont, Alexander D.
Advisor(s): Erickson, Jeffrey G.
Department / Program: Computer Science
Discipline: Computer Science
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: M.S.
Genre: Thesis
Subject(s): spacetime meshing discontinuous Galerkin adaptive meshing advancing front
Abstract: We describe the spacetime discontinuous Galerkin method, a new type of finite-element method which promises dramatic improvement in solution speed for hyperbolic problems. These methods require the generation of spacetime meshes that satisfy a special causality constraint. This work focuses on the extension of the existing 2d×time spacetime meshing algorithm known as TentPitcher to 3d×time problems. We review existing work based on TentPitcher. Then, we extend TentPitcher to 3d×time and derive methods for handling mesh adaptivity operations. Next, we describe the software we have developed to implement our algorithms and give preliminary results of testing. We also identify unresolved theoretical and engineering issues associated with our new methods and suggest directions for further research.
Issue Date: 2012-02-06
URI: http://hdl.handle.net/2142/29810
Rights Information: Copyright 2011 Alexander Mont.
Date Available in IDEALS: 2012-02-06
Date Deposited: 2011-12
 

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