Proceedings of the Twentieth Annual Symposium on Computational Geometry 2004
DOI: 10.1145/997817.997863
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Spacetime meshing with adaptive refinement and coarsening

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 × [0, T ] in constant running time per tetrahedron in IR 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 G… Show more

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Cited by 46 publications
(50 citation statements)
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“…Likewise, Ungor et al [60] and, some time later, Abedi et al [61] have put some efforts towards the development of 2D+t grids by a mesh-marching technique.…”
Section: Formulationmentioning
confidence: 99%
“…Likewise, Ungor et al [60] and, some time later, Abedi et al [61] have put some efforts towards the development of 2D+t grids by a mesh-marching technique.…”
Section: Formulationmentioning
confidence: 99%
“…For example, TentPitcher is a novel algorithm for solving hyperbolic systems via the Spacetime Discontinuous Galerkin (SDG) method developed at the Center for Process Simulation and Design at UIUC [1]. In converting this algorithm to run in parallel, we made extensive use of the multi-paradigm capabilities of ParFUM.…”
Section: Multi-paradigm Applicationsmentioning
confidence: 99%
“…Moreover, some applications need to perform incremental and unsynchronized modifications to their parallel meshes. One application that needs parallel mesh modification is the adaptive space-time meshing algorithm [24,25], described in Section 5.1. In order to support different forms of mesh modification in ParFUM, we decided to create a simple but robust abstraction that would support a wide range of application needs.…”
Section: Modification Of Parallel Meshesmentioning
confidence: 99%
“…The Spacetime Discontinuous Galerkin (SDG) method [24,25] provides a powerful way to analyze phenomena such as shock wave propagation in solids, evolution equations for state variables in inelastic constitutive models and Hamilton-Jacobi level set models for interface kinetics.…”
Section: Spacetime Discontinuous Galerkinmentioning
confidence: 99%