NDLI: Spacetime meshing with adaptive refinement and coarsening

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Spacetime meshing with adaptive refinement and coarsening

Content Provider	ACM Digital Library
Author	Thite, Shripad Abedi, Reza Chung, Shuo-Heng Garland, Michael Guoy, Damrong Haber, Robert Sullivan, John M. Erickson, Jeff Zhou, Yuan Fan, Yong
Abstract	We propose a new algorithm for constructing finite-element meshes suitable for spacetime discontinuous Galerkin solutions of linear hyperbolic PDEs. Given a triangular mesh of some planar domain Ω and a target time value T, our method constructs a tetrahedral mesh of the spacetime domain Ω X [0,T] in constant running time per tetrahedron in $ℝ^{3}$ using an advancing front method. Elements are added to the evolving mesh in small patches by moving a vertex of the front forward in time. Spacetime discontinuous Galerkin methods allow the numerical solution within each patch to be computed as soon as the patch is created. Our algorithm employs new mechanisms for adaptively coarsening and refining the front in response to a posteriori error estimates returned by the numerical code. A change in the front induces a corresponding refinement or coarsening of future elements in the spacetime mesh. Our algorithm adapts the duration of each element to the local quality, feature size, and degree of refinement of the underlying space mesh. We directly exploit the ability of discontinuous Galerkin methods to accommodate discontinuities in the solution fields across element boundaries.
Starting Page	300
Ending Page	309
Page Count	10
File Format	PDF
ISBN	1581138857
DOI	10.1145/997817.997863
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2004-06-08
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Unstructured meshes Adaptivity Advancing front Spacetime discontinuous galerkin Tetrahedral meshes Mesh generation
Content Type	Text
Resource Type	Article

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