Spacetime Meshing for Discontinuous Galerkin Methods
Thite, Shripad Vidyadhar
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https://hdl.handle.net/2142/81695
Description
Title
Spacetime Meshing for Discontinuous Galerkin Methods
Author(s)
Thite, Shripad Vidyadhar
Issue Date
2005
Doctoral Committee Chair(s)
Jeff Erickson
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
To support an accurate and efficient solution procedure using SDG methods and to exploit the flexibility of these methods, we give a meshing algorithm to construct an unstructured simplicial spacetime mesh over an arbitrary simplicial space domain. Our algorithm is the first adaptive spacetime meshing algorithm suitable for efficient solution of nonlinear phenomena using spacetime discontinuous Galerkin finite element methods. Given a triangulated d-dimensional Euclidean space domain M (a simplicial complex) corresponding to time t = 0 and initial conditions of the underlying hyperbolic spacetime PDE, we construct an unstructured simplicial mesh of the ( d + 1)-dimensional spacetime domain O. Our algorithm uses a near-optimal number of spacetime elements, each with bounded temporal aspect ratio for any finite prefix of O. When d ≤ 2, our algorithm varies the size of spacetime elements to an a posteriori numerical estimate. Certain facets of our mesh satisfy gradient constraints that allow interleaving mesh generation with the SDG salver. Our meshing algorithm thus supports an efficient parallelizable solution strategy by SDG methods.
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